DIGITAL IMAGE PROCESSING IN OPTICAL COHERENCE … Fiakkou.pdf · DIGITAL IMAGE PROCESSING IN . OPTICAL COHERENCE TOMOGRAPHY IMAGING . FOR THE EVALUATION OF WATERMELON PROPERTIES

DIGITAL IMAGE PROCESSING IN OPTICAL COHERENCE TOMOGRAPHY IMAGING

FOR THE EVALUATION OF WATERMELON PROPERTIES

By

Maria Fiakkou

Submitted to the University of Cyprus in partial fulfillment

of the requirements for the degree of Master of Science in Electrical Engineering

Department of Electrical and Computer Engineering

May 2015

DIGITAL IMAGE PROCESSING IN OPTICAL COHERENCE TOMOGRAPHY IMAGING

FOR THE EVALUATION OF WATERMELON PROPERTIES

By

Maria Fiakkou

Examination committee:

Dr. Constantinos Pitris Associate Professor, Department of ECE, Research Supervisor

Dr. George Ellinas Associate Professor, Department of ECE, Committee Member

Dr. Christina Orphanidou Special Scientist, Department of ECE, Committee Member

Abstract

Watermelon is one of the most popular summer fruits and it is cultivated all over the world.

Nevertheless, you can never determine with certainty the quality and the freshness of a

watermelon when you choose one. In this thesis the Optical Coherence Tomography was used for

imaging of watermelon cells and peels in an attempt to evaluate the watermelon properties and

determine quality. More specifically, at what extent the cytological changes have an impact in the

ripening and firmness of the watermelon.

Samples of OCT imaging were acquired for watermelon flesh and peel. Subsequently several

algorithms of digital image processing were applied on OCT imaging samples. In particular,

quantification of connective tissue and peel was performed as well as manual an automatic

segmentation of the watermelon cells. Manual segmentation was performed in an attempt to test

the reliability of the automatic segmentation. The yielded dataset were used afterwards for

statistical analysis and classification.

Notwithstanding, the above during the experimental process, back reflections and noise artifacts

affect significantly the imaging. To smooth out their effect on the imaging, and the possible

alternations of the results, median filter and morphological operations were used. This method

optimizes the images and resolve OCT physical issues.

The majority of the results obtained from the statistical analysis and classification do not lead to

desirable and reasonable conclusions. Few samples though gave satisfactory and useful results for

the evaluation of watermelon properties.

Keywords: Optical Coherence Tomography, Digital Image Processing, Quantification, Watershed

Transformation, Manual and Automatic Segmentation, Watermelon Properties.

Περίληψη

Το καρπούζι είναι ένα από τα πιο δημοφιλή καλοκαιρινά φρούτα και καλλιεργείται σε όλο τον

κόσμο. Παρ’ όλα αυτά, δεν μπορεί ποτέ με βεβαιότητα να προσδιοριστεί η ποιότητα και η

φρεσκάδα του καρπουζιού όταν επιλέγεται. Στην παρούσα διατριβή απεικόνιση των κυττάρων του

καρπουζιού αλλά και της φλούδας εκτελέστηκε με την χρήση του Οπτικού Τομογράφου Συνοχής

(OCT), σε μια προσπάθεια αξιολόγησης των ιδιοτήτων του καρπουζιού και καθορισμού της

ποιότητας του. Πιο συγκεκριμένα, σε ποιο βαθμό οι κυτταρολογικές αλλαγές έχουν αντίκτυπο

στην ωρίμανση και την συνεκτικότητα του καρπουζιού.

Δείγματα απεικόνισης Οπτικού Τομογράφου Συνοχής από την σάρκα και φλούδα του καρπουζιού

αποκτήθηκαν. Στη συνέχεια, διάφοροι αλγόριθμοι ψηφιακής επεξεργασίας εικόνας

εφαρμόστηκαν στα δείγματα αυτά. Ειδικότερα, έγινε διεξαγωγή ποσοτικοποίησης του συνδετικού

ιστού και φλούδας όπως επίσης και κατάτμηση των κυττάρων με την χρήση του Μετασχηματισμού

Απορροής. Σε μια προσπάθεια αξιολόγησης της αξιοπιστίας και ορθότητας της κατάτμησης των

κυττάρων, χειροκίνητη κατάτμηση διεξήχθητε. Τα προκύπτοντα σύνολα δεδομένων

χρησιμοποιήθηκαν σε μεταγενέστερο στάδιο για στατιστική ανάλυση και ταξινόμηση.

Παρ’ όλα όσα είχαμε αναφέρει κατά την διάρκεια της πειραματικής διαδικασίας παρουσία

θορύβου και αντανακλάσεων εμφανίζονταν επηρεάζοντας σημαντικά την απεικόνιση. Για την

εξομάλυνση του φαινομένου αυτού το όποιο θα αλλοίωνε τα αποτελέσματα, μεσαίο φίλτρο και

μορφολογικές λειτουργίες εφαρμόστηκαν. Η μέθοδος αυτή βελτιστοποιεί τις εικόνες και επιλύει

φυσικά προβλήματα που προκύπτουν κατά την απεικόνιση με την χρήση του Οπτικού

Τομογράφου Συνοχής.

Τα πλείστα αποτελέσματα τα όποια προκύπτουν από την στατιστική ανάλυση και ταξινόμηση δεν

οδηγούν σε επιθυμητά και λογικά συμπεράσματα. Μια μερίδα όμως δειγμάτων δίνει

ικανοποιητικά και χρήσιμα αποτελέσματα για την εκτίμηση των ιδιοτήτων του καρπουζιού.

Λέξεις – κλειδιά: Οπτικός Τομογράφος Συνοχής, Ψηφιακή Επεξεργασία Εικόνας, Ποσοτικοποίηση,

Μετασχηματισμός Απορροής, Χειροκίνητη και Αυτόματη Κατάτμηση, Ιδιότητες Καρπουζιού.

Acknowledgments

Foremost, I would like to express my sincere gratitude to my advisor Dr. Constantino Pitri, for the

continuous support of my Master research, for his patience, motivation, and immense knowledge.

His guidance helped me in all the time of research.

Besides my advisor, I would like to thank especially Dr. Mario Kyriacou, Senior Agricultural

Research, and Mr. George Soteriou, Agricultural Research of the Agricultural Research Institute

Cyprus, for the excellent cooperation and the concession of watermelons, which was necessary for

the completion of this research.

My sincere thanks also go to Dr. Evgenia Bousi for the valuable help and cooperation for the

performance and completion of the experiments.

I would like also to thank my special friends who are always by my side and support me during my

studies and in my whole life. Last but not least, I would like to express with appreciation and

respect, my gratitude to my family for the morals and principles passed to me during my life.

Table of Contents

1 Introduction ................................................................................................................... 1

1.1. Brief Overview in Optical Coherence Tomography (OCT) ........................................................... 1

1.2. Digital Image Processing ............................................................................................................... 2

1.3. Motivation ...................................................................................................................................... 3

1.4. Scope of Thesis ............................................................................................................................... 3

1.5. Chapters Overview ......................................................................................................................... 4

2 Background and Literature Review ................................................................................5

2.1. Optical Coherence Tomography (OCT) ........................................................................................ 5

2.1.1. Introduction to Optical Coherence Tomography ...................................................................... 5

2.1.2. Time-Domain Optical Coherence Tomography (TD OCT) ...................................................... 7

2.1.3. Frequency-Domain Optical Coherence Tomography (FD OCT) .............................................. 8

2.1.4. Application of OCT ................................................................................................................... 10

2.2. Previous Research in OCT Imaging of Watermelon ................................................................... 11

3 Experimental Procedure & Image Processing in OCT Imaging ..................................... 13

3.1. Experimental Procedure ............................................................................................................... 13

3.2. Quantification of Watermelon Peels ............................................................................................ 15

3.3. Quantification of Watermelon Connective Tissue ..................................................................... 18

3.4. Image Segmentation based on Watershed Transform .................................................................. 20

3.5. Manual Segmentation of OCT Watermelon Imaging ................................................................ 24

3.6. Semitransparency for Comparison Purposes ............................................................................. 27

3.7. Measurement of Region Properties ............................................................................................ 28

4 Multivariate Techniques and Algorithms ..................................................................... 31

4.1. Definitions of Statistical Data ...................................................................................................... 31

4.2. Statistical Data Acquisition ......................................................................................................... 34

4.3. Statistical Analysis based on Regression Analysis ..................................................................... 35

4.4. Classification based on Statistical Multivariate Analysis .......................................................... 37

4.5. Correlation and Error Estimation based on Statistical Analysis ............................................... 40

4.6. Manual versus Automatic Segmentation based on Measurements of Region Properties ....... 42

5 Results ......................................................................................................................... 44

5.1. Regression Analysis Results ........................................................................................................ 44

5.2. Classification Results ................................................................................................................... 47

5.2.1. Classification Results based on Watermelon Peel Statistical Data ........................................ 47

5.2.2. Classification Results based on OCT Imaging of Watermelon Flesh Statistical Data .......... 50

5.2.3. Classification Results based on Manual OCT Imaging of Watermelon Flesh Statistical Data

............................................................................................................................................................... 52

5.3. Correlation and Mean Percentage Error Estimation Results .................................................... 54

5.3.1. Correlation and Mean Percentage Error Estimation Result based on OCT Imaging of

Watermelon Peel Statistical Data ........................................................................................................ 54

5.3.2. Correlation and Mean Percentage Error Estimation Result based on OCT Imaging of

Watermelon Statistical Data ................................................................................................................ 56

5.3.3. Correlation and Mean Percentage Error Estimation Result based on Manual OCT Imaging

of Watermelon Statistical Data ............................................................................................................ 58

5.4. Automatic versus Manual Segmentation Results ...................................................................... 60

6 Summary and Future Works ....................................................................................... 62

6.1. Summary and Conclusions .......................................................................................................... 62

6.2. Errors and Future Works ............................................................................................................ 63

Bibliography ............................................................................................................... 64

List of Figures

Figure 2.1: Schematic of OCT System based on Michelson interferometer. ............................................ 6

Figure 2.2: Typical fiber-optic implementation of TD OCT system, interferogram, and the A-scan

envelope. ......................................................................................................................................................... 8

Figure 2.3: Typical fiber-optic implementation of FD OCT system, spectrogram, and back-reflection

profile. ............................................................................................................................................................. 9

Figure 2.4: Typical fiber-optic implementation of SS OCT system, interferogram, and back-reflection

profile. ........................................................................................................................................................... 10

Figure 3.1: The area points which is taken around the heart of the watermelon market with X. ..........14

Figure 3.2: The area points which is taken at the darkest green of the watermelon peel market with X.

........................................................................................................................................................................ 15

Figure 3.3: Sample Image of Watermelon Peel. .......................................................................................16

Figure 3.4: Sample Binary Image of Watermelon Peel after the Application of Median Filter and

Morphological Closing. ................................................................................................................................ 18

Figure 3.5: Sample Image which contains only the part with the Watermelon Peel. ............................ 18

Figure 3.6: Sample OCT Image of Watermelon before processing. ........................................................ 20

Figure 3.7: Sample OCT Image of Watermelon after processing. ........................................................... 20

Figure 3.8: Image viewed as a surface, with labeled watershed ridge line and catchments basins. ...... 21

Figure 3.9: Sample of inverse OCT Image of Watermelon. ..................................................................... 22

Figure 3.10: Sample Binary Image of Watermelon after the Application of Median Filter and

Morphological Closing. ................................................................................................................................ 23

Figure 3.11: Distance Metric of the OCT Image of Watermelon. ............................................................ 23

Figure 3.12: Watershed Transformation of OCT Image of Watermelon. ............................................... 24

Figure 3.13: Sample OCT Watermelon Image of Manual Segmentation. .............................................. 25

Figure 3.14: Sample Binary OCT Watermelon Image of Manual Segmentation. .................................. 26

Figure 3.15: Distance Metric of Manual Segment OCT Image of Watermelon. ..................................... 26

Figure 3.16: Watershed Transformation of Manual Segment OCT Image of Watermelon. ................. 27

Figure 3.17: Application of Semitransparent technique onto manual and automatic segmentation. .. 28

Figure 3.18: (a) Binary Manual Segment Image, (b) Binary Image containing only the region

between 800 and 200,000 pixels, (c) Binary Image containing the centroid of each region (marked

with *), the red circle corresponds to the cell #4, (d) Binary Image containing only the enable region

(cell #4). ........................................................................................................................................................ 29

Figure 3.19: (a) Binary Manual Segment Image, (b) Binary Image containing only the region

between 4000 and 90,000 pixels, (c) Binary Image containing the centroid of each region (marked

with *), the red circle corresponds to the cell #19, (d) Binary Image containing only the enable region

(cell #19). ....................................................................................................................................................... 30

Figure 4.1: Characteristic Curve of Negative Skewness. .......................................................................... 33

Figure 4.2: Characteristic Curve of Positive Skewness. ........................................................................... 33

Figure 4.3: (a) Watershed Transformation of Manual Segmented OCT Image of Watermelon, (b)

Watershed Transformation of Automatic Segmented OCT Image of Watermelon (postgraduate data).43

Figure 4.4: (a) Watershed Transformation of Manual Segmented OCT Image of Watermelon, (b)

Watershed Transformation of Automatic Segmented OCT Image of Watermelon (undergraduate data).

....................................................................................................................................................................... 43

Figure 5.1: Regression Equation and Line for Pen versus Age. ............................................................... 45

Figure 5.2: Regression Equation and Line for Pen versus Weight. ........................................................ 46

Figure 5.3: Regression Equation and Line for Age versus Weight. ........................................................ 47

Figure 5.4: Canonical Variables and Classification Error per Age (OCT Imaging of Watermelon Peel).

....................................................................................................................................................................... 48

Figure 5.5: Canonical Variables and Classification Error per Pen (OCT Imaging of Watermelon Peel).

....................................................................................................................................................................... 49

Figure 5.6: Canonical Variables and Classification Error per Weight (OCT Imaging of Watermelon

Peel). .............................................................................................................................................................. 49

Figure 5.7: Canonical Variables and Classification Error per Age (OCT Imaging of Watermelon Flesh).

....................................................................................................................................................................... 50

Figure 5.8: Canonical Variables and Classification Error per Pen (OCT Imaging of Watermelon Flesh).

........................................................................................................................................................................ 51

Figure 5.9: Canonical Variables and Classification Error per Weight (OCT Imaging of Watermelon

Flesh). ............................................................................................................................................................. 51

Figure 5.10: Canonical Variables and Classification Error per Age (Manual OCT Imaging of

Watermelon Flesh). ...................................................................................................................................... 52

Figure 5.11: Canonical Variables and Classification Error per Pen (Manual OCT Imaging of

Watermelon). ................................................................................................................................................ 53

Figure 5.12: Canonical Variables and Classification Error per Weight (Manual OCT Imaging of

Watermelon). ................................................................................................................................................ 53

Figure 5.13: Correlation and MPE Estimation of Age (OCT Imaging of Watermelon Peel). ................ 55

Figure 5.14: Correlation and MPE Estimation of Pen (OCT Imaging of Watermelon Peel). ................ 55

Figure 5.15: Correlation and MPE Estimation of Weight (OCT Imaging of Watermelon Peel). .......... 56

Figure 5.16: Correlation and MPE Estimation of Age (OCT Imaging of Watermelon Cells). ............... 57

Figure 5.17: Correlation and MPE Estimation of Pen (OCT Imaging of Watermelon Cells). ............... 57

Figure 5.18: Correlation and MPE Estimation of Weight (OCT Imaging of Watermelon Cells). ......... 58

Figure 5.19: Correlation and MPE Estimation of Age (Manual OCT Imaging of Watermelon Cells). . 59

Figure 5.20: Correlation and MPE Estimation of Pen (Manual OCT Imaging of Watermelon Cells). 59

Figure 5.21: Correlation and MPE Estimation of Weight (Manual OCT Imaging of Watermelon Cells).

....................................................................................................................................................................... 60

Figure 5.22: (a) Outlines of manual and automatic segmentation, (b) Subtraction of manual and

automatic segment cell (new data) ...............................................................................................................61

Figure 5.23: (a) Outlines of manual and automatic segmentation, (b) Subtraction of manual and

automatic segment cell (old data).................................................................................................................61

List of Tables

Table 4.1: Statistical data of the intensity images. ................................................................................... 34

Table 4.2: Statistical data of power spectral density. ............................................................................... 35

Table 4.3: Measurements of Agricultural Research Institute.................................................................. 35

Table 5.1: Classification error (OCT Imaging of Watermelon Peel). ....................................................... 48

Table 5.2: Classification error (OCT Imaging of Watermelon Flesh). .................................................... 50

Table 5.3: Classification error (Manual OCT Imaging of Watermelon Flesh). ....................................... 52

Table 5.4: Correlation and mean error estimation result (OCT Imaging of Watermelon Peel). ........... 54

Table 5.5: Correlation and mean percentage error estimation results (OCT Imaging of Watermelon

Cells). ............................................................................................................................................................. 56

Table 5.6: Correlation and mean percentage error estimation results (Manual OCT Imaging of

Watermelon Cells). ....................................................................................................................................... 58

Abbreviations

AR Autoregressive

ARI Agricultural Research Institute

DFT Discrete Fourier Transform

FD OCT Frequency/Fourier Domain Optical Coherence Tomography

FFT Fast Fourier Transform

GUI Graphical User Interference

LCI Low Coherence Interferometer

LOOCV Leave-One-Out Cross Validation

MANOVA Multivariate One-Way Analysis of Variance

MPE Mean Percentage Error

MRI Magnetic Resonance Imaging

OCT Optical Coherence Tomography

OFDI Optical Frequency Domain Imaging

PCA Principal Component Analysis

PSD Power Spectral Density

SD OCT Spectral Domain OCT

SS OCT Swept Source Optical Coherence Tomography

TD OCT Time Domain Optical Coherence Tomography

1 Introduction

1.1. Brief Overview in Optical Coherence Tomography (OCT)

The term tomography refers to the method of producing two-dimensional data derived from

three-dimensional object to construct a slice image of the solid object's internal structure [1].

In the last decade, many tomographic imaging techniques have been developed, like

Ultrasound, Magnetic Resonance Imaging (MRI) and Computer-Generated Imaging [17].

Optical Coherence Tomography is a fundamentally novel technique of optical imaging

modality. This technique has been developed for noninvasive cross sectional imaging in

biological systems [5]. Furthermore, OCT has a determinant role in imaging due to the

accuracy of micrometer resolution and millimeter penetration depth.

Optical Coherence Tomography is based on the detection of infrared light waves to acquire

micron scale, cross-sectional, and three dimensional (3D) image of the subsurface

microstructure of biological tissues. It is analogous to B-mode ultrasound imaging, except that

the echo time delay and the intensity of back-reflected or back-scattered infrared light instead

of the acoustic waves, is measured. The principal operation of OCT is based on fiber optic

Michelson interferometer, which performs measurements with a low coherence length light

source. The “sample arm” of the interferometer illuminates the light on the tissue and collects

the backscattered light and the “reference arm” of the interferometer has a reference path

P a g e 2 Chapter 1: Introduction

delay that is scanned as a function of time. Optical interference between the light from the

sample and the reference arms occurs only when the optical delays correspond to within the

coherence length of the light source [1]. Two basic approaches of OCT have been developed

through the years, the Time Domain OCT (TD OCT) and the Fourier or Frequency Domain

OCT (FD OCT).

The rapid evolution of OCT reflected in the number of publications. Based on the PubMed

database for biomedical literature, the number of publications with the term “Optical

Coherence Tomography” increased slowly until 200 and had a stable increase of more than

200 publications per year [3].

1.2. Digital Image Processing

Human Vision is the most advanced and complex perception mechanism. It provides

information needed for simple as well as very complex tasks. Also, it is acceptable that the

image has a great impact in life. The importance of image is described in a well-known

proverb that says “One picture is worth a thousand words”. Several media adjust the images

into their requirements using digital image processing in order to achieve the transmission of

the necessary information [16].

Digital Image Processing refers to processing digital images by means of a digital computer.

Note that a digital image composed of a finite number of elements, each of which has a

particular location and value. These elements are referred to as picture elements, image

elements, pels and pixels. Pixel is the term most widely used to denote the elements of a

digital image [17]. Digital image processing allows a wide range of algorithms to apply to the

images and avoid problems such as the built-up noise and signal distortion.

There is no general agreement regarding where image processing stops and other related

areas such as image analysis and computer vision start. Sometimes a distinction is made by

defining image processing as a discipline in which both the input and output are digital

images.

Many techniques of digital image processing were developed in the last decade. These

reflected in the large number of papers published in international scientific journals each year,

as well as in a good number of specialized books in digital image processing.

An important characteristic underlying the design of image processing systems is the

significant level of testing and experimentation that normally is required before arriving at the

acceptable solution. This characteristic implies that the ability to formulate approaches and


quickly prototype possible solutions generally plays a major role in reducing the cost and time

required to arrive at a viable system implementation [17].

1.3. Motivation

The initial motivation for the research in the watermelon was given by the Agricultural

Research Institute in an effort to interpret the physical attributes of watermelons. The primary

research was performed within the framework of my undergraduate studies (a brief overview

of this can be found in section 2.2) and due to the unexpected excellent results is given a

further motivation to study this subject in order to certify the validity of these results.

In combination with the aforementioned is also given the motivation to use OCT imaging to

study the watermelon cells, due to the fact that until now only the Electron Microscopy has

obtained their study. The procedure to obtain a sample using Electron Microscopy is time

consuming and expensive in contrast the procedure to obtain a sample using OCT. It is

important to be mentioned that the imaging of the watermelon peels used experimentally

given that no research, so far, has given satisfactory results.

Furthermore, digital image processing is used in an effort to enhance the resolution and the

quality of OCT imaging. Note that, when OCT became a research hotspot, most researchers

were interested in physics mechanism, instrumentation and practical applications. As the

research goes on, more people think of using image processing to solve the resulting problems.

They realize that some of the problems may not be easily solved by physical methods.

1.4. Scope of Thesis

This research project involves two main objectives for achieving. The first objective aims to

establish an algorithm for the improvement of the quality and accuracy of OCT imaging.

Furthermore, the second objective is to evolve a novel method that aims to create a reliable

and efficient solution which will provide information about the properties of watermelon.

More specific the requirement of the improvement of OCT imaging occurs due to the existence

of noise artifacts and back reflections in the resulting OCT imaging. These faults in the OCT

imaging are expected to cause alterations regarding the results; therefore algorithms are

implemented to avoid these consequences of alterations. Likewise, this algorithm gives the

ability to enhance the resolution and the quality of the OCT imaging.

In order to develop the appropriate method for the watermelons properties, a further, more

detailed and quantitative analysis of the watermelon changes, was performed. This study was


facilitated by the creation of an algorithm that were identified automatically and quantitative

the cytological changes and the changes in the configuration of the peel during the ripening of

them.

Apart of the application of quantitative analysis of the watermelon peel and connective tissue,

automatic and manual segmentations were examined in order to check whether the latter

response to the first.

1.5. Chapters Overview

The current research is organized as follow:

Chapter 2: Background and Literature Review. This chapter gives an outline of the

fundamental principles of the innovative Optical Coherence Tomography approaches and the

main applications. Additionally, it presents the previous research which is the base and the

main motivation of the current research.

Chapter 3: Experimental Procedure and Image Processing in OCT Imaging. The

experimental procedure which is followed to acquire the OCT imaging samples of watermelon

and the implementation of the image processing in these samples, are covered and described

in this chapter.

Chapter 4: Multivariate Techniques and Algorithms. This chapter provides the

definitions of the statistical data and the manner of the statistical data acquisition.

Furthermore, covers all statistical analysis techniques, which is followed within the framework

of this research.

Chapter 5: Results. This chapter demonstrates and analyzes the obtaining results of the

statistical analysis.

Chapter 6: Summary and Future Works. This chapter gives a brief overview of this

thesis and possible future work.

2 Background and Literature Review

Following the brief reference in Optical Coherence Tomography, an extensive approach and

description is given in the current chapter. In addition, it gives an overview of the previous

work in OCT imaging of the watermelon.

2.1. Optical Coherence Tomography (OCT)

2.1.1. Introduction to Optical Coherence Tomography

Optical Coherence Tomography is a novel noninvasive, high-resolution tomographic imaging

technique using near-infrared light to acquire micron scale, cross-sectional, and three

dimensional (3D) image of the subsurface microstructure of biological specimens in situ and

in real time, which introduced in 1991. OCT imaging has a number of features that make it

attractive for a wide range of application.

The physical principle of OCT is analogous to B-mode ultrasound imaging, except that the

echo time delay and the intensity of back-reflected or back-scattered infrared light rather the

acoustic waves, is measured. The infrared light wavelengths used in OCT are up to two orders

of magnitude higher than ultrasound wavelengths, so OCT technology can yield a lateral and

axial spatial resolution of 1-10 μm, which is 10 to 25 times better than that of available high

P a g e 6 Chapter 2: Background and Literature Review

frequency ultrasound imaging. It is important to be mentioned that OCT imaging is sufficient

to reveal the fine biological structures, due to the advantage of high resolution, instead of

ultrasound imaging which is not. Additionally, the penetration depth of OCT imaging is

approximately 1-2 mm depending on tissue structure, focus depth of the probe used, and

pressure applied to the tissue surface. The resolution in combination with the penetration

depth gives the ability to OCT function as a type of “optical biopsy”, which is approaching

those of standard excisional biopsy and histopathology, but without the need to remove and

process the tissue specimens.

The classical layout of an OCT system is based on the fiber optic Michelson interferometer

(Figure 2.1.1) with a low coherence length light source (wavelength ranging from 700-1400

nm) from a superluminescent diode. It is important to mention that the wavelength range

used for OCT has to be selected in a way that guarantees high penetration into the specimen.

In the interferometer, the beam from the light source is directed onto a beam splitter that

divides the beam into a reference and a sample arm. The “sample arm” of the interferometer

illuminates the light on the tissue and collects the backscattered light. The “reference arm” of

the interferometer has a reference path delay that is scanned as a function of time. The

broadband nature of light causes interference of the optical fields to occur only when the path

lengths of the reference and the sample arm are matched to within the coherence length of the

light source. The interference signal carries information about the sample at a depth

determined by the reference path lengths.

Figure 2.1: Schematic of OCT System based on Michelson interferometer.

Source

Detector

50/50

Sample

Reference

z z

Δlc

Long Coherence Length Short Coherence Length


The OCT System can be broadly classifier as Time-Domain OCT (TD OCT) and the Frequency-

Domain OCT (FD OCT).

Important parameters for OCT

Axial (or depth) Resolution is an important parameter in OCT system. It is used to measure

how fine the structures can be resolved in the depth direction. In all types of OCT systems, the

achievable resolution depends on the temporal coherence length of the light source. Larger

bandwidth of source and wider tuning bandwidth give better axial resolution.

Sensitivity in OCT refers to ability of the system to detect smallest amount back-reflection

from the sample under observation. Higher sensitivity gives also the ability of increase the

imaging speed.

2.1.2. Time-Domain Optical Coherence Tomography (TD OCT)

The first generation of OCT systems, denoted “time-domain OCT” (TD OCT), which was firstly

demonstrated in 1991 for cross-sectional imaging of retina and coronary artery. Since then,

OCT has rapidly developed as a noninvasive biomedical imaging modality between 1991 and

2003. It is remarkable, that the first commercial OCT device was released in 1996 for retinal

imaging and by 2002 gained Federal Drug Administration approval.

TD OCT has the advantage that can achieve detection sensitivity above 100dB and up to

several kHz axial scan speed, which gives the ability of real time imaging of tissue at a frame

rate on the order of 1-10 frames per second.

In TD OCT, multiple parallel Low Coherence Interferometer (LCI) scans performed to

generate two dimensional (2D) images. In OCT, a typical measurement system uses a low

temporal coherence light source, such as a superluminescent diode or a broad bandwidth laser,

which illuminate the Michelson interferometer. The measurement object is placed in the

sample arm of the interferometer [1, 3]. A measurement beam emitted by the light source is

reflected or backscattered from the object with different delay times, depending on the various

optical properties of the different layers within the object [1]. By changing the pathlength of

the reference arm, and synchronously recording the magnitude of the intensity of the resulting

interference fringes, a longitudinal profile of reflectivity in respect to depth is obtained. A

fringe signal is detected only when the optical path difference in the interferometer is shorter

than the coherence length of the light source. Locating the maximum fringe visibility position

allows one to determine the location of internal structures of the object with a resolution in


the micrometer scale. Figure 2.1.2 presents a simple TD OCT system with the interference

signal and the A-scan envelope.

Figure 2.2: Typical fiber-optic implementation of TD OCT system, interferogram, and the A-scan envelope.

2.1.3. Frequency-Domain Optical Coherence Tomography (FD OCT)

The concept of Frequency Domain OCT (FD OCT), which is also known as Fourier Domain

OCT, introduced in 2003 that aimed to enable 10-100 fold improvements in detection

sensitivity and the speed of optical delay lines over the time-domain configuration. Instead of

the improvement of OCT performance, FD OCT enables 3D-OCT imaging in vivo. [1, 3]

In Fourier-Domain detection, the difference in length between sample and reference arm is

fixed, and echoes of light are obtained by Fourier transforming the interference spectrum.

Generally the interference spectrum can be performed using two complementary techniques,

first by analyzing the interfering signal with the spectrometer which referred to as spectral

domain OCT (SD OCT), or, second by sweeping the wavelength of the light directed to the

interferometer as a function of time. The latter is denoted as swept source OCT or optical

frequency domain imaging (OFDI).

Spectral Radar: Optical Coherence Tomography in the Fourier Domain

(FD OCT/SD OCT)

Spectral/Fourier domain detection uses a spectrometer and a high-speed line scan camera to

measure the interference spectrum in parallel. As aforementioned, the reference arm of FD

OCT is kept constant against the TD OCT.

Broad bandwidthsource

Detector

Beam splitter

Tissue

Scanning reference mirror

λ2

ΔL

dz

Single Reflection Site

Analog to digitalconverter Display

z

Filter Demodulate


In FD OCT, the depth information is provided by an inverse Fourier transform of the

spectrum of the backscatter light. The amplitude of the spectrum of the backscattered sample

light amplitude is measured using spectrometer. The inverse Fourier transform of the

recorder spectral intensity yields the same signal as obtained by standard low interferometry

and provides a back-reflection profile as a function of depth. The broadband source used is

similar to TD OCT. FD OCT measures the signal in the Fourier domain and by Fourier

transformation, delivers the scattering profile in spatial domain. The Fourier transform

provides the location of the peak at that frequency that corresponds to the scatterer location

[1]. Figure 2.1.3 presents a simple FD OCT system with the spectrogram and the back-

reflection profile.

Figure 2.3: Typical fiber-optic implementation of FD OCT system, spectrogram, and back-reflection profile.

The measurable axial range of FD OCT is limited by the resolution of spectrometer, which is in

sharp contrast with TD OCT. However, FD OCT has the advantage of higher sensitivity over

conventional TD OCT, which increases the imaging speed.

Swept Source Optical Coherence Tomography (SS OCT) or Wavelength

Tuning

Swept Source OCT (SS OCT) or Wavelength Tuning is an alternative approach which use a

frequency-swept laser light source and a photodetector to measure the interference spectrum.

SS OCT technology can perform imaging at longer wavelengths of 1000 and 1300 nm and

reduces optical scattering and improves image penetration depths. Moreover, SS OCT enables

three dimensional (3D) OCT imaging of highly scattering tissues. [1, 3, 6]

Broad bandwidthsource

Beam splitter

Tissue

Reference mirror

Digitizer FFT Display

GratingCCD


zλ


By the usage of SS OCT technique as in the case of SD OCT, the reference arm length is fixed

and no moving parts are required for axial scan. This is an advantage which significantly

increases the speed of scanning. Additionally, another advantage is the use of a single

photodetector that provides a simple elimination of the unwanted DC intensity by a high-pass

filtering of the photodetector signal. This enhances the usable dynamic range of the detection

system considerably. In comparison with the FD OCT, SS OCT provides similar high-speed

data acquisition but without the drawbacks of the spectral limitation of the spectral

limitations of the charge-coupled device (CCD) camera. Figure 2.1.4 presents a simple SS OCT

system with the interferogram and the back-reflection profile. [1, 6]

Figure 2.4: Typical fiber-optic implementation of SS OCT system, interferogram, and back-reflection profile.

2.1.4. Application of OCT

Optical Coherence Tomography has evolved from an experimental laboratory tool to a new

diagnostic imaging modality with a wide spectrum of clinical applications in medical practice

including ophthalmology, cardiology, oncology, gastroenterology, dermatology, dentistry,

urology, gynecology among others [1]. OCT was initially applied for imaging in ophthalmology.

Nevertheless, additional advances in OCT technology have made it possible to use OCT in a

wide variety of applications. Medical applications are still dominating in the OCT application.

Besides the closely related surface tomography techniques, only a few non-medical OCT

applications have been investigated so far [9].

Most developed medical OCT applications:

Ophthalmology: Ophthalmic applications of OCT have been expanded rapidly, due to the

reason of the relatively transparent nature and accessibility of the human eye [1]. Another

Tunable lasersource

Beam splitter

Tissue

Reference mirror

Analog to digitalconverter FFT Display

λ

Time


z

t

Detector


reason is the interferometric sensitivity and precision of OCT which fits quite well the near-

optical quality of many ophthalmological structures. Still another reason is the independence

of depth resolution from sample beam aperture which enables high sensitivity layer structure

recording at the fundus of the eye [9]. It constitutes an invaluable diagnostic tool in the areas

of retina diseases and glaucoma [1].

Cardiology: The domain of cardiology has been extensively investigated. Firstly, OCT was

applied to the examination of coronary artery structure and the evaluation of atherosclerotic

plague morphology and stenting complications. Subsequently, cellular, mechanical, and

molecular analysis was performed including the estimation of macrophage load. Moreover,

the application of OCT to cardiology was greatly enhanced by technological developments

such as rotational catheter-based probes, very high imaging speed systems, and functional

OCT modalities [1].

Oncology: Imaging has been performed in a wide range of malignancies including

gastrointestinal, respiratory and reproductive tract, skin, breast, blander, brain, ear, nose, and

throat cancers. OCT has been used to evaluate the larynx, and has been shown to effectively

quantify the thickness of the epithelium and evaluate the integrity of the basement membrane.

It was also used to visualize the structure of the lamina propria [1]. Moreover there are

additional applications for oncology but is at the experimental level. This is happen because of

the improvement of accuracy needed.

Non-medical OCT applications:

Low-coherence interferometry has already been used in optical production technology and

other technical fields. For example, LCI or ‘interference with white light’ has been used for

many years in industrial metrology, e.g. as position sensor , for thickness measurement of thin

films , and for other measures that can be converted to a displacement. Recently, LCI has been

proposed as a key technology for high density data storage on multilayer optical discs [9].

2.2. Previous Research in OCT Imaging of Watermelon

Within the framework of my undergraduate studies, I have implemented a similar research for

the OCT imaging of watermelon. It is important to record an overview of this research for the

reason that constitutes the base foundation of the current research.

The aim was to find a tool which allows the agriculturist to separate and identify the ripening

and examines also the cytological changes into two varieties of watermelons. This research

was based in OCT imaging, in combination with image processing.


The aspects which were covered within the framework of my undergraduate research are the

following:

Experimental Procedure: Using the IVS 300 Optical Coherence Tomography, imaging of two

varieties of watermelons was performed and saved for image processing.

Image Processing: Many methods of image processing were performed such as quantification

of connective tissue (using median filter and morphological opening and closing), and

segmentation of the watermelon cells (using watershed transformation). These methods are

explained further in the next chapter because are also used in the current research. Based on

the resulting images of the image processing, statistical data was acquired.

Statistical Data Acquisition: Statistical data was used for the production of histograms and

the estimation of the p-value. Likewise, these data was used for classification purposes.

Results: Based on histograms, the physical interpretation of the watermelon was given and it

was consistent according the opinion of agriculturist. In addition, by using classification

method it was revealed that the usage of OCT imaging could absolutely distinguish (100%) the

varieties and age of watermelons.

As referred, within this research, interesting and unexpectedly excellent results were given

and, thus, further research in this field was motivated.

3 Experimental Procedure &

Image Processing in OCT Imaging

Optical Coherence Tomography (OCT) Image has not been validated for the quality and

accuracy of micrometer-level information, therefore many researches leading in Image

Processing to solve physical problems.

This Chapter describes the experimental procedure and the image processing, which followed

within the framework of this research. For the implementation of image processing the

numerical computing programming language named Matlab is used.

3.1. Experimental Procedure

In the context of the completion of this research, two experiments methods were performed in

order to gather various samples of OCT Images of Watermelon flesh and peel. The

experimental procedure held in the Laboratory of Biomedical and Applied Optics at University

of Cyprus, during the summer months (July and August). For the experiments needs, the

watermelons were supplied by the Agricultural Research Institute of Cyprus.

The experiments dates were determined based on harvest days of the watermelons which were

25th and 29th of July 2013 and 2nd and 5th of August 2013. In each period, ten watermelons

P a g e 14 Chapter 3: Experimental Procedure & Image Processing in OCT Imaging

were used. Some of these were enough ripe, others were unripe and others were at the

appropriate age of harvest. The watermelons which were used for the experiments were

grafted onto cucurbit hybrids.

The steps for the implementation of the experimental procedure for the imaging of

watermelon flesh were the following:

i. Each watermelon was cutting transversely in the middle with specialize knife, so as

not to cause alternation to the cells.

ii. Using the Optical Coherence Tomography, eight samples of each watermelon flesh

were taken around the hearth, in the center of the watermelon (Figure 3.1).

Figure 3.1: The area points which is taken around the heart of the watermelon market with X.

iii. Image Properties:

• Diameter of Imaging: 6cm (around the center) to avoid imaging of seeds and

ovary of the watermelon.

• Total Images : 4 days x 10 watermelons x 8 samples = 320 images of the

watermelon flesh

iv. Saving of OCT Images.

Furthermore, the steps for the implementation of the experimental procedure for the imaging

of watermelon peel were the following:

i. Using the Optical Coherence Tomography, two samples of each watermelon peel were

taken at the darkest green area of the peel. (Figure 3.2). The imaging was applied in

the darkest green area of peel, for the reason that according the agriculturists this

area changes during the ripening period.


Figure 3.2: The area points which is taken at the darkest green of the watermelon peel market with X.

v. Image Properties:

• Area of Imaging: darkest green of the peel.

• Total Images: 4 days x 10 watermelons x 2 samples = 80 images of the

watermelon peel.

vi. Saving of OCT Images.

3.2. Quantification of Watermelon Peels

The aim of the process covered in the next pages was to create an image which contained the

part only with the watermelon peels. To achieve this objective the image noise has been

reduced, in order to not alter the results. The OCT Images used for quantification of

watermelon peels, were collected with the methodology which referred in section 3.1.

The steps for the implementation of this process quoted in the current section of this chapter.

The programming code regarding the implementation it can be found in Appendix A.

Step 1: Import of OCT Image of Watermelon Peels

Firstly, the two images imported of the peel from each watermelon opened and displayed

(Figure 3.3), simultaneously. In order to open the images the absolute value of FFT and the

logarithmic of data were performed.


Figure 3.3: Sample Image of Watermelon Peel.

Step 2: Application of Median Filter and Morphological Closing and

Conversion of the OCT Image to Binary

At this step images normalized in order their pixels values lies in the range of zero (0) and one

(1). A median filter was performed after the completion of the normalized procedure.

The Median Filter is a non-linear operation, which is used in image processing to remove or

reduce the “salt and pepper” noise. Noise reduction is an effective method, often use as pre-

processing step to improve the results of later processing. Median filtering is widely used in

image processing because, under certain conditions, it preserves edges while removing noise

[13].

Once the median filter was applied, the threshold level was computed with the usage of Otsu

Algorithm. The Otsu method has the ability to choose the threshold to minimize the intraclass

variance of black and white pixels. The threshold level can be used to convert an intensity

image to a binary image [17]. Thereinafter, the intensity images were converted to binary

images.

The process about conversion images to binary followed by the usage of the Morphological

Closing. This operation is a combination of the operations Erosion and Dilation, where are

fundamental to morphological image processing.

Dilation is an operation that “grows” or “thickens” objects in a binary image. The specific

manner and extent of this thickening is controlled by a shape referred as a structuring element.

Structuring element typically are represented by matrix of zeros (0s) and ones (1s).

Mathematically, dilation is defined in terms of set operations. The dilation of A by B, is

defined as


𝐴⨁𝐵 = {𝑧|�𝐵��𝑧 ∩ 𝐴 ≠ ∅}

where ∅ the empty set and B represents the structuring element.

Erosion “shrinks” or “thins” objects in a binary image. As in dilation, the manner and extent of

shrinking is controlled by a structuring element.

Mathematically, the definition of erosion is similar to the dilation. The erosion of A by B is

defined as

𝐴⊖ 𝐵 = {𝑧|(𝐵)𝑧⋂𝐴𝑐 ≠ ∅}

The Morphological Closing of A by B, denoted 𝐴 ∙ 𝐵, is a dilation followed by an erosion using

the same structuring element for both operation:

𝐴 ∙ 𝐵 = (𝐴⨁𝐵) ⊖𝐵

where A represents a binary image and B represents a matrix of zeros (0s) and ones (1s) that

specifies the structuring element.

Morphological Closing tends to smooth the contours of objects. It generally joins narrow

breaks, fills long thin gulfs, and fills holes smaller than the structuring element. The

structuring element which is used for the purpose of this process is a flat, disk-shaped with

radius R [17].

The Figure 3.4 below shows the results of the above processing. It is clear to see that the most

content of the images were removed, but the surface of the peel is distinguishable and

consecutive.


Figure 3.4: Sample Binary Image of Watermelon Peel after the Application

of Median Filter and Morphological Closing.

Step 3: Creation of an Image containing only Watermelon Peel

In the final step of this procedure, the images were amended 550 pixels below the front

surface of the peel. The Figure 3.5 shows a sample image which contains only the part with the

watermelon peel.

Figure 3.5: Sample Image which contains only the part with the

Watermelon Peel.

As aforementioned above, the aim of this process was about to reduce the noise and create an

image comprising only the part of the watermelon peel. Upon the completion of this process,

statistics were obtained for subsequent statistical analysis and classification. Further analysis

and discussion for these statistics provided in Chapter 4 and 5.

3.3. Quantification of Watermelon Connective Tissue

The aim of the process described in this section is to create an image which will contain only

the connective tissues and the cell walls. To achieve this target the image noise was reduced

and the back-reflections were removed, in order not to alter the results. The OCT Images were


used for quantification of watermelon tissue, were gathered with the methodology which is

referred in section 3.1.

To achieve this objective, using Matlab, a graphical user interface (GUI) was created in order

to improve image quality and resolution. With the usage of GUI, the following commands

were available for application at the images: (some of these were explained further in section

3.2)

Median Filter: removing or reducing the “salt and pepper” noise and preserving edges.

Morphological Image Closing: smoothing the contours of objects, joining narrow breaks,

filling long thin gulfs and holes.

Removal of Vertical Lines: removing the vertical line (back-reflections) of the image.

Colormap: adjusting the image color for perceptual vision (the applicable properties was gray,

brown, blue and red). Colormap blue was applied because it made the content of the image

more visible.

Lower and Upper Limit: expanding midrange color resolution by mapping low values to the

first color and high values to the last color in the colormap by specifying lower and upper

value limit, respectively.

Export: use to save image to various file formats. For the purpose of the research, the images

saved as a jpeg format.

The above mention features were applied and the result of this procedure can be found in

Figure 3.6 and 3.7 which show the same sample image of watermelon before and after

processing, respectively.


Figure 3.6: Sample OCT Image of Watermelon before processing.

Figure 3.7: Sample OCT Image of Watermelon after processing.

It is important to note, that the result was remarkable when the above-mentioned commands

were applied. In Figure3.6 the content of the image was not visible enough, but after the

processing (Figure 3.7) it was. In fact, a proportion of noise was removed and the color of the

image was strengthened. However, the second amplified the back-reflections, something

which it is expected that it will alternate the future results.

On the completion of the process mentioned above, images of watermelon opened and

normalized in order their pixels values lies in the range of zero (0) and one (1). Following that,

statistics were obtained for future statistical analysis and classification. Further analysis and

discussion for the interpretation of these statistics are provided in Chapters 4 and 5.

The programming code used regarding the processing that described in this section can be

found in Appendix B.

3.4. Image Segmentation based on Watershed Transform

To segment the image into homogeneous regions that corresponds to the cells of the OCT

Watermelon Image, Watershed Transform has been performed.

According to geography, watershed is the ridge of high land dividing areas that are drained by

different river systems. A catchment basin is the geographical area into a river or reservoir.

For further determination of watershed, a topological surface with two areas can be assumed,

as seen in Figure 3.8. If we imagine rain falling on this surface, it is clear that the water would

collect in the two areas labeled as catchment basins. Rain falling exactly on the labeled


watershed ridge line would be equally likely to collect in either of the two catchments basins

[17].

Figure 3.8: Image viewed as a surface, with labeled watershed ridge line and catchments basins.

The Watershed Transform can be used to solve a variety of image segmentation problems.

The watershed transform finds the catchment basins and ridge lines in a gray scale image. In

terms of solving image segmentation problems, the key concept is to change the starting image

into another image whose catchment basins are the object or regions we want to identify [17].

For the implementation of this process, the following steps were applied. The programming

code is given in Appendix B.

Step 1: Import of OCT Image of Watermelon

For the application of Watershed Transformation, the OCT Images of Watermelon which were

process via GUI were used. So in this step truecolor RGB OCT Images opened and converted

to the grayscale intensity images. Afterwards, the images were normalized. The Figure 3.9

illustrates a sample of the inverse OCT Image of Watermelon.


Figure 3.9: Sample of inverse OCT Image of Watermelon.

Step 2: Conversion of the OCT Image to Binary and Application of

Morphological Opening

In this step, the threshold level computed with the usage of Otsu Algorithm, as referred before,

and the intensity grayscale image converted to binary image. The process of conversion the

images to binary followed by the usage of the Morphological Opening.

The Morphological Opening of A by B, denoted 𝐴°𝐵, is simply erosion of A by B, followed by

dilation, using the same structuring element for both operation:

𝐴°𝐵 = (𝐴⊖ 𝐵)⨁ 𝐵

where A represents a binary image and B represents a matrix of zeros (0s) and ones (1s) that

specifies the structuring element.

Morphological Opening removes completely region of an object that cannot contain the

structuring element, smooths object contours, breaks thin connections, and removes thin

protrusions. The structuring element which is also used for the purpose of this process is a flat,

disk-shaped with radius R. [17]

The figure 3.10 illustrates the results of the above processing.


Figure 3.10: Sample Binary Image of Watermelon after the Application of Median Filter and Morphological Closing.

Step 3: Computation of Distance Metric

A tool commonly used in conjunction with the watershed transform for segmentation is the

distance transform. The Distance Transform of a binary image is a relative simple concept: It

is the distance from every pixel to the nearest non zero-valued pixel. The method which is

used to compute the distance transform was the chessboard. The chessboard distance between

(x1, y1) and (x2, y2) is max(|x1 - x2|,| y1 - y2|).

The Figure 3.11 shows the distance metric of the OCT Image of Watermelon. This image has a

maximum value at the center of each cell and a minimum at the periphery (along the

membrane).

Figure 3.11: Distance Metric of the OCT Image of Watermelon.

Step 4: Watershed Segmentation Using the Distance Transform


Following the computation of distance metric, the Watershed Transform was applied, in order

to segment the image into homogeneous regions. The inverse image which is created in Step 3

was used as the initial image to perform the Watershed Transformation. So in the center of

each cell, a minimum value (valley) exists.

The result of the Watershed Segmentation appears in Figure 3.12.

Figure 3.12: Watershed Transformation of OCT Image of Watermelon.

As aforementioned, the scope of this process was to segment the image into homogeneous

region which corresponds to the cells of the OCT Watermelon Image. When this process was

completed, statistics were obtained for subsequent analysis and classification. Further analysis

and discussion for these statistics are provided in Chapters 4 and 5.

3.5. Manual Segmentation of OCT Watermelon Imaging

Up to this step of research, automatic algorithm was performed in order to segment the

images into regions. The results of the above-mentioned process were not the desirable, since

the Watershed Segmentation splits the image into smaller regions, which was visible that they

do not exist. To improve the accuracy of image segmentation, manual segmentation was

examined, in order to compare with the automatic algorithm of segmentation.

The procedure followed to perform manual segmentation can be characterized as subjective.

Nevertheless, all images that were under this, their containing the same level of subjectivity,

because their generated by a particular person, called as “expert”.

In order to generate the images for the manual segmentation, the images which were the

results of the process via GUI were used. These images were printed and the “expert” draws in


transparent papers step-by-step the outline of each cell in OCT image. Thereinafter, these

papers scanned and saved as digital image (jpeg format) for subsequent use.

The programming code regarding the implementation of the manual segmented image which

followed can be found in Appendix C.

Step 1: Import of Manual Segment OCT Imaging of Watermelon.

Once the procedure of manual segmentation was completed, OCT Watermelon Images opened

through the use of Matlab. Therefore the images have been cropped in the right dimensions

and were displayed. The Figure 3.13 shows a sample image of manual segmentation.

Figure 3.13: Sample OCT Watermelon Image of Manual Segmentation.

Step 2: Conversion of the Manual Segment OCT Imaging to Binary

While, the OCT Images opened, the threshold level was computed so as to convert an intensity

to a binary image. The Figure 3.14 shows a sample manual segmentation binary OCT

Watermelon Image.


Figure 3.14: Sample Binary OCT Watermelon Image of Manual Segmentation.

Step 3: Computation of Distance Metric

Distance Transform0m is the distance from every pixel to the nearest non zero-valued pixel.

The method which is used to compute the distance transform was the chessboard, which is

previously explained.

The Figure 3.15 shows the distance metric of the OCT Image of Watermelon. This image has a

maximum value at the center of each cell and a minimum at the periphery (along the

membrane).

Figure 3.15: Distance Metric of Manual Segment OCT Image of Watermelon.

Following that statistics were obtained by the usage of the binary image for future analysis and

classification. Further analysis and discussion for these statistics are provided in Chapters 4

and 5.

Step 4: Watershed Segmentation


As mentioned above Watershed Transformation is capable to segment the image into

homogeneous regions. In case of manual segmentation Watershed must have better and

reliable results due to the outline of each cell being closed and consecutive. The inverse binary

image that was created in Step 2 was used as the initial image to perform the Watershed

Transformation. In the center of each cell, a minimum value exists.

The results of the Watershed Transformation in manual segment images illustrates in Figure

3.16. It is observable that a few cells do not recognized due to that the outline is not

consecutive.

Figure 3.16: Watershed Transformation of Manual Segment OCT Image of Watermelon.

The aim of the manual segmentation was to segment the image into homogeneous region

which corresponds to the cells of the OCT Watermelon Imaging, which was created form the

“expert”. This method was followed in order to compare with the automatic algorithm. Once

this process was completed, statistics were obtained for subsequent statistical analysis and

classification. Further analysis and discussion for these statistics are provided in Chapters 4

and 5.

3.6. Semitransparency for Comparison Purposes

An effort was operated to ascertain the accuracy and the correctness of automatic

segmentation in comparison with the manual segmentation. To achieve this, semitransparent

technique was used. This technique gives the ability to make an object transparent onto

another object and make it visible what information the object would obscure if it was

completely opaque. The semitransparent technique was applied onto the image of the manual

segmentation and the resulting image of the watershed transformation. Figure 3.17

demonstrates the resulting image of this application.


Figure 3.17: Application of Semitransparent technique onto manual and automatic segmentation.

If the segmented cell by the usage of manual segmentation lies into correspond area of the

automatic segmentation, since the result of the automatic segmentation is correct. As seen,

the result obtained is not the expected, thus another operation follows in order to provide a

more adequate manner of comparison.

3.7. Measurement of Region Properties

The target of this procedure is to specify properties for each component (object) within an

image. By measuring properties of OCT and manual OCT imaging are given the ability to use

them to compare and draw conclusions about the reliability and the accuracy of segmentation.

Initially, the manual segment image was opened and converted into binary image and with the

usage of latter the connected component of each image were labeled, in order to find out the

specific properties of each one of them. For the research needs, the properties that were

measured are the following:

Area: the Area property returns a scalar that specifies the actual number of pixels in the

region. In Figure 3.19 (b), the area between 800 and 200,000 pixels is chosen in order to

remove the small areas which are obtained because some outlines are not continuous.

Centroid: the Centroid property returns a 1-by-Q vector that specifies the center of mass of the

region. The first element of Centroid is the horizontal coordinate (x-coordinate) of the center

of mass, and the second element is the vertical coordinate (y-coordinate). Using these

coordinates the centroid of each cell was plotted and the result can be found in Figure 3.18 (c),

the centroids of each cell can be recognized by the blue star (*).

Image: the Image property returns a binary image (logical) of the same size as the bounding

box of the region. The “on” pixels correspond to the region, and all other pixels are “off”. In

Figure 3.18 (d), the enable region corresponds to the cell which labeled with the number 4.


Also, in Figure 3.18 (c) this cell represented with a red circle. In order to create this red circle

the property Minor and Major Axis Length and Centroid were used to define the center and

the radius of the circle.

Minor Axis Length: the minor axis length property returns a scalar that specifies the length in

pixels of the minor axis of the ellipse that has the same normalized second central moments as

the region.

Major Axis Length: the major axis length property returns a scalar that specifies the length in

pixels of the major axis of the ellipse that has the same normalized second central moments as

the region.

Figure 3.18: (a) Binary Manual Segment Image, (b) Binary Image containing only the region between 800 and 200,000 pixels, (c) Binary

Image containing the centroid of each region (marked with *), the red circle corresponds to the cell #4, (d) Binary Image containing only the enable

region (cell #4).

For comparison purposes, the image which was obtained by the automatic segmentation used

in order to measure their region properties. For this image centroid, image, minor and major


axis length properties were also measured. Consequently, using the properties of each region

is given the ability to use them and compare each region separately.

The same method was also followed in the samples of image which is obtained during my

undergraduate research (described in section 2.2). These old data was used due to the better

quality of imaging and expected to have lower proportion of error. Figure 3.19 shows the

results of the measurement of the aforementioned properties.

Figure 3.19: (a) Binary Manual Segment Image, (b) Binary Image containing only the region between 4000 and 90,000 pixels, (c) Binary

Image containing the centroid of each region (marked with *), the red circle corresponds to the cell #19, (d) Binary Image containing only the enable

region (cell #19).

On the completion of the application of several methods for digital image processing, as

referred above, statistical characteristics of each method were acquired and used for statistical

analysis and classification.

The programming code for the implementation of this procedure is given in Appendix D.

4 Multivariate Techniques and Algorithms

The statistical analysis of the statistical data acquired from the methods that described in

Chapter 3 is essential for mean percentage error estimation, estimation of relationships

among variables (correlation), classification and estimation of classification error. For the

aforementioned estimations advance techniques, such as Regression Analysis, Leave-One-Out

Cross Validation (LOOCV), Principal Component Analysis (PCA), Multivariate Analysis of

Variance (MANOVA), Discriminant Analysis and Correlation were used.

This Chapter describes the techniques for the statistical analysis, mentions the statistical data

and the acquisition of them. For the purpose of the statistical procedure, techniques and

algorithms have been implemented in Matlab.

4.1. Definitions of Statistical Data

Mean: mean and expected value are used synonymously to refer to one measure of the

central tendency either of a probability distribution or of the random variable characterized by

that distribution. Specifically, the sum of the observations divided by the number of the

observations.

The mathematical approach for the mean can be expressed in the following formula:

P a g e 32 Chapter 4: Multivariate Techniques and Algorithms

�̅� =𝑠𝑠𝑠 𝑜𝑜 𝑜𝑜𝑠𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑠

𝑜𝑠𝑠𝑜𝑜𝑜 𝑜𝑜 𝑜𝑜𝑠𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑠=∑ 𝑥𝑖𝑛𝑖=1

𝑜

where �̅� is the mean, xi is the observation, and n represents the number of observations.

Median: is the number which is separating the higher half of a data sample, a population, or

a probability distribution, from the lower half. The median of a finite list of numbers can be

found by arranging all the observations from lowest value to highest value and picking the

middle one.

The mathematical approach for the median can be expressed in the following formula:

𝜇 = �

𝑥�𝑛+12 � , 𝑜 𝑜𝑜𝑜

𝑥�𝑛2�+ 𝑥�𝑛+12 �

2, 𝑜 𝑜𝑜𝑜𝑜

where μ is the mean, x is the observation, and n represents the number of observations.

Variance: measures how far a set of numbers (observations) is spread out. A variance of

zero indicates that all the values are identical. A small variance indicates that the data points

tend to be very close to the mean and hence to each other, while a high variance indicates that

the data points are very spread out around the mean and from each other.

The mathematical approach for the variance can be expressed in the following formula:

𝜎2 = ∑ (𝑥𝑖 − �̅�)2𝑛𝑖=1

𝑜 − 1

where σ2 is the variance, xi is the observation, �̅� is the mean value and n represents the

number of observations.

Standard Deviation: is a measure that is used to quantify the amount of variation or

dispersion of set of data values. A standard deviation close to zero indicates that the data point

tend to be very close to the mean of the set, while a high standard deviation indicates that the

data points are spread out over a wider range of values. Standard Deviation is equal to the

positive square root of variance.

The mathematical approach for the standard deviation can be expressed in the following

formula:

𝜎 = +�𝜎2


where σ is the standard deviation and the sub root (𝜎2) contains the square of variance.

Skewness: is a measure of the asymmetry of the probability distribution of a real-valued

random variable about its mean. The skewness value can be positive or negative, or even

undefined.

Negative skew indicates that the tail on the left side of the probability density function is

longer or fatter than the right side. Conversely, positive skew indicates that the tail on the

right side is longer or fatter than the left side.

Figure 4.1: Characteristic Curve of Negative Skewness.

Figure 4.2: Characteristic Curve of Positive Skewness.

Kurtosis: is any measure of the “peakedness” of the probability distribution of a real-valued

random variable. Kurtosis is a descriptor of the shape of a probability distribution.

Distributions with negative or positive excess kurtosis are called paltykurtic distributions and

leptokurtic distributions respectively.

Autoregressive Power Spectral Density - Burg’s method: Power spectral

density (PSD) describes how the power of a signal or time series is distributed over the

different frequencies [14].

Assume a matrix x, the PSD is computed independently for each column and stored in the

corresponding column in matrix pxx, pxx is the distribution of power per unit frequency. The

frequency is expressed in units of rad/sample.


At this point it is important to mention essential parameters for watermelons

(measured and provided by the ARI) which are referred in the following procedures:

Age of watermelon: is defined by the planting day of watermelon until the harvest day.

Weight of watermelon: is defined by the weight of watermelon in kilos (kg).

Firmness of watermelon: was recorded as the maximum resistance force to penetration

around the heart of each fruit in cross-section to depth of 50 mm (measurement unit: kg). In

this thesis is also referred as pen [18].

4.2. Statistical Data Acquisition

As referred in Chapter 3, statistical data acquisition of OCT imaging was performed, upon the

completion of image processing. These data saved in tables and was used for subsequent

statistical analysis.

Using the intensity image, namely the pixel value, of each OCT imaging of watermelon peel

and flesh, mean, median, variance, standard deviation, kurtosis and skewness were measured.

Note that, similar tables were acquired using the result images of the watershed

transformation. In Table 4.1 demonstrates a sample table of OCT imaging of the watermelon

flesh. Each row corresponds to the statistical data value obtained by a watermelon intensity

image.

Table 4.1: Statistical data of the intensity images.

Intensity Variance

Intensity Mean

Intensity Median

Intensity Standard Deviation

Intensity Kurtosis

Intensity Skewness

0,0616 0,8819 0,9804 0,2483 8,7597 -2,6466

··· ··· ··· ··· ··· ···

··· ··· ··· ··· ··· ···

0,0590 0,8840 0,9765 0,2429 9,1818 -2,7110

Furthermore, power spectral density (PSD) measured in each case of study. The Table 4.2 is

the distribution of power per unit frequency. Each row corresponds to power spectral density

by a watermelon OCT imaging. The number of order and the nfft points which used for the

statistical acquisition was chosen by the trial and error method. The term order defined as the


order of the autoregressive (AR) model used to produce the PSD estimate and the term nfft

determines the points in the DFT (Discrete Fourier Transform).

Table 4.2: Statistical data of power spectral density.

Points in Discrete Fourier

Transform

1 ··· 256 ···

Sample 1

29,2384 ··· 0,0367 ···

···

··· ··· ··· ···

···

··· ··· ··· ···

Sample 152

30,0521 ··· 0,0351 ···

The measurements provided by the Agricultural Research Institute for the research are

presented in Table 4.3.

Table 4.3: Measurements of Agricultural Research Institute.

Sample Set Date Harvest Date

Fruit Age (days)

Weight (kg)

Pressure - Pen (kg)

1 14/06/2013 25/07/2013 41 5,7 3,9

··· ··· ··· ··· ··· ···

10 17/06/2013 25/07/2013 38 4,3 3,9

1 23/06/2013 29/07/2013 39 3,6 4,7

··· ··· ··· ··· ··· ···

10 21/06/2013 29/07/2013 38 4,7 5,1

··· ··· ··· ··· ··· ···

The acquisition of the statistical data gives the ability to apply several statistical analysis

methods for comparison and classification purposes. The explanation and the results of the

statistical analysis are given in the current chapter and in Chapter 5, respectively.

4.3. Statistical Analysis based on Regression Analysis

Regression analysis is a statistical process for the estimation of the relationships among

variables [13]. It gives the ability to predict continuous dependent variables from a number of


independent variables. It can be used to identify the form of curve which provides the best fit

through a dataset. For the purpose of research polynomial regression analysis was performed.

Polynomial Regression is a form of linear regression in which the independent variable x and

the dependent variable y is modeled as an n-th degree polynomial. Polynomial regression fits

using the least squares method. The least squares method minimizes the variance of the

unbiased estimators of the coefficients, under the conditions of the Gauss-Markov theorem.

The mathematical approach for the polynomial analysis can be expressed in the following

general formula:

𝑦 = 𝑝1𝑥𝑛 + 𝑝2𝑥𝑛−1 + ⋯+ 𝑝𝑛𝑥 + 𝑝𝑛+1

where x is the independent variable, y is the dependent variable, n represents the degree of

the polynomial and p represents the coefficient of the polynomial.

Another significant coefficient closely related with the regression analysis is the R squared

(R2). R squared denotes the coefficient of determination, which indicates the proportionate

amount of variation in the response variable y explained by the independent variables x in the

regression model. The larger the R-squared is the more variability is explained by the

regression model. The R-squared is range from 0 up to 1, and denotes the strength of the

linear association between x and y.

R-squared is the proportion of the total sum squares which is explained by the following

model:

𝑅2 = 1 −∑ (𝑦𝑖 − 𝑜𝑖)2𝑖

∑ (𝑦𝑖 − 𝑦�)2𝑖

where the numerator of the fraction represents the residual sum of squares and the

denominator of the fraction represents the total sum of squares.

For the purpose of this research regression analysis is used in order to yield models for the

data that the Agricultural Research Institute provided for studying. The parameters measured

by the ARI were age, pen and the weight. Regression analysis was performed repetitively using

each time a combination of two out of the three variables given by ARI. One parameter was

used as independent and the other one as dependent variable.

The results of the application of regression analysis will discuss in Chapter 5. Moreover, the

related algorithm can be found in Appendix E.


4.4. Classification based on Statistical Multivariate Analysis

Several method of statistical analysis is used in different aspects in terms of research and

experiments. Many research used different statistical analysis methods in order to lead in an

optimum results of their experiments.

In this part of research an effort is given to classify the watermelons according the ripening

day, the weight and the pen, with the usage of the following methods. Therefore, statistics

which arisen by the processing of OCT imaging and by the ARI, have been used.

Leave-One-Out Cross Validation (LOOCV)

Cross Validation is an evaluation method which is used to measure the predictive performance

of statistical method. Generally, the operation method is to split the statistical data into two

dataset, the training and the testing. The training dataset contains the known data on which

the training of algorithm run and a dataset of unknown data against which the model is tested.

In case of leave-one-out cross validation, for a dataset with N observations, N experiments

perform. Therefore for each experiment, N-1 observations are used for training and the

remaining observation for testing.

The computational time of LOOCV is expensive due to the number of experiments instead of

this the predictive performance is accurate enough.

Principal Components Analysis (PCA)

Principal Components Analysis (PCA) is statistical procedure which gives the ability of

identifying patterns in data, by reducing a complex data set to lower dimension, without loss

of information and expressing the data in such a way as to highlight the importance of values

[10]. PCA uses an orthogonal transformation to convert a set of observations of possibly

correlated variables into a set of values of linearly uncorrelated variables, the principal

components. The number of principal components is less or equal to the number of original

variables. This transformation is defined in such a way that the first principal component has

the largest possible variance and each succeeding component in turn has the highest variance

possible under the constraint that it is orthogonal to the preceding components [11].

Assume an m-by-n data matrix X to perform principal component analysis with standardized

variables, that is, based on correlations and compute the principal component coefficients.

The rows of X correspond to observations and the columns to variables. The result of the PCA


command is an n-by-n matrix, each column containing coefficients for one principal

component. The columns are in order of decreasing component variance.

Mathematical Approach of PCA

The starting point for PCA is a random vector x with n elements, and x has zero empirical

mean, is centered by subtracting its mean. A linear combination of the vector x can be defined

as:

𝑦1 = �𝑤𝑘𝑥𝑘 = 𝐰1T𝐱

𝑛

𝑘=1

where w11, …, wn1 represent elements of an n-dimensional weight vector w1.

If y1 has maximum variance then is the first PC of x, variance depends on both the norm and

orientation of the weight vector w1 the constraint that the norm equals to 1 must be imposed,

||w1||=1. The variance of y1 is defined as:

𝐸{𝑦12} = 𝐸 ��𝐰𝟏T𝐱�2� = 𝐰𝟏

𝐓𝐸{𝐱𝐱𝑇}𝐰1 = 𝐰1𝑇𝐂𝐱𝐰1

where Cx is the m-by-n covariance of x. The weight vector that maximizes the above equation

must be calculated so that ||w1||=1, it is well known that the eigenvectors of the covariance Cx,

e1, …, en are the solutions for the maximization variance. Thus, the first PC is given by:

𝑦1 = 𝐞𝟏𝑻𝐱

Generalized the equation of variance y1 to k PCs, 𝑦𝑘 = 𝐰𝟏𝑻𝐱 one can find the rest PCs under the

constraint that yk is uncorrelated with all the previously found PCs. It follows that:

𝐰𝑘 = 𝒆𝑘

Thus the k-th PC is

𝑦𝑘 = 𝐞𝑘𝑇𝐱

It has been proved that the PC basis vector wk is eigenvectors ek of the covariance matrix Cx it

follows that:

𝐸{𝑦𝑚2 } = 𝐞𝑚𝑇 𝐸{𝐱𝐱𝑇}𝐞𝑚 = 𝐞𝑚𝑇 𝐂𝐱𝐞𝑚 = 𝑜𝑚


where dm are the eigenvalues of Cx. Thus, by ordering the eigenvectors found from the

covariance matrix by eigenvalue, from highest to lowest, this gives PCs in order of significance

[11] [12].

Discriminant Analysis and Classification

Discriminant Analysis is a statistical analysis which is used to predict a categorical dependent

variable by one or more independent variables. Moreover, discriminant analysis is a

classification method used to determine in which category each sample belongs.

A number of types for classifier exist such as linear, mahalanobis, quadratic etc., which it

gives the ability to specify the type of discriminant function. Linear discriminant analysis fits

a multivariate normal density to each group, with a pooled estimate of covariance.

Mahalanobis discriminant analysis uses Mahalanobis distances with stratified covariance

estimates. The mahalanobis distance of an observation x = (x1, …, xn)T from a group of

observations with mean μ= (μ1. …, μn)T and covariance matrix S is defined as:

𝐷𝑚(𝑥) = �(𝑥 − 𝜇)𝛵 × 𝑆−1(𝑥 − 𝜇)

Quadratic discriminant analysis, it computes the sample mean of each class. Then it computes

the sample covariances by first subtracting the sample mean of each class from the

observations of that class, and taking the empirical covariance of each class.

Within the framework of the current research the above mention type of discriminant analysis

was used, in order to find out the type that minimized the classification error.

Multivariate One-Way Analysis of Variance (MANOVA)

Multivariate Analysis of Variance is a statistical test procedure, which is used to determine

multivariate means among several groups. It is closely related to Discriminant Analysis and

Classification [15].

The data in MANOVA may be considered as forming a matrix X in which the columns

correspond to a measured variable. X is an m-by-n matrix of data values, and each row is a

vector of measurements on n variables for a single observation. In order to compare

multivariate means of the columns of X grouped by group, MANOVA was performed. Group

is a grouping variable defined as a categorical variable. Two observations are in the same

group if they have the same value in the group array. The observations in each group

represent a sample from a distribution (population). The function MANOVA tests the null


hypothesis that the means of each group are the n-dimensional multivariate vector, and that

any difference observed in the sample X is due to random chance.

Steps of Classification

Step 1: Application of leave-one-out cross validation (LOOCV). For each experiment all

observations (N) of the watermelon were split into training and testing datasets. The training

dataset contains the known data (N-1 observations) on which the training of algorithm run

and a dataset of unknown data (1 observation) against which the model is tested.

Step 2: Application of principal component analysis (PCA) to reduce the data dimensions. The

number of principal component which was used in each classification was determined by trial

and error method in order to give the lower classification error.

Step 3: Application of mahalanobis discriminant analysis for classification purposes. The type

of discriminating function was selected by trial and error method.

Step 4: Application of multivariate one-way analysis of variance (MANOVA) to determine

whether the mean of a variable differs significantly among groups, using canonical variable

values. Each column in the matrix of canonical value is a linear combination of the mean-

centered original variables.

Step 5: Estimation of Classification Error.

The programming code for the implementation of the classification can be found in Appendix

F.

4.5. Correlation and Error Estimation based on Statistical

Analysis

In this part of research an effort is given in order to estimate error and correlation of the

watermelons according the ripening day, the weight and the pen. The statistics which are

arisen by the image processing of OCT imaging and by the ARI, have been also used for the

completion of this procedure.

Correlation

Correlation is a statistical technique that can show whether and how strongly pairs of

variables are related. The quantity R, called linear correlation coefficient, measures the


correlation. The value of R is range from -1 up to +1. The + sign represents positive linear

correlations, and the – sign represents negative linear correlations.

The mathematic formula for computing R is:

𝑅(𝑥, 𝑦) = 𝑐𝑜𝑜𝑜(𝑥,𝑦) =𝑐𝑜𝑜(𝑥, 𝑦)𝜎𝑥𝜎𝑦

=𝐸[(𝑥 − 𝜇𝑥)�𝑦 − 𝜇𝑦�]

𝜎𝑥𝜎𝑦

where E is the expected value operator, cov means covariance, and corr is a widely used

alternative notation for the correlation coefficient.

Positive correlation: If x and y have a strong positive linear correlation, r is close to +1. An r

value of exactly +1 indicates a perfect positive fit. Positive values indicate a relationship

between x and y variables such that as values for x increase, values for y also increase.

Negative correlation: If x and y have a strong negative linear correlation, r is close to -1. An r

value of exactly -1 indicates a perfect negative fit. Negative values indicate a relationship

between x and y such that as values for x increase, values for y decrease.

No correlation: If there is no linear correlation or a weak linear correlation, r is close to 0. A

value near zero means that there is a random, nonlinear relationship between the two

variables.

Steps of Percentage Error Estimation and Correlation

Step 1: Application of leave-one-out cross validation (LOOCV). For each experiment all

observations of the watermelon except one are used for training and the remaining

observation for testing.

Step 2: Application of principal component analysis (PCA) to reduce the data dimensions. The

number of principal component which was used in each classification was determined by trial

and error.

Step 3: Estimation of mean percentage error.

The formula for Mean Percentage Error is the following:

𝑀𝑀𝐸 =100%𝑜

× �𝑜𝑖 − 𝑜𝑖𝑜𝑖

𝑛

𝑖=1


where 𝑜𝑖represents the actual value of the quantity being forecast, 𝑜𝑖represents the forecast,

and n is the number of times for which the variable is forecast.

Step 4: Computation of correlation coefficient.

The programming code for the implementation of the correlation is given in Appendix G.

4.6. Manual versus Automatic Segmentation based on

Measurements of Region Properties

The question of this procedure is to find out whether manual or automatic segmentation is

adequate to distinguish the watermelon cells. If the comparisons of the segmentations have a

high proportion of similarities, implies that the automatic segmentation is functional, accurate

and reliable. A Matlab code was generated in order to contribute to the comparison of both

aforementioned segmentations. As referred in section 3.7, samples from both (undergraduate

and postgraduate research) experiments which used.

Initially, the measurement of the centroid of each region in the manual segmented image was

used as a reference point. Using this point, the corresponding centroid in the automatic

segmented image was found. Subsequently, both centroids were situated in the same

coordinates and the outline of each region in manual segmented image and the corresponding

outline of the automatic segmented image plotted in the same figure. In order to complete this

procedure the pixel values of the one region were deducted from the other corresponding

region.

Figure 4.3 and 4.4 show the resulting watershed from the manual (a) and automatic (b)

segmentation, which should be comparing.


Figure 4.3: (a) Watershed Transformation of Manual Segmented OCT Image of Watermelon, (b) Watershed Transformation of Automatic

Segmented OCT Image of Watermelon (postgraduate data).

Figure 4.4: (a) Watershed Transformation of Manual Segmented OCT Image of Watermelon, (b) Watershed Transformation of Automatic

Segmented OCT Image of Watermelon (undergraduate data).

The results of the statistical analysis can give an evaluation for the physical interpretation of

the watermelon properties.

5 Results

This Chapter demonstrates the results which obtained within the framework of the

completion of the image processing and the statistical analysis. It is necessary to interpret the

results in order to understand the actual meaning of the experiment and understand the

errors which yielded.

5.1. Regression Analysis Results

Regression analysis is performed and the polynomial model equation was computed in each

case of study. This statistical method gives the ability to predict the relationship among

variables.

At the first case of study, pen was used as an independent variable and age as a dependent

variable. The resulting polynomial approach for this model is a linear first order equation,

which represented as follows:

𝑝𝑜𝑜 = 0.026 × 𝑜𝑎𝑜 + 4.313

The coefficient of determination (R2) for this case was 0.010, which means that 1% of the total

variation in pen can be explained by linear relationship between pen and age. The other 99%

P a g e 45 Chapter 5: Results

in pen remains unexplained. Also, as seen in Figure 5.1 the regression line is away from the

points, so it is not able to explain the variation. Summarized this model is not predictable.

Figure 5.1: Regression Equation and Line for Pen versus Age.

The second case of study was performed regression analysis for pen and weight, the first was

independent variable and the latter was dependent variable. The resulting polynomial

approach for this model is a linear first order equation, which represented as following:

𝑝𝑜𝑜 = 0.546 × 𝑤𝑜𝑜𝑎ℎ𝑜 + 7.564

The coefficient of determination (R2) for this case was 0.130, which means that 13% of the

total variation in pen can be explained by linear relationship between pen and weight. The rest

87% in pen remains unexplained. Also, as seen in Figure 5.2 the regression line is away from

the points, so it is not able to explain the variation. Therefore, this model is not predictable

enough.


Figure 5.2: Regression Equation and Line for Pen versus Weight.

The latter case of study was also to predict regression curve and equation for age and weight,

the first was independent variable and the latter was dependent variable. The resulting

polynomial approach for this model is a linear first order equation, which represented as

following:

𝑜𝑎𝑜 = 1.207 × 𝑤𝑜𝑜𝑎ℎ𝑜 + 34.076

The coefficient of determination (R2) for this case was 0.042, which means that 4.2% of the

total variation in age can be explained by linear relationship between age and weight. The

other 95.8% in age remains unexplained. Also, as seen in Figure 5.3 the regression line is away

from the points, so it is not able to explain the variation. To sum up this model is not

predictable.


Figure 5.3: Regression Equation and Line for Age versus Weight.

The data values are scattered and there are no relationship among this data. In conclusion, it

is observable that regression analysis cannot estimate a predictable model for pen, age and

weight of watermelon.

5.2. Classification Results

Classification of the watermelon peel and flesh according the age, the weight and the pen,

performed, and the classification error are estimated. In each case, an effort is produced to

observe whether the statistical data which were obtained after the image processing can be

classify according the parameters which measured by ARI. The results of this procedure are

presented in the current section that aims to determine the statistical and physical

interpretation.

The classification algorithm was responsible to classify the observations among two groups,

above or below to 35, 5, 4 for age, pen and weight respectively. It is important to note that the

classification error should be at least below the 0.1. If it is close to zero (0), the predictable

observation classified to the correct group of the known data set.

5.2.1. Classification Results based on Watermelon Peel Statistical Data

The classification results obtained using manual OCT imaging of watermelon peel statistical

data, are shown in Table 5.1 and in Figure 5.4, 5.5 and 5.6.


Table 5.1: Classification error (OCT Imaging of Watermelon Peel).

Variable – Parameter Classification Error (%)

Age 24.324

Pen 43.243

Weight 27.027

Figure 5.4: Canonical Variables and Classification Error per Age (OCT

Imaging of Watermelon Peel).


Figure 5.5: Canonical Variables and Classification Error per Pen

(OCT Imaging of Watermelon Peel).

Figure 5.6: Canonical Variables and Classification Error per Weight (OCT

Imaging of Watermelon Peel).

It is observed that none of these parameters can be used to classify the new observation in the

correct data set, since the classification error in each case is higher than the limit of 10%.

Therefore, the OCT imaging of watermelon peel cannot used to predict the group which each

watermelon belongs.


5.2.2. Classification Results based on OCT Imaging of Watermelon Flesh

Statistical Data

The classification results obtained using OCT imaging of watermelon flesh statistical data, are

shown in Table 5. 2 and in Figure 5.7, 5.8 and 5.9.

Table 5.2: Classification error (OCT Imaging of Watermelon Flesh).


Age 22.222

Pen 22.222

Weight 22.222

Figure 5.7: Canonical Variables and Classification Error per Age (OCT

Imaging of Watermelon Flesh).


Figure 5.8: Canonical Variables and Classification Error per Pen (OCT


Figure 5.9: Canonical Variables and Classification Error per Weight (OCT


It is observed that none of these parameters can used to classify the new observation in the

correct data set, since the classification error is 22.222% in each case which is higher than the

limit of 10%. Therefore, the OCT imaging of watermelon flesh cannot be used to predict in


which group the watermelon belongs, thus, it is not possible to gain any information about the

properties of watermelon.

5.2.3. Classification Results based on Manual OCT Imaging of

Watermelon Flesh Statistical Data

The classification results obtained using manual OCT imaging of watermelon peel statistical

data, are shown in Table 5.3 and in Figure 5.10, 5.11 and 5.12.

Table 5.3: Classification error (Manual OCT Imaging of Watermelon Flesh).


Age 25.000

Pen 6.250

Weight 31.250

Figure 5.10: Canonical Variables and Classification Error per Age (Manual

OCT Imaging of Watermelon Flesh).


Figure 5.11: Canonical Variables and Classification Error per Pen (Manual

OCT Imaging of Watermelon).

Figure 5.12: Canonical Variables and Classification Error per Weight

(Manual OCT Imaging of Watermelon).

It is observed that the parameters age and weight cannot be used to classify the new

observation in the correct data set, since the classification error in each case is higher than the

limit of 10%. However, the parameter pen, as seen, can be used to predict the group in which

the watermelon belongs and thus determine its properties.


5.3. Correlation and Mean Percentage Error Estimation

Results

Correlation Coefficients and Mean Percentage Error of the watermelon peel and cells

according to the ripening day, the weight and the pen, are estimated. In each case of study, an

effort is effected to examine whether the parameters, which measured by ARI, are related with

the statistical data which were obtained after the image processing. The results of this

procedure are presented in the current section that aims to determine the statistical and

physical interpretation.

A mean percentage error should be at least below the 20 %. If it is approaching the zero (0),

then the experimental value is close enough to the targeted value. Additionally, a correlation

greater than 0.8 is generally described as strong, whereas a correlation less than 0.5 is

generally described as weak. A study utilizing scientific data requires a strong correlation. It is

not enough to have only a low mean percentage error, but a high correlation coefficient is

needed, so that these two statistical values are interrelated.

5.3.1. Correlation and Mean Percentage Error Estimation Result based

on OCT Imaging of Watermelon Peel Statistical Data

Once the procedure for the estimation of the correlation and the mean percentage error for

the statistical data of the OCT imaging of watermelon peel completed, the results obtained can

be found in this part of research (Table 5.4 and Figure 5.13, 5.14 and 5.15).

Table 5.4: Correlation and mean error estimation result (OCT Imaging of Watermelon Peel).

Variable – Parameter Mean Error (%) Correlation Coefficient

Age 14.301 -0.082

Pen 30.079 -0.0178

Weight 21.028 0.364


Figure 5.13: Correlation and MPE Estimation of Age (OCT Imaging of Watermelon Peel).

Figure 5.14: Correlation and MPE Estimation of Pen (OCT Imaging of Watermelon Peel).


Figure 5.15: Correlation and MPE Estimation of Weight (OCT Imaging of Watermelon Peel).

Based on the results obtained, it is observed that the only variable that presented mean

percentage error lower than 20% is the age. However this cannot be validated because the

correlation coefficient approaches zero (o), something which indicates that there is no

correlation among the variables. The variables pen and weight do not satisfy any of the

conditions mentioned above, so cannot be used as a way to identify the relation between them.

Summarized, these variables have weak correlation and a high percentage error, thus cannot

use the OCT imaging of the watermelon peel to provide any information about the physical

interpretation of the watermelon properties.


on OCT Imaging of Watermelon Statistical Data

Using OCT imaging of watermelon flesh statistical data, the results obtained are shown in

Table 5.5 and in Figure 5.16, 5.17 and 5.18.

Table 5.5: Correlation and mean percentage error estimation results (OCT Imaging of Watermelon

Cells).


Age 9.648 0.745


Pen 26.344 -0.039

Weight 21.136 0.389

Figure 5.16: Correlation and MPE Estimation of Age (OCT Imaging of Watermelon Cells).

Figure 5.17: Correlation and MPE Estimation of Pen (OCT Imaging of Watermelon Cells).


Figure 5.18: Correlation and MPE Estimation of Weight (OCT Imaging of Watermelon Cells).

Based on the results obtained, it is observed that the only variable that presented low mean

percentage error and a remarkable correlation coefficient is the age. The mean percentage

error for the variable age is below 10% (9.648%) and the correlation coefficient is around 0.8

(0.745), so the OCT imaging of the watermelon cells can be possibly used to predict the actual

age of watermelon. The variable pen and weight do not satisfy the necessary conditions, so are

considered that cannot predict or evaluate the watermelon properties. Summarized, it is

observable that the statistical data of OCT imaging of watermelon can be used to determine

the watermelon age.


on Manual OCT Imaging of Watermelon Statistical Data

Using manual OCT imaging of watermelon flesh statistical data, the results obtained are

shown in Table 5.6 and in Graph 5.19, 5.20 and 5.20.

Table 5.6: Correlation and mean percentage error estimation results (Manual OCT Imaging of

Watermelon Cells).


Age 12.115 0.570


Pen 30.861 -0.511

Weight 18.900 0.448

Figure 5.19: Correlation and MPE Estimation of Age (Manual OCT Imaging of Watermelon Cells).

Figure 5.20: Correlation and MPE Estimation of Pen (Manual OCT Imaging of Watermelon Cells).


Figure 5.21: Correlation and MPE Estimation of Weight (Manual OCT Imaging of Watermelon Cells).

Based on the results obtained, it is observed that the variable age, pen and weight cannot be

used to estimate the actual value of these properties for the watermelon. The correlation

coefficients are around 0.5, something that denote weak correlation among the variables. In

the case of age and weight, the mean percentage errors are remarkable, but the correlation

coefficient is lower than the essential conditions. Summarized, it is observable that the

statistical data of the manual OCT imaging of watermelon cannot be used to determine the

watermelon properties.

5.4. Automatic versus Manual Segmentation Results

In an attempt to evaluate the reliability of automatic and manual segmentation, a procedure

was performed, for comparison purposes. If the comparisons of the segmentations have a high

proportion of similarities, implies that is adequate to distinguish the watermelon cells by

manual and automatic manner and lead on reliable results.

Unfortunately, the results of this procedure were not the expected, since the proportion of

error was extremely high when the manual segmented cell subtracted from the automatic

segmented cell. Figure 5.22 can confirm that the automatic segmentation is not reliable to

segment the cells. Likewise Figure 5.23 can confirm that neither the automatic segmentation

of the old data can use to distinguish and segment the cells.


Figure 5.22: (a) Outlines of manual and automatic segmentation, (b) Subtraction of manual and automatic segment cell (new data)

Figure 5.23: (a) Outlines of manual and automatic segmentation, (b) Subtraction of manual and automatic segment cell (old data).

In conclusion, the results obtained from the completion of this research were not expected and

desired due to possible errors in the experiments or absence relations between the measurable

parameters of the watermelons. However, some of these results can lead in a logical conclusion

due to the low MPE and classification error.

6 Summary and Future Works

This Chapter consist a brief overview of this thesis and it suggests possible future work for the

optimization of this research.

6.1. Summary and Conclusions

The usage of the Optical Coherence Tomography, in conjunction with the developed

algorithms, for the purposes of this thesis aimed to optimize the quality and resolution of the

OCT imaging. Apart from this, an effort was given to interpret the physical characteristics

(estimation of age and pen) of the watermelons based on the cytological changes,

quantification of the watermelon peels and connective tissues. In case the research yielded the

expected and desired results, it would constitute a pioneer tool for the agriculturist and a step

towards the optimization of the OCT image.

The majority of the results obtained from the statistical analysis and classification do not lead

to desirable and reasonable conclusions. This was a result of errors during the experiments or

even due to the absences of relation between the samples of watermelons.

To sum up, it worth mentioning that the image processing and the statistical analysis yielded a

low mean percentage error (9,648%) and a high correlation coefficient (0,745) giving the


ability to predict the age of the watermelon. In addition, the manual segmentation of the cells

and the algorithms created are giving the possibility of classification since they had a low

classification error (6,250%).

6.2. Errors and Future Works

During the OCT imaging and the development of algorithms some issues came up which will

be important to be taking into consideration for the improvement of the algorithms and the

guarantee of more reliable and useful results.

The experimental process of OCT imaging gave back reflections and noise artifacts, due to

technical problems, which was the main issue during the image processing. A possible

solution is the technical improvement of the imaging and, maybe, the creation of additional

algorithms for the deduction of back reflections which had serious effect on the results of the

research.

In conclusion, additional research, development and improvement of the existing and also

new algorithms for the extraction of more information from the OCT images that would be

useful for the agriculturist. It worth mentioning that two additional characteristics have been

studied by this thesis in addition to the work performed during my undergraduate studies.

Bibliography

[1] Chen Yu, Bousie Evgenia, Pitris Constantinos, Fujimoto G. James. Optical Coherence Tomography:

Introduction and Theory

[2] Testoni Alberto Pier. “Optical Coherence Tomography”. The Scientific World Journal. Volume 7. pp.

87-108, January 2007.

[3] Walther Julia, Caertner, Cimalla Peter, Burkhardt Anke, Kirsten Lars, Meissner Sven, Koch Edmund.

“Optical Coherence Tomography in biomedical research”. Volume 400. pp. 2721-2743, May 2011.

[4] Podoleanu Gh. A. “Optical Coherence Tomography”, March 2012.

[5] Huang David, Swanson A. Eric, Lin P. Charles, Schuman S. Joel, Stinson G. William, Ghang Warren,

Hee R. Michael, Flotte Thomas, Gregory Kenton, Puliafito A. Carmen, Fujimoto G. James. “Optical

Coherence Tomography”. Science. Volume 254.

[6] Ali Murtaza, Parlapalli Renuka. “Signal Processing Overview of Optical Coherence Tomography

Systems for Medical Imaging”, June 2010.

[7] Kai Yu, Liang Ji, Lei Wang, Ping Xue. “How to optimize OCT image”. Volume 9. June 2001.

[8] McCabe M. James, Croce J. Kevin. “Optical Coherence Tomography”

[9] A F Fercher, W Drexler, C K Hitzenberger, T Lasser. “Optical Coherence Tomography – Principles

and Applications”, January 2003.

[10] Smith I. Lindsay. “A tutorial on Principal Components Analysis”, February 2002.

[11] M. Mudrova, A. Prochazka. “Principal Component Analysis in Image Processing”.

[12] Kartakoullis Andreas. “Spectral Analysis of Optical Coherence Tomography Signals”, May 2008.

[13] “Regression Analysis Tutorial”

[14] Kazlauskas Kazys. “The Burg Algorithm with the Exrapolation for Improving the Frequency

Estimation”, December 2010.

[15] French Aaron, Macedo Marcelo, Poulsen John, Waterson Tyler, Yu Angela. “Multivariate Analysis

of Variance (MANOVA)”

[16] Pitas Ioannis. “Digital Image Processing Algorithms and Applications”

[17] Gonzalez C. Rafael, Woods E. Richard, Eddins L. Steven. “Digital Image Processing Using Matlab”

[18] Kyriacou C. Marios, Soteriou Georgios, “Quality and Postharvest Performance of Watermelon Fruit

in response to grafting on interspecific cucurbit rootstocks ”. Journal of Food Quality, August 2014.

Appendices

Appendix A

clear; close all; clc; count=0; DoPlot=0; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Load Image Day=cellstr(['25072013';'29072013';'02082013';'05082013']); for i=1:size(Day) folders = dir(Day{i}); for j=1:size(folders) for ImNum=1:2; if size(folders(j).name, 2) > 2 FileName=sprintf('C:\\Users\\Maria\\Desktop\\New folder\\Watermelon OCT\\2013\\%s\\%s\\fl%d',Day{i},folders(j).name,1); FileName1=sprintf('C:\\Users\\Maria\\Desktop\\New folder\\Watermelon OCT\\2013\\%s\\%s\\fl%d',Day{i},folders(j).name,2); count=count+1; InterpFile='datainterp1000.mat'; DoLog=1; DoAbs=1; [IM h fs snr llim ulim] = OpenOCTFDImage(FileName,InterpFile,2,0,DoAbs,DoLog,0,1); DoLog=1; DoAbs=1; [IM1 h fs snr llim ulim] = OpenOCTFDImage(FileName1,InterpFile,2,0,DoAbs,DoLog,0,1); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Display OCT Image if DoPlot DisplayOCTFDImage(IM, h, llim, ulim, octcolor(256,0,'blue')); DisplayOCTFDImage(IM1, h, llim, ulim, octcolor(256,0,'blue')); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Normalize IM=IM-min(min(IM)); % Normalize between 0 and 1 IM=IM./max(max(IM)); IM1=IM1-min(min(IM1)); % Normalize between 0 and 1 IM1=IM1./max(max(IM1)); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Filter and convert to binary fIM=medfilt2(IM,[11 11]); % Filter the image cf=1.25; level = cf*graythresh(fIM); % Convert the image to binary BW = im2bw(fIM,level);

se=strel('disk',40); % Perform close to close gaps BW=imclose(BW,se); fIM1=medfilt2(IM1,[11 11]); % Filter the image cf=1.25; level = cf*graythresh(fIM1); % Convert the image to binary BW1 = im2bw(fIM1,level); se=strel('disk',40); % Perform close to close gaps BW1=imclose(BW1,se); if DoPlot figure; imagesc(BW); % Display the image axis xy; colormap(gray); figure; imagesc(BW1); % Display the image axis xy; title('Thresholded Image'); colormap(gray); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Find the front surface [m n]=size(IM); for q=20:n-20 temp=find(BW(:,q),1,'last'); y(q)=temp; sIM(:,q-19)=IM(y(q)-700:y(q)-150,q); %spectrum IM_nolog / Statistics log_abs end; [m n]=size(IM1); % Find the top surface for q=20:n-20 temp=find(BW1(:,q),1,'last'); y(q)=temp; sIM1(:,q-19)=IM1(y(q)-700:y(q)-150,q); %spectrum IM_nolog / Statistics log_abs end; if DoPlot figure; imagesc(sIM); colormap(gray); axis xy; figure; imagesc(sIM1); colormap(gray); axis xy; end; fprintf('%d\n',count); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Statistics [m n]=size(sIM); temp1=reshape(sIM,[m*n 1]); [m n]=size(sIM1); temp2=reshape(sIM1,[m*n 1]); temp=[temp1;temp2]; S(count,:)= pburg(temp, 4, 4096); S(count,1)=var(temp); S(count,2)=mean(temp); S(count,3)=median(temp); S(count,4)=std(temp); S(count,5)=kurtosis(temp); S(count,6)=skewness(temp); end; end; end; end;

Appendix B

clc; close all; clear; count=0; DoPlot=0; Day=cellstr(['02082013';'05082013';]);%'29072013';'02082013';'05082013'25072013]); for i=1:size(Day) folders = dir(Day{i}); for j=1:size(folders) for ImNum=1:8; if size(folders(j).name, 2) > 2 FileName=sprintf('C:\\Users\\Maria\\Desktop\\New folder\\Watermelon OCT\\2013\\jpegs\\%s\\%s\\im%d.jpg',Day{i},folders(j).name,ImNum); count=count+1; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Image Normalization I = imread(FileName); I = double(rgb2gray(I)); I = I(1:end-50,:); I = I-min(min(I)); I = I/max(max(I)); I=1-I; if DoPlot figure; subplot(2,2,1); imagesc(I);colormap(gray); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Conversion to Binary Image thr=graythresh(I); BW=im2bw(I,0.3*thr); se=strel('disk',3); BW = imopen(BW,se); if DoPlot subplot(2,2,2); imagesc(BW); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Dinstance Metric D = bwdist(~BW,'chessboard'); D(~BW) = -Inf; D = -D; if DoPlot subplot(2,2,3); imagesc(D); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Watershed Transformation L = watershed(D,8); if DoPlot subplot(2,2,4); imagesc(L); end; Lrgb = label2rgb(L, 'jet', 'w', 'shuffle'); if DoPlot figure; subplot(2,1,1); imagesc(I);colormap(gray); subplot(2,1,2);imagesc(Lrgb); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Statistics of the Segmented Image

NumOfRegions=max(max(L)); for q=1:NumOfRegions ind=find(L==q); A(q)=length(ind); end; S(count,:)= pburg(A, 4, 4096); S(count,1)=var(A); S(count,2)=mean(A); S(count,3)=median(A); S(count,4)=std(A); S(count,5)=kurtosis(A); S(count,6)=skewness(A); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% Statistics of the Intensity Image [m n]=size(I); temp=reshape(I,[m*n 1]); S(count,:)= pburg(temp, 4, 4096); S(count,1)=var(temp); S(count,2)=mean(temp); S(count,3)=median(temp); S(count,4)=std(temp); S(count,5)=kurtosis(temp); S(count,6)=skewness(temp); end; end; end; end;

Appendix C

clear; close all; clc; count=0; DoPlot=0; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Load Image Day=cellstr(['02082013';'05082013']);%;'29072013';'25072013';]); for i=1:size(Day) folders = dir(Day{i}); allNames = {folders.name}; Folders = folders(~strcmpi(allNames, 'Thumbs.db')); for j=1:size(Folders) for ImNum=1:8; if size(Folders(j).name, 2) > 2 FileName=sprintf('C:\\Users\\Maria\\Desktop\\New folder\\Watermelon OCT\\2013JPEG\\%s\\%s\\Image%d.jpg',Day{i},Folders(j).name,ImNum); count=count+1; IM=imread(FileName); [m n]= size(IM); cIM = imcrop(IM,[700 1000 3250 1400]); if DoPlot figure(); subplot(2,1,1); imagesc(cIM); title('OCT Image of Watermelon'); axis on; end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Convert to binary level = graythresh(cIM); BW = im2bw(cIM,level); if DoPlot subplot(2,1,2);imagesc(BW);colormap(gray); title('Binary OCT Image of Watermelon'); end; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Distance Metric D = bwdist(~BW,'chessboard'); D(~BW) = -Inf; D = -D; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Watershed based transformation L = watershed(-BW); % Perform watershed if DoPlot subplot(2,1,2); imagesc(L); title('Watershed-based Segmentation'); end; I=1-L; if DoPlot figure imagesc(I);colormap(gray); end; Lrgb = label2rgb(L, 'jet', 'w'); if DoPlot figure; subplot(2,1,1); imagesc(I);colormap(gray); subplot(2,1,2); imagesc(Lrgb); end;

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Get Statistics NumOfRegions=max(max(L)); % Calculate the area of each region for q=1:NumOfRegions ind=find(L==q); A(q)=length(ind); end; S(count,:)= pburg(A, 4, 4096); S(count,1)=var(A); S(count,2)=mean(A); S(count,3)=median(A); S(count,4)=std(A); S(count,5)=skewness(A); S(count,6)=kurtosis(A); end; end; end; end;

Appendix D

clc; close all; clear; %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % I= imread('OCTImage_02082013_003-01072013_Im1.jpg'); subplot (2,2,1); subimage(I); title('Manually Segment Image');colormap(gray);xlabel('(a)') BW=im2bw(I); f=bwlabel(BW); propiedArea=regionprops(f, 'Area'); area_values=[propiedArea.Area]; idx=find((800<= area_values)& (area_values <=200000)); h=ismember(f,idx); f=f.*h; subplot (2,2,2); subimage(f); title('Area Between 800 and 200000');xlabel('(b)') subplot (2,2,3);imagesc(f);colormap('jet');title('Centroid of each region'); xlabel('(c)') props=regionprops(f, 'Image','Centroid', 'MajorAxisLength', 'MinorAxisLength'); centers = props(4).Centroid; diameters = mean([props.MajorAxisLength props.MinorAxisLength],2); radii = (diameters+diameters)/2; centroids = cat(1, props.Centroid); hold on plot(centroids(:,1), centroids(:,2), 'b*') hold on viscircles(centers,radii); hold off subplot (2,2,4); subimage (props(4).Image);colormap('gray') title('Cell #4'); xlabel('(d)') %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% IM = imread('02082013_003-01072013_im1.jpg'); IM = double(rgb2gray(IM)); IM = IM(1:end-50,:); IM = IM-min(min(IM)); IM = IM/max(max(IM)); IM=1-IM; figure; subplot(2,2,1); imagesc(IM);colormap(gray);title('Original OCT Image'); thr=graythresh(IM); bw=im2bw(IM,0.3*thr); se=strel('disk',3); bw = imopen(bw,se); subplot(2,2,2); imagesc(bw); title('Binary Image'); D = bwdist(~bw,'chessboard'); D(~bw) = -Inf; D = -D; subplot(2,2,3); imagesc(D);title('Distance Metric'); L = watershed(D,8); subplot(2,2,4); imagesc(L);title('Watershed of Original OCT Image'); propsOCT=regionprops(L, 'Image','Centroid','MajorAxisLength','MinorAxisLength'); %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% DoPlot=1; count=0; [m1 n1]=size(I);

[mIM nIM]=size(IM); MC=m1/mIM; NC=n1/nIM; for p=2:4;%length(props) ManImage=props(p).Image; ind=props(p).Centroid; if ~isnan(ind), TheRegion=L(floor(ind(2)/MC),floor(ind(1)/NC)); else TheRegion=0; end; if TheRegion C=propsOCT(TheRegion).Centroid; C=round([C(2) C(1)]); count=count+1; OCTImage=propsOCT(TheRegion).Image; [m1 n1]=size(ManImage); [m2 n2]=size(OCTImage); OCTImage=imresize(OCTImage,[round(m2*MC) round(n2*NC)]); [m2 n2]=size(OCTImage); NewIm=zeros([max(m1,m2) max(n1,n2)]); [M N]=size(NewIm); dm=propsOCT(TheRegion).MajorAxisLength; dn=propsOCT(TheRegion).MajorAxisLength; % OCTSeg=IM(max(C(1)-dm,1):min(C(1)+dm,mIM),max(C(2)-dn,1):min(C(2)+dn,nIM)); if DoPlot NewIm(M/2-m1/2+1:M/2+m1/2,N/2-n1/2+1:N/2+n1/2)=edge(ManImage,'prewitt'); NewIm(M/2-m2/2+1:M/2+m2/2,N/2-n2/2+1:N/2+n2/2)=NewIm(M/2-m2/2+1:M/2+m2/2,N/2-n2/2+1:N/2+n2/2)+2*edge(OCTImage,'prewitt'); figure; subplot(1,2,1);imagesc(NewIm);title('Outlines of Manual and Automatic Segment Cell'); xlabel('(a)') NewIm=zeros([max(m1,m2) max(n1,n2)]); end; NewIm(M/2-m1/2+1:M/2+m1/2,N/2-n1/2+1:N/2+n1/2)=ManImage; NewIm(M/2-m2/2+1:M/2+m2/2,N/2-n2/2+1:N/2+n2/2)=NewIm(M/2-m2/2+1:M/2+m2/2,N/2-n2/2+1:N/2+n2/2)-OCTImage; NewIm=abs(NewIm); if DoPlot, subplot(1,2,2);imagesc(NewIm); title('Subtraction of Manual from Automatic Segment Cell'); xlabel('(b)') end; perc_err(count)=sum(sum(NewIm))/sum(sum(ManImage)); end; end; figure subplot (2,1,1); imagesc(f); colormap('jet'); title('Watershed of Manually Segmented Image');xlabel('(a)') subplot(2,1,2); imagesc(L);title('Watershed of Automatic Segmented Image');colormap('jet');;xlabel('(b)')

Appendix E

clear; close all; clc; data= xlsread('WatermelonEXP2013_correct.xlsx'); age= data(:,1); pen= data(:,2); weight= data(:,3); figure(1); p= polyfit(age,pen,1); f= polyval(p, age); plot(age, pen, 'bo', age, f, 'r'); title('Age Vs. Pen'); xlabel('Age'); ylabel('Pen'); mu= mean (pen); J= sum((f-pen).^2); S= sum((pen-mu).^2); R2= 1-J/S; text(26 , 3, sprintf('pen= %3.3f*age + %3.3f',p(1),p(2)), 'Color', 'k'); text(26 , 2.5, sprintf('R^2= %3.3f',R2), 'Color', 'k'); figure(2); p= polyfit(weight,pen,1); f= polyval(p, weight); plot(weight, pen, 'bo', weight, f, 'r'); title('Weight Vs. Pen'); xlabel('Weight'); ylabel('Pen'); mu= mean (pen); J= sum((f-pen).^2); S= sum((pen-mu).^2); R2= 1-J/S; text(2.15 , 3, sprintf('pen= %3.3f*weight + %3.3f',p(1),p(2)), 'Color', 'k'); text(2.15 , 2.5, sprintf('R^2= %3.3f',R2), 'Color', 'k'); figure(3); p= polyfit(weight,age,1); f= polyval(p, weight); plot(weight, age, 'bo', weight, f, 'r'); title('Weight Vs. Age'); xlabel('Weight'); ylabel('Age'); mu= mean (age); J= sum((f-age).^2); S= sum((age-mu).^2); R2= 1-J/S; text(2.15,30, sprintf('age= %3.3f*weight + %3.3f',p(1),p(2)), 'Color', 'k'); text(2.15,28, sprintf('R^2= %3.3f',R2), 'Color', 'k');

Appendix F

close all; clc; clear all; load Statistics.mat; A= [S]; load StatisticsSpectrum_Order4_Points4096.mat; A= [ A S]; data= xlsread('WatermelonEXP2013.xlsx'); age= data(:,1); S=A(:,:); [m n]= size(S); for q=1:8:m Snew(q,:)= (S(q,:)+S(q+1,:)+S(q+2,:)+S(q+3,:)+S(q+4,:)+S(q+5,:)+S(q+6,:)+S(q+7,:))/8; agenew(q,:)= (age(q,:)+age(q+1,:)+age(q+2,:)+age(q+3,:)+age(q+4,:)+age(q+5,:)+age(q+6,:)+age(q+7,:))/8; S_new=Snew(1:8:end,:); age_new=agenew(1:8:end,:); end; C=zeros(size(age_new)); C(find(age_new>35))=1; [m n]= size(S_new); for p=1:m Stest= S_new(p,:); Strain= S_new([1:p-1 p+1:m], :); Ptrain= age_new([1:p-1 p+1:m], :); Ctrain=C([1:p-1 p+1:m], :); coeff=pca(Strain(:,:)); Npca= [ 2 3 4 6]; PCdataTest= Stest*coeff(:,Npca); PCdataTrain= Strain*coeff(:,Npca); A= pinv(PCdataTrain)*Ptrain; Ptest(p,1)= PCdataTest*A; Ctest(p,1)=classify(PCdataTest, PCdataTrain, Ctrain, 'mahalanobis'); end; C_error = (length(find(abs(C-Ctest)))/length(Ctrain))*100; [D,P,stats] = manova1(PCdataTrain,Ctrain); c1 = stats.canon(:,1); c2 = stats.canon(:,2); figure; gscatter(c2,c1,Ctrain,[],'ox') legend('Age < 35','Age > 35'); text(-2,-2,sprintf('Err: %3.3f',C_error)); title('Classification Age (OCT Imaging of Watermelon)')

Appendix G

close all; clc; clear all; load Statistics.mat; A= [S]; load StatisticsSpectrum_Order4_Points4096.mat; A= [A S]; data= xlsread('WatermelonEXP2013.xlsx'); age= data(:,1); S=A(:,:); [m n]= size(S); for q=1:8:m Snew(q,:)= (S(q,:)+S(q+1,:)+S(q+2,:)+S(q+3,:)+S(q+4,:)+S(q+5,:)+S(q+6,:)+S(q+7,:))/8; agenew(q,:)= (age(q,:)+age(q+1,:)+age(q+2,:)+age(q+3,:)+age(q+4,:)+age(q+5,:)+age(q+6,:)+age(q+7,:))/8; S_new=Snew(1:8:end,:); age_new=agenew(1:8:end,:); end; C=zeros(size(age_new)); [m n]= size(S_new); for p=1:m Stest= S_new(p,:); Strain= S_new([1:p-1 p+1:m], :); Ptrain= age_new([1:p-1 p+1:m], :); Ctrain=C([1:p-1 p+1:m], :); coeff=princomp(Strain(:,:)); Npca=[1 2 3 5 6 7]; PCdataTest= Stest*coeff(:,Npca); PCdataTrain= Strain*coeff(:,Npca); A= pinv(PCdataTrain)*Ptrain; Ptest(p,1)= PCdataTest*A; end; P_error= mean((abs(Ptest-age_new)./age_new))*100; R=corrcoef(age_new,Ptest); R=R(1,2); plot(age_new,Ptest,'*'); axis([20 60 20 60]); hold on plot(20:60,20:60); hold off; text(25,25,sprintf('Err: %3.3f R: %3.3f',P_error,R)); title('Error Age (OCT Imaging of Watermelon Cells)');

Documents

DIGITAL IMAGE PROCESSING IN OPTICAL COHERENCE … Fiakkou.pdf · DIGITAL IMAGE PROCESSING IN . OPTICAL COHERENCE TOMOGRAPHY IMAGING . FOR THE EVALUATION OF WATERMELON PROPERTIES