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A
MINI PROJECT REPORT ON
IMAGE ENHANCEMENT FOR IMPROVING FACE DETECTION UNDER NON UNIFORM LIGHTING
CONDITIONS
Submitted in partial fulfillment for the award of the degree of
BACHELOR OF TECHNOLOGY
IN
ELECTRONICS AND COMMUNICATION ENGINEERING
By
N.NIKITHA (08601A0480) V.SUKUMAR (08601A04C0)
Under the esteemed guidance of
Mrs. P.SHRAVANI Asst. Professor
Department of Electronics and Communication Engineering
SSJ ENGINEERING COLLEGE(Affiliated to J.N.T.U Hyderabad)
2010-2011
SSJ ENGINEERING COLLEGE(Approved by A.I.C.T.E, Affiliated to J.N.T.U, Hyderabad)
Hyderabad-500075, A .P.
Department of Electronics and Communication Engineering
CERTIFICATE
This is certify that the Project entitled
“IMAGE ENHANCEMENT FOR IMPROVING FACE DETECTION UNDER NON UNIFORM LIGHTING CONDITIONS”
is a bonafide work done for the partial fulfillment for the award of Degree of Bachelor of Technology in Electronics and Communication Engineering from SSJ Engineering College affiliated to the Jawaharlal Nehru Technological University, Hyderabad during the academic year of 2011-2012. The results embodied in this project report have not been submitted to any University for the award of any degree.
By
N.NIKITHA (08601A0480)V.SUKUMAR (08601A04C0)
Internal Guide Head of the Department Mrs. P. SHRAVANI Mr. S.JAGADEESH Asst. Professor Associate Professor
External Examiner
2
ACKNOWLEDGMENT
My sincere thanks to Prof C. Ashok, principal, Sri Sai Jyothi engineering
college, v.n.pally, Rangareddy for providing this opportunity to carry out the present
academic seminar work.
I gratefully acknowledge Mr. S. Jagadeesh, professor and head of department
of ECE, for his encouragement and advice during the course of this work.
We sincerely thank our internal guide Mr. Naresh Kumar for giving us the
encouragement for the successful completion of project work and providing the
necessary facilities.
We are grateful to the VISION KREST EMBEDDEDTECHNOLOGIES,
for providing us an opportunity to carry out this project within the time.
I would like to express my thanks to all the faculty members, ECE, who have
rendered valuable pieces of advice in completion of academic seminar report.
BY
N.NIKITHA (08601A0480)
V.SUKUMAR(08601A04C0)
3
ABSTRACT
A robust and efficient image enhancement technique has been developed to
improve the visual quality of digital images that exhibit dark shadows due to the
limited dynamic ranges of imaging and display devices which are incapable of
handling high dynamic range scenes. The proposed technique processes images in
two separate steps: dynamic range compression and local contrast enhancement.
Dynamic range compression is a neighborhood dependent intensity
transformation which is able to enhance the luminance in dark shadows while keeping
the overall tonality consistent with that of the input image. The image visibility can
be largely and properly improved without creating unnatural rendition in this manner.
A neighborhood dependent local contrast enhancement method is used to enhance the
images contrast following the dynamic range compression. Experimental results on
the proposed image enhancement technique demonstrates strong capability to
improve the performance of convolution face finder compared to histogram
equalization and multiscale Retinex with color restoration without compromising the
false alarm rate.
4
CONTENTS
Chapters Page.No
1. INTRODUCTION 8
1.1 Introduction 8
1.2 Image processing 9
2. IMAGE PROCESSING
2.1 Introduction
2.2 Digital data
2.3 Data formats for digital satellite imagery
2.4 Image resolution
2.5 How to improve your image
2.6 Digital image processing
2.7 Pre-processing of the remotely sensed image
3. AERIAL IMAGERY
3.1 Uses of imagery
3.2 Types of aerial photography
3.3 Non linear image enhancement techniques
4. WAVELETS
4.1 Continuous wavelet transform
4.2 Discrete wavelet transform
4.3 Algorithm
5
4.4 Wavelet dynamic range compression and contrast
enhancement
5. RESULT ANALYSIS
5.1 Results
5.2 Conclusion
5.3 Future work
REFERENCES
APPENDIX
6
LIST OF FIGURES
Chapters
3. Aerial Imagery
3.1 Aerial imagery of the test building
4. Wavelets
4.1 Wavelets of CWT
4.2 Same transform rotated to 250 degrees looking from 45
degrees above
4.3 Cosine signals corresponding to various scales
4.4 Block diagram
4.5 DWT waveforms
LIST OF TABLES
Chapters
2. Image Processing
2.1 Elements of image interpretation
7
CHAPTER 1
INTRODUCTION
1.1 INTRODUCTION
Aerial images captured from aircrafts, spacecrafts, or satellites usually suffer
from lack of clarity, since the atmosphere enclosing Earth has effects upon the images
such as turbidity caused by haze, fog, clouds or heavy rain. The visibility of such
aerial images may decrease drastically and sometimes the conditions at which the
images are taken may only lead to near zero visibility even for the human eyes. Even
though human observers may not see much than smoke, there may exist useful
information in those images taken under such poor conditions. Captured images are
usually not the same as what we see in a real world scene, and are generally a poor
rendition of it.
High dynamic range of the real life scenes and the limited dynamic range of
imaging devices results in images with locally poor contrast. Human Visual System
(HVS) deals with the high dynamic range scenes by compressing the dynamic range
and adapting locally to each part of the scene. There are some exceptions such as
turbid (e.g. fog, heavy rain or snow) imaging conditions under which acquired images
and the direct observation possess a close parity .The extreme narrow dynamic range
of such scenes leads to extreme low contrast in the acquired images.
To deal with the problems caused by the limited dynamic range of the
imaging devices, many image processing algorithms have been developed .These
algorithms also provide contrast enhancement to some extent. Recently we have
developed a wavelet-based dynamic range compression (WDRC) algorithm to
improve the visual quality of digital images of high dynamic range scenes with non-
8
uniform lighting conditions .The WDRC algorithm is modified in by introducing an
histogram adjustment and non-linear color restoration process so that it provides color
constancy and deals with “pathological” scenes having very strong spectral
characteristics in a single band. The fast image enhancement algorithm which
provides dynamic range compression preserving the local contrast and tonal rendition
is a very good candidate in aerial imagery applications such as image interpretation
for defense and security tasks. This algorithm can further be applied to video
streaming for aviation safety. In this project application of the WDRC algorithm in
aerial imagery is presented. The results obtained from large variety of aerial images
show strong robustness and high image quality indicating promise for aerial imagery
during poor visibility flight conditions.
1.2 IMAGE PROCESSING
In electrical engineering and computer science, image processing is any form
of signal processing for which the input is an image, such as a photography or video
frame the output of image processing may be either an image or, a set of
characteristics or parameters related to the image. Most image-processing techniques
involve treating the image as a two-dimensional signal and applying standard signal-
processing techniques to it.
Image processing usually refers to digital image processing, but optical and
analog image processing also are possible. This article is about general techniques
that apply to all of them. The acquisition of images (producing the input image in the
first place) is referred to as imaging. Image processing is a physical process used to
convert an image signal into a physical image. The image signal can be either digital
or analog. The actual output itself can be an actual physical image or the
characteristics of an image. The most common type of image processing is
photography. In this process, an image is captured using a camera to create a digital
9
or analog image. In order to produce a physical picture, the image is processed using
the appropriate technology based on the input source type.
In digital photography, the image is stored as a computer file. This file is
translated using photographic software to generate an actual image. The colors,
shading, and nuances are all captured at the time the photograph is taken the software
translates this information into an image.
Euclidean geometry transformations such as enlargement, reduction, and
rotation.
Color corrections such as brightness and contrast adjustments, color mapping,
color balancing, quantization, or color translation to a different color space.
Digital compositing or optical compositing (combination of two or more
images), which is used in film-making to make a "matte".
Interpolation, demosaicing, and recovery of a full image from a raw image
format using a Bayer filter pattern.
Image registration, the alignment of two or more images.
Image differencing and morphing.
Image recognition, for example, may extract the text from the image using
optical character recognition or checkbox and bubble values using optical
mark recognition.
Image segmentation.
High dynamic range imaging by combining multiple images.
Geometric hashing for 2-D object recognition with affine invariance.
1.2.1 DIGITAL IMAGE PROCESSING
Digital image processing is the use of computer algorithms to perform image
processing on digital images. As a subcategory or field of digital signal processing,
digital image processing has many advantages over analog image processing. It
10
allows a much wider range of algorithms to be applied to the input data and can avoid
problems such as the build-up of noise and signal distortion during processing. Since
images are defined over two dimensions (perhaps more) digital image processing may
be modeled in the form of Multidimensional Systems.
Many of the techniques of digital image processing, or digital picture
processing as it often was called, were developed in the 1960s at the Jet Propulsion
Laboratory, Massachusetts Institute of Technology, Bell Laboratories, University of
Maryland, and a few other research facilities, with application to satellite imagery,
wire-photo standards conversion, medical imaging, videophone, character
recognition, and photograph enhancement. The cost of processing was fairly high,
however, with the computing equipment of that era. That changed in the 1970s, when
digital image processing proliferated as cheaper computers and dedicated hardware
became available. Images then could be processed in real time, for some dedicated
problems such as television standards conversion. As general-purpose computers
became faster, they started to take over the role of dedicated hardware for all but the
most specialized and computer-intensive operations.
With the fast computers and signal processors available in the 2000s, digital
image processing has become the most common form of image processing and
generally, is used because it is not only the most versatile method, but also the
cheapest. Digital image processing technology for medical applications was inducted
into the Space Foundation Space Technology Hall of Fame in 1994. Digital
image processing allows the use of much more complex algorithms for image
processing, and hence, can offer both more sophisticated performance at simple tasks,
and the implementation of methods which would be impossible by analog means.In
particular, digital image processing is the only practical technology for:
Classification
Feature extraction
Pattern recognition
11
Projection
Multi-scale signal analysis
Some techniques which are used in digital image processing include:
Pixelization
Linear filtering
Principal components analysis
Independent component analysis
Hidden Markov models
Anisotropic diffusion
Partial differential equations
Self-organizing maps
Neural networks
Wavelets
12
CHAPTER 2
IMAGE PROCESSING
2.1INTRODUCTION
Image Processing and Analysis can be defined as the "act of examining
images for the purpose of identifying objects and judging their significance" Image
analyst study the remotely sensed data and attempt through logical process in
detecting, identifying, classifying, measuring and evaluating the significance of
physical and cultural objects, their patterns and spatial relationship.
2.2 DIGITAL DATA
In a most generalized way, a digital image is an array of numbers depicting
spatial distribution of a certain field parameters (such as reflectivity of EM radiation,
emissivity, temperature or some geophysical or topographical elevation. Digital
image consists of discrete picture elements called pixels. Associated with each pixel
is a number represented as DN (Digital Number), that depicts the average radiance of
relatively small area within a scene. The range of DN values being normally 0 to 255.
The size of this area effects the reproduction of details within the scene. As the pixel
size is reduced more scene detail is preserved in digital representation.
Remote sensing images are recorded in digital forms and then processed by
the computers to produce images for interpretation purposes. Images are available in
two forms - photographic film form and digital form. Variations in the scene
characteristics are represented as variations in brightness on photographic films. A
particular part of scene reflecting more energy will appear bright while a different
part of the same scene that reflecting less energy will appear black. Digital image
consists of discrete picture elements called pixels. Associated with each pixel is a
13
number represented as DN (Digital Number) that depicts the average radiance of
relatively small area within a scene. The size of this area effects the reproduction of
details within the scene. As the pixel size is reduced more scene detail is preserved in
digital representation.
2.3 DATA FORMATS FOR DIGITAL SATELITTE
IMAGERY
Digital data from the various satellite systems supplied to the user in the form of
computer readable tapes or CD-ROM. As no worldwide standard for the storage and
transfer of remotely sensed data has been agreed upon, though the CEOS (Committee
on Earth Observation Satellites) format is becoming accepted as the standard. Digital
remote sensing data are often organised using one of the three common formats used
to organise image data. For an instance an image consisting of four spectral channels,
which can be visualized as four superimposed images, with corresponding pixels in
one band registering exactly to those in the other bands. These common formats are:
Band Interleaved by Pixel (BIP)
Band Interleaved by Line (BIL)
Band Sequential (BQ)
Digital image analysis is usually conducted using Raster data structures - each
image is treated as an array of values. It offers advantages for manipulation of pixel
values by image processing system, as it is easy to find and locate pixels and their
values. Disadvantages becomes apparent when one needs to represent the array of
pixels as discrete patches or regions, where as Vector data structures uses polygonal
patches and their boundaries as fundamental units for analysis and manipulation.
Though vector format is not appropriate to for digital analysis of remotely sense data.
14
2.4 IMAGE RESOLUTION
Resolution can be defined as "the ability of an imaging system to record fine
details in a distinguishable manner". A working knowledge of resolution is essential
for understanding both practical and conceptual details of remote sensing. Along with
the actual positioning of spectral bands, they are of paramount importance in
determining the suitability of remotely sensed data for a given applications. The
major characteristics of imaging remote sensing instrument operating in the visible
and infrared spectral region are described in terms as follow:
Spectral resolution
Radiometric resolution
Spatial resolution
Temporal resolution
2.4.1 Spectral Resolution refers to the width of the spectral bands. As different
material on the earth surface exhibit different spectral reflectances and emissivities.
These spectral characteristics define the spectral position and spectral sensitivity in
order to distinguish materials. There is a tradeoff between spectral resolution and
signal to noise. The use of well -chosen and sufficiently numerous spectral bands is a
necessity, therefore, if different targets are to be successfully identified on remotely
sensed images.
2.4.2 Radiometric Resolution or radiometric sensitivity refers to the number of
digital levels used to express the data collected by the sensor. It is commonly
expressed as the number of bits (binary digits) needs to store the maximum level. For
example Landsat TM data are quantised to 256 levels (equivalent to 8 bits). Here also
there is a tradeoff between radiometric resolution and signal to noise. There is no
point in having a step size less than the noise level in the data. A low-quality
instrument with a high noise level would necessarily, therefore, have a lower
15
radiometric resolution compared with a high-quality, high signal-to-noise-ratio
instrument.
2.4.3 Spatial Resolution of an imaging system is defines through various
criteria, the geometric properties of the imaging system, the ability to distinguish
between point targets, the ability to measure the periodicity of repetitive targets
ability to measure the spectral properties of small targets.
The most commonly quoted quantity is the instantaneous field of view
(IFOV), which is the angle subtended by the geometrical projection of single detector
element to the Earth's surface. It may also be given as the distance, D measured along
the ground, in which case, IFOV is clearly dependent on sensor height, from the
relation: D = hb, where h is the height and b is the angular IFOV in radians. An
alternative measure of the IFOV is based on the PSF, e.g., the width of the PDF at
half its maximum value.
A problem with IFOV definition, however, is that it is a purely geometric
definition and does not take into account spectral properties of the target. The
effective resolution element (ERE) has been defined as "the size of an area for which
a single radiance value can be assigned with reasonable assurance that the response is
within 5% of the value representing the actual relative radiance". Being based on
actual image data, this quantity may be more useful in some situations than the IFOV.
Other methods of defining the spatial resolving power of a sensor are based on the
ability of the device to distinguish between specified targets. Of the concerns the ratio
of the modulation of the image to that of the real target. Modulation, M, is defined as:
M = Emax -Emin / Emax + Emin
Where Emax and Emin are the maximum and minimum radiance values recorded
over the image.
16
2.4.4 Temporal Resolution refers to the frequency with which images of a given
geographic location can be acquired. Satellites not only offer the best chances of
frequent data coverage but also of regular coverage. The temporal resolution is
determined by orbital characteristics and swath width, the width of the imaged area.
Swath width is given by 2tan(FOV/2) where h is the altitude of the sensor, and FOV
is the angular field of view of the sensor.
2.5 How to Improve Your Image?
Analysis of remotely sensed data is done using various image processing techniques
and methods that includes:
Analog image processing
Digital image processing.
2.5.1 Visual or Analog processing techniques is applied to hard copy data
such as photographs or printouts. Image analysis in visual techniques adopts certain
elements of interpretation, which are as follow:
The use of these fundamental elements of depends not only on the area being
studied, but the knowledge of the analyst has of the study area. For example the
texture of an object is also very useful in distinguishing objects that may appear the
same if the judging solely on tone (i.e., water and tree canopy, may have the same
mean brightness values, but their texture is much different. Association is a very
powerful image analysis tool when coupled with the general knowledge of the site.
Thus we are adept at applying collateral data and personal knowledge to the task of
image processing. With the combination of multi-concept of examining remotely
sensed data in multispectral, multitemporal, multiscales and in conjunction with
multidisciplinary, allows us to make a verdict not only as to what an object is but also
its importance. Apart from this analog image processing techniques also includes
optical photogrammetric techniques allowing for precise measurement of the height,
width, location, etc. of an object.
17
Digital Image Processing is a collection of techniques for the manipulation of
digital images by computers. The raw data received from the imaging sensors on the
satellite platforms contains flaws and deficiencies. To overcome these flaws and
deficiencies inorder to get the originality of the data, it needs to undergo several steps
of processing. This will vary from image to image depending on the type of image
format, initial condition of the image and the information of interest and the
composition of the image scene.
TABLE: 2.1 ELEMENTS OF IMAGE INTERPRETATION
Elements of Image Interpretation
Primary Elements
Black and White Tone
Color
Stereoscopic Parallax
Spatial Arrangement of Tone
& Color
Size
Shape
Texture
Pattern
Based on Analysis of Primary
Elements
Height
Shadow
Contextual Elements Site
Association
2.6 Digital Image Processing undergoes three general steps:
Pre-processing
Display and enhancement
Information extraction
18
2.6.1 Pre-processing consists of those operations that prepare data for subsequent
analysis that attempts to correct or compensate for systematic errors. The digital
imageries are subjected to several corrections such as geometric, radiometric and
atmospheric, though all these correction might not be necessarily be applied in all
cases. These errors are systematic and can be removed before they reach the user. The
investigator should decide which pre-processing techniques are relevant on the basis
of the nature of the information to be extracted from remotely sensed data. After pre-
processing is complete, the analyst may use feature extraction to reduce the
dimensionality of the data. Thus feature extraction is the process of isolating the most
useful components of the data for further study while discarding the less useful
aspects (errors, noise etc). Feature extraction reduces the number of variables that
must be examined, thereby saving time and resources.
2.6.2 Image Enhancement operations are carried out to improve the
interpretability of the image by increasing apparent contrast among various features
in the scene. The enhancement techniques depend upon two factors mainly
The digital data (i.e. with spectral bands and resolution)
The objectives of interpretation
As an image enhancement technique often drastically alters the original
numeric data, it is normally used only for visual (manual) interpretation and not for
further numeric analysis. Common enhancements include image reduction, image
rectification, image magnification, transect extraction, contrast adjustments, band
ratioing, spatial filtering, Fourier transformations, principal component analysis and
texture transformation.
2.6.3 Information Extraction is the last step toward the final output of the
image analysis. After pre-processing and image enhancement the remotely sensed
data is subjected to quantitative analysis to assign individual pixels to specific classes.
Classification of the image is based on the known and unknown identity to classify
19
the remainder of the image consisting of those pixels of unknown identity. After
classification is complete, it is necessary to evaluate its accuracy by comparing the
categories on the classified images with the areas of known identity on the ground.
The final result of the analysis consists of maps (or images), data and a report. These
three components of the result provide the user with full information concerning the
source data, the method of analysis and the outcome and its reliability.
2.7 Pre-Processing of the Remotely Sensed Images
When remotely sensed data is received from the imaging sensors on the satellite
platforms it contains flaws and deficiencies. Pre-processing refers to those operations
that are preliminary to the main analysis. Preprocessing includes a wide range of
operations from the very simple to extremes of abstractness and complexity. These
categorized as follow:
1. Feature Extraction
2. Radiometric Corrections
3. Geometric Corrections
4. Atmospheric Correction
The techniques involved in removal of unwanted and distracting elements
such as image/system noise, atmospheric interference and sensor motion from an
image data occurred due to limitations in the sensing of signal digitization, or data
recording or transmission process. Removal of these effects from the digital data are
said to be "restored" to their correct or original condition, although we can, of course
never know what are the correct values might be and must always remember that
attempts to correct data what may themselves introduce errors. Thus image
restoration includes the efforts to correct for both radiometric and geometric errors.
2.7.1 Feature Extraction
Feature Extraction does not mean geographical features visible on the image
but rather "statistical" characteristics of image data like individual bands or
20
combination of band values that carry information concerning systematic variation
within the scene. Thus in a multispectral data it helps in portraying the necessity
elements of the image. It also reduces the number of spectral bands that has to be
analyzed. After the feature extraction is complete the analyst can work with the
desired channels or bands, but in turn the individual bandwidths are more potent for
information. Finally such a pre-processing increases the speed and reduces the cost of
analysis.
2.7.2 Radiometric corrections
Radiometric Corrections are carried out when an image data is recorded by the
sensors they contain errors in the measured brightness values of the pixels. These
errors are referred as radiometric errors and can result from the
1. Instruments used to record the data
2. From the effect of the atmosphere
Radiometric processing influences the brightness values of an image to correct
for sensor malfunctions or to adjust the values to compensate for atmospheric
degradation. Radiometric distortion can be of two types:
1. The relative distribution of brightness over an image in a given band can be
different to that in the ground scene.
2. The relative brightness of a single pixel from band to band can be distorted
compared with spectral reflectance character of the corresponding region on
the ground.
21
CHAPTER 3
AERIAL IMAGERY
Aerial imagery can expose a great deal about soil and crop conditions. The
“Birds eye” view an aerial image provides, combined with field knowledge, allows
growers to observe issues that affect yield. Our imagery technology enhances the
ability to be proactive and recognize a Problematic area, thus minimizing yield loss
and limiting exposure to other areas of your field. Hemisphere GPS Imagery uses
infrared technology to help you see the big picture to identify these everyday issues.
Digital infrared sensors are very sensitive to subtle differences in plant health and
growth rate. Anything that changes the appearance of leaves (such as curling, wilting,
and defoliation) has an effect on the image. Computer enhancement makes these
Variations within the canopy stand out, often indicating disease, water, weed, or
fertility problems.
Because of Hemisphere GPS technology, aerial imagery is over 30 times more
detailed than any commercially available satellite imagery and is available in selected
areas for the 2010 growing season. Images can be taken on a scheduled or as needed
basis. Aerial images provide a snapshot of the crop condition. The example on the
right shows healthy crop conditions in red and less than healthy conditions in green.
These snapshots of crop variations can then be turned into variable rate prescription
maps (PMaps), which is shown on the right Imagery can be used to identify crop
stress over a period of time. In the images to the left, the
Problem areas identified with yellow arrows show potential plant damage (e.g.
disease, insects, etc.).
Aerial images, however, store information about the electro-magnetic radiance
of the complete scene in almost continuous form. Therefore they support the
localization of break lines and linear or spatial objects. The Map Mart Aerial Image
Library covers all of the continental United States as well as a growing number of
International locations. The aerial imagery ranges in date from 1926 to the present
22
day depending upon the location. Imagery can be requested and ordered by selecting
an area on an interactive map or larger areas, such as cities or counties can be
purchased in bundles. Many of the current digital datasets are available for download
within a few minutes of purchase.
Aerial image measurement includes non-linear, 3-dimensional, and materials
effects on imaging. Aerial image measurement excludes the processing effects of
printing and etching on the wafer. The successful application of aerial image
emulation for CDU measurement traditionally, aerial image metrology systems are
used to evaluate defect printability and repair success.
Figure:3.1 Areal image of the test the building
Whereas, digital aerial imagery should remain in the public domain and be archived
to secure its availability for future scientific, legal, and historical purposes.
Aerial photography is the taking of photographs of the ground from an elevated
position. The term usually refers to images in which the camera is not supported by a
ground-based structure. Cameras may be hand held or mounted, and photographs may
be taken by a photographer, triggered remotely or triggered automatically. Platforms
23
for aerial photography include fixed-wing aircraft, helicopters, balloons, blimps and
dirigibles, rockets, kites, poles, parachutes, vehicle mounted poles . Aerial
photography should not be confused with Air-to-Air Photography, when aircraft serve
both as a photo platform and subject.
3.1 USES OF IMAGERY:
Aerial photography is used in cartography (particularly in photogrammetric
surveys, which are often the basis for topographic maps), land-use planning,
archaeology, movie production, environmental studies, surveillance, commercial
advertising, conveyancing, and artistic projects. In the United States, aerial
photographs are used in many Phase I Environmental Site Assessments for property
analysis. Aerial photos are often processed using GIS software.
3.1.1 Radio-controlled aircraft
Advances in radio controlled models have made it possible for model
aircraft to conduct low-altitude aerial photography. This has benefited real-estate
advertising, where commercial and residential properties are the photographic
subject. Full-size, manned aircraft are prohibited from low flights above populated
locations.[3] Small scale model aircraft offer increased photographic access to these
previously restricted areas. Miniature vehicles do not replace full size aircraft, as full
size aircraft are capable of longer flight times, higher altitudes, and greater equipment
payloads. They are, however, useful in any situation in which a full-scale aircraft
would be dangerous to operate. Examples would include the inspection of
transformers atop power transmission lines and slow, low-level flight over
agricultural fields, both of which can be accomplished by a large-scale radio
controlled helicopter. Professional-grade, gyroscopically stabilized camera platforms
are available for use under such a model; a large model helicopter with a 26cc
gasoline engine can hoist a payload of approximately seven kilograms (15 lbs).
24
Recent (2006) FAA regulations grounding all commercial RC model flights
have been upgraded to require formal FAA certification before permission to fly at
any altitude in USA. Because anything capable of being viewed from a public space
is considered outside the realm of privacy in the United States, aerial photography
may legally document features and occurrences on private property.
3.2 TYPES OF AERIAL PHOTOGRAPH
3.2.1 Oblique photographs
Photographs taken at an angle are called oblique photographs. If they are
taken almost straight down are sometimes called low oblique and photographs taken
from a shallow angle are called high oblique.
3.2.2 Vertical photographs
Vertical photographs are taken straight down. They are mainly used in
photogrammetric and image interpretation. Pictures that will be used in
photogrammetric was traditionally taken with special large format cameras with
calibrated and documented geometric properties.
3.2.3 Combinations
Aerial photographs are often combined. Depending on their purpose it can be
done in several ways. A few are listed below.
Several photographs can be taken with one handheld camera to later be
stitched together to a panorama.
In pictometry five rigidly mounted cameras provide one vertical and four low
oblique pictures that can be used together.
25
In some digital cameras for aerial photogrammetric photographs from several
imaging elements, sometimes with separate lenses, are geometrically
corrected and combined to one photograph in the camera.
3.2.4 Orthophotos
Vertical photographs are often used to create orthophotos, photographs which
have been geometrically "corrected" so as to be usable as a map. In other words, an
orthophoto is a simulation of a photograph taken from an infinite distance, looking
straight down from nadir. Perspective must obviously be removed, but variations in
terrain should also be corrected for. Multiple geometric transformations are applied to
the image, depending on the perspective and terrain corrections required on a
particular part of the image. Orthophotos are commonly used in geographic
information systems, such as are used by mapping agencies (e.g. Ordnance Survey) to
create maps. Once the images have been aligned, or 'registered', with known real-
world coordinates, they can be widely deployed.
Large sets of orthophotos, typically derived from multiple sources and divided
into "tiles" (each typically 256 x 256 pixels in size), are widely used in online map
systems such as Google Maps. Open Street Map offers the use of similar orthophotos
for deriving new map data. Google Earth overlays orthophotos or satellite imagery
onto a digital elevation model to simulate 3D landscapes.
3.2.5 Aerial video
With advancements in video technology, aerial video is becoming more
popular. Orthogonal video is shot from aircraft mapping pipelines, crop fields, and
26
other points of interest. Using GPS, video may be embedded with meta data and later
synced with a video mapping program.
This ‘Spatial Multimedia’ is the timely union of digital media including
still photography, motion video, stereo, panoramic imagery sets, immersive media
constructs, audio, and other data with location and date-time information from the
GPS and other location designs. Aerial videos are emerging Spatial Multimedia
which can be used for scene understanding and object tracking. The input video is
captured by low flying aerial platforms and typically consists of strong parallax from
non-ground-plane structures. The integration of digital video, global positioning
systems (GPS) and automated image processing will improve the accuracy and cost-
effectiveness of data collection and reduction. Several different aerial platforms are
under investigation for the data collection
3.3 NON-LINEAR IMAGE ENHANCEMENT
TECHNIQUE
We propose a non-linear image enhancement method, which allows selective
enhancement based on the contrast sensitivity function of the human visual system.
We also proposed. An evaluation method for measuring the performance of the
algorithm and for comparing it with existing approaches. The selective enhancement
of the proposed approach is especially suitable for digital television applications to
improve the perceived visual quality of the images when the source image contains
less satisfactory amount of high frequencies due to various reasons, including
interpolation that is used to convert standard definition sources into high-definition
images. Non-linear processing can presumably generate new frequency components
and thus it is attractive in some applications.
27
3.3.1 PROPOSED ENHANCEMENT METHOD
3.3.1.1 Basic Strategy
The basic strategy of the proposed approach shares the same principle of the
methods that is, assuming that the input image is denoted by I, then the enhanced
image O is obtained by the following processing
O = I + NL(HP( I ))
where HP() stands for high-pass filtering and NL() is a nonlinear operator. As will
become clear in subsequent sections, the non-linear processing includes a scale step
and a clipping step. The HP() step is based on a set of Gabor filters.
The performance of a perceptual image enhancement algorithm is typically
judged through a subjective test. In most current work in the literature, such as this
subjective test is simplified to simply showing an enhancement image along with the
original to a viewer. While a viewer may report that a blurry image is indeed
enhanced, this approach does not allow systematic comparison between two
competing methods.
Furthermore, since the ideal goal of enhancement is to make up the high-
frequency components that are lost in the imaging or other processes, it would be
desired to show whether an enhancement algorithm indeed generates the desired high
frequency components. The tests in do not answer this question. (Note that, although
showing the Fourier transform of the enhanced image may illustrate whether high-
frequency components are added this is not an accurate evaluation of a method, due
to the fact that the Fourier transform provides only a global measure of the signal
spectrum. For example, disturbing ringing artifacts may appear as false high-
frequency components in the Fourier transform.
28
CHAPTER 4
WAVELETS
Wavelet is a waveform of effectively limited duration that has an average
value of zero. The Wavelet transform is a transform of this type. It provides the time-
frequency representation. (There are other transforms which give this information too,
such as short time Fourier transforms, Wigner distributions, etc.)
Often times a particular spectral component occurring at any instant can be
of particular interest. In these cases it may be very beneficial to know the time
intervals these particular spectral components occur. For example, in EEGs, the
latency of an event-related potential is of particular interest (Event-related potential is
the response of the brain to a specific stimulus like flash-light, the latency of this
response is the amount of time elapsed between the onset of the stimulus and the
response). Wavelet transform is capable of providing the time and frequency
information simultaneously, hence giving a time-frequency representation of the
signal.
How wavelet transform works is completely a different fun story, and should
be explained after short time Fourier Transform (STFT). The WT was developed
as an alternative to the STFT. The STFT will be explained in great detail in the
second part of this tutorial. It suffices at this time to say that the WT was developed to
overcome some resolution related problems of the STFT, as explained in Part II.
To make a real long story short, we pass the time-domain signal from various
high pass and low pass filter, which filters out either high frequency or low frequency
portions of the signal. This procedure is repeated, every time some portion of the
signal corresponding to some frequencies being removed from the signal.
29
Here is how this works: Suppose we have a signal which has frequencies up to
1000 Hz. In the first stage we split up the signal in to two parts by passing the signal
from a high pass and a low pass filter (filters should satisfy some certain conditions,
so-called admissibility condition) which results in two different versions of the same
signal: portion of the signal corresponding to 0-500 Hz (low pass portion), and 500-
1000 Hz (high pass portion). Then, we take either portion (usually low pass portion)
or both, and do the same thing again. This operation is called decomposition.
Assuming that we have taken the low pass portion, we now have 3 sets of data, each
corresponding to the same signal at frequencies 0-250 Hz, 250-500 Hz, 500-1000 Hz.
Then we take the low pass portion again and pass it through low and high
pass filters; we now have 4 sets of signals corresponding to 0-125 Hz, 125-250 Hz,
250-500 Hz, and 500-1000 Hz. We continue like this until we have decomposed the
signal to a pre-defined certain level. Then we have a bunch of signals, which actually
represent the same signal, but all corresponding to different frequency bands. We
know which signal corresponds to which frequency band, and if we put all of them
together and plot them on a 3-D graph, we will have time in one axis, frequency in
the second and amplitude in the third axis. This will show us which frequencies exist
at which time ( there is an issue, called "uncertainty principle", which states that, we
cannot exactly know what frequency exists at what time instance , but we can only
know what frequency bands exist at what time intervals , more about this in the
subsequent parts of this tutorial).
Higher frequencies are better resolved in time, and lower frequencies are
better resolved in frequency. This means that, a certain high frequency component
can be located better in time (with less relative error) than a low frequency
component. On the contrary, a low frequency component can be located better in
frequency compared to high frequency component.
Take a look at the following grid:
30
f ^
|******************************************* continuous
|* * * * * * * * * * * * * * * wavelet transform
|* * * * * * *
|* * * *
|* *
--------------------------------------------> time
Interpret the above grid as follows: The top row shows that at higher
frequencies we have more samples corresponding to smaller intervals of time. In
other words, higher frequencies can be resolved better in time. The bottom row
however, corresponds to low frequencies, and there are less number of points to
characterize the signal, therefore, low frequencies are not resolved well in time.
^frequency
|
|
|
| *******************************************************
|
| * * * * * * * * * * * * * * * * * * * discrete time
| wavelet transform
| * * * * * * * * * *
|
| * * * * *
| * * *
|----------------------------------------------------------> time
In discrete time case, the time resolution of the signal works the same as
above, but now, the frequency information has different resolutions at every stage
too. Note that, lower frequencies are better resolved in frequency, where as higher
31
frequencies are not. Note how the spacing between subsequent frequency components
increase as frequency increases.
Below, are some examples of continuous wavelet transform:
Let's take a sinusoidal signal, which has two different frequency
components at two different times: Note the low frequency portion first, and then the
high frequency.
Figure 4.1 WAVEFORM OF CWT
Note however, the frequency axis in these plots are labeled as scale. The
concept of the scale will be made clearer in the subsequent sections, but it should be
noted at this time that the scale is inverse of frequency. That is, high scales
correspond to low frequencies, and low scales correspond to high frequencies.
Consequently, the little peak in the plot corresponds to the high frequency
components in the signal, and the large peak corresponds to low frequency
components (which appear before the high frequency components in time) in the
signal.
32
The continuous wavelet transform of the above signal
Figure 4.2 SAME TRANSFORM ROTATED-250 DEGREES,LOOKING
FROM 45 DEG ABOVE
You might be puzzled from the frequency resolution shown in the plot,
since it shows good frequency resolution at high frequencies. Note however that, it is
the good scale resolution that looks good at high frequencies (low scales), and good
scale resolution means poor frequency resolution and vice versa.
4.1 CONTINUOUS WAVELET TRANSFORM
The continuous wavelet transform was developed as an alternative approach
to the short time Fourier transform to overcome the resolution problem. The wavelet
analysis is done in a similar way to the STFT analysis, in the sense that the signal is
multiplied with a function, {\it the wavelet}, similar to the window function in the
STFT, and the transform is computed separately for different segments of the time-
domain signal. However, there are two main differences between the STFT and the
CWT:
33
1. The Fourier transforms of the windowed signals are not taken, and therefore single
peak will be seen corresponding to a sinusoid, i.e., negative frequencies are not
computed.
2. The width of the window is changed as the transform is computed for every single
spectral component, which is probably the most significant characteristic of the
wavelet transform. The continuous wavelet transform is defined as follows
As seen in the above equation, the transformed signal is a function of two
variables, tau and s, the translation and scale parameters, respectively. psi(t) is the
transforming function, and it is called the mother wavelet . The term mother
wavelet gets its name due to two important properties of the wavelet analysis as
explained below:
The term wavelet means a small wave. The smallness refers to the condition
that this (window) function is of finite length (compactly supported). The wave
refers to the condition that this function is oscillatory. The term mother implies that
the functions with different region of support that are used in the transformation
process are derived from one main function, or the mother wavelet. In other words,
the mother wavelet is a prototype for generating the other window functions.
The term translation is used in the same sense as it was used in the STFT; it
is related to the location of the window, as the window is shifted through the signal.
This term, obviously, corresponds to time information in the transform domain.
However, we do not have a frequency parameter, as we had before for the STFT.
Instead, we have scale parameter which is defined as $1/frequency$. The term
frequency is reserved for the STFT. Scale is described in more detail in the next
section.
34
4.1.1The Scale
The parameter scale in the wavelet analysis is similar to the scale used in
maps. As in the case of maps, high scales correspond to a non-detailed global view
(of the signal), and low scales correspond to a detailed view. Similarly, in terms of
frequency, low frequencies (high scales) correspond to a global information of a
signal (that usually spans the entire signal), whereas high frequencies (low scales)
correspond to a detailed information of a hidden pattern in the signal (that usually
lasts a relatively short time). Cosine signals corresponding to various scales are given
as examples in the following figure .
Figure 4.3 COSINE SIGNALS CORRESPONDING TO VARIOUS SCALES
35
Fortunately in practical applications, low scales (high frequencies) do not last
for the entire duration of the signal, unlike those shown in the figure, but they usually
appear from time to time as short bursts, or spikes. High scales (low frequencies)
usually last for the entire duration of the signal.
Scaling, as a mathematical operation, either dilates or compresses a signal.
Larger scales correspond to dilated (or stretched out) signals and small scales
correspond to compressed signals. All of the signals given in the figure are derived
from the same cosine signal, i.e., they are dilated or compressed versions of the same
function. In the above figure, s=0.05 is the smallest scale, and s=1 is the largest scale.
In terms of mathematical functions, if f(t) is a given function f(st) corresponds to a
contracted (compressed) version of f(t) if s > 1 and to an expanded (dilated) version
of f(t) if s < 1 .
However, in the definition of the wavelet transform, the scaling term is used
in the denominator, and therefore, the opposite of the above statements holds, i.e.,
scales s > 1 dilates the signals whereas scales s < 1 , compresses the signal.
4.2 DISCRETE WAVELET TRANSFORM
The foundations of the DWT go back to 1976 when Croiser, Esteban, and
Galand devised a technique to decompose discrete time signals. Crochiere, Weber,
and Flanagan did a similar work on coding of speech signals in the same year. They
named their analysis scheme as sub band coding. In 1983, Burt defined a technique
very similar to sub band coding and named it pyramidal coding which is also known
as multiresolution analysis. Later in 1989, Vetterli and Le Gall made some
improvements to the sub band coding scheme, removing the existing redundancy in
the pyramidal coding scheme. Sub band coding is explained below. A detailed
coverage of the discrete wavelet transform and theory of multiresolution analysis can
be found in a number of articles and books that are available on this topic, and it is
beyond the scope of this tutorial.
36
4.2.1 The Sub band Coding and The Multi resolution Analysis
The main idea is the same as it is in the CWT. A time-scale representation of a
digital signal is obtained using digital filtering techniques. Recall that the CWT is a
correlation between a wavelet at different scales and the signal with the scale (or the
frequency) being used as a measure of similarity. The continuous wavelet transform
was computed by changing the scale of the analysis window, shifting the window in
time, multiplying by the signal, and integrating over all times. In the discrete case,
filters of different cutoff frequencies are used to analyze the signal at different scales.
The signal is passed through a series of high pass filters to analyze the high
frequencies, and it is passed through a series of low pass filters to analyze the low
frequencies.
The resolution of the signal, which is a measure of the amount of detail
information in the signal, is changed by the filtering operations, and the scale is
changed by up sampling and down sampling (sub sampling) operations. Sub sampling
a signal corresponds to reducing the sampling rate, or removing some of the samples
of the signal. For example, sub sampling by two refers to dropping every other
sample of the signal. Sub sampling by a factor n reduces the number of samples in the
signal n times.
Up sampling a signal corresponds to increasing the sampling rate of a signal
by adding new samples to the signal. For example, up sampling by two refers to
adding a new sample, usually a zero or an interpolated value, between every two
samples of the signal. Up sampling a signal by a factor of n increases the number of
samples in the signal by a factor of n.
Although it is not the only possible choice, DWT coefficients are usually
sampled from the CWT on a dyadic grid, i.e., s0 = 2 and 0 = 1, yielding s=2j and
=k*2j, as described in Part 3. Since the signal is a discrete time function, the terms
37
function and sequence will be used interchangeably in the following discussion. This
sequence will be denoted by x[n], where n is an integer.
The procedure starts with passing this signal (sequence) through a half band
digital low pass filter with impulse response h[n]. Filtering a signal corresponds to the
mathematical operation of convolution of the signal with the impulse response of the
filter. The convolution operation in discrete time is defined as follows:
A half band low pass filter removes all frequencies that are above half of the
highest frequency in the signal. For example, if a signal has a maximum of 1000 Hz
component, then half band low pass filtering removes all the frequencies above 500
Hz.
The unit of frequency is of particular importance at this time. In discrete
signals, frequency is expressed in terms of radians. Accordingly, the sampling
frequency of the signal is equal to 2 radians in terms of radial frequency. Therefore,
the highest frequency component that exists in a signal will be radians, if the signal
is sampled at Nyquist’s rate (which is twice the maximum frequency that exists in the
signal); that is, the Nyquist’s rate corresponds to rad/s in the discrete frequency
domain. Therefore using Hz is not appropriate for discrete signals. However, Hz is
used whenever it is needed to clarify a discussion, since it is very common to think of
frequency in terms of Hz. It should always be remembered that the unit of frequency
for discrete time signals is radians.
After passing the signal through a half band low pass filter, half of the
samples can be eliminated according to the Nyquist’s rule, since the signal now has a
highest frequency of /2 radians instead of radians. Simply discarding every other
sample will subsample the signal by two, and the signal will then have half the
38
number of points. The scale of the signal is now doubled. Note that the low pass
filtering removes the high frequency information, but leaves the scale unchanged.
Only the sub sampling process changes the scale. Resolution, on the other hand, is
related to the amount of information in the signal, and therefore, it is affected by the
filtering operations. Half band low pass filtering removes half of the frequencies,
which can be interpreted as losing half of the information. Therefore, the resolution is
halved after the filtering operation. Note, however, the sub sampling operation after
filtering does not affect the resolution, since removing half of the spectral
components from the signal makes half the number of samples redundant anyway.
Half the samples can be discarded without any loss of information. In summary, the
low pass filtering halves the resolution, but leaves the scale unchanged. The signal is
then sub sampled by 2 since half of the number of samples are redundant. This
doubles the scale.
This procedure can mathematically be expressed as
Having said that, we now look how the DWT is actually computed: The
DWT analyzes the signal at different frequency bands with different resolutions by
decomposing the signal into a coarse approximation and detail information. DWT
employs two sets of functions, called scaling functions and wavelet functions, which
are associated with low pass and high pass filters, respectively. The decomposition of
the signal into different frequency bands is simply obtained by successive high pass
and low pass filtering of the time domain signal. The original signal x[n] is first
passed through a half band high pass filter g[n] and a low pass filter h[n]. After the
filtering, half of the samples can be eliminated according to the Nyquist’s rule, since
the signal now has a highest frequency of /2 radians instead of . The signal can
therefore be sub sampled by 2, simply by discarding every other sample. This
39
constitutes one level of decomposition and can mathematically be expressed as
follows:
Where yhigh[k] and ylow[k] are the outputs of the high pass and low pass filters,
respectively, after sub sampling by 2.
This decomposition halves the time resolution since only half the number of
samples now characterizes the entire signal. However, this operation doubles the
frequency resolution, since the frequency band of the signal now spans only half the
previous frequency band, effectively reducing the uncertainty in the frequency by
half. The above procedure, which is also known as the sub band coding, can be
repeated for further decomposition. At every level, the filtering and sub sampling will
result in half the number of samples (and hence half the time resolution) and half the
frequency band spanned (and hence double the frequency resolution). Figure
illustrates this procedure, where x[n] is the original signal to be decomposed, and h[n]
and g[n] are low pass and high pass filters, respectively. The bandwidth of the signal
at every level is marked on the figure as "f".
40
Figure 4.4 BLOCK DIAGRAM
The Sub band Coding Algorithm As an example, suppose that the original
signal x[n] has 512 sample points, spanning a frequency band of zero to rad/s. At
the first decomposition level, the signal is passed through the high pass and low pass
filters, followed by sub sampling by 2. The output of the high pass filter has 256
points (hence half the time resolution), but it only spans the frequencies /2 to
rad/s (hence double the frequency resolution). These 256 samples constitute the first
level of DWT coefficients. The output of the low pass filter also has 256 samples, but
it spans the other half of the frequency band, frequencies from 0 to /2 rad/s. This
signal is then passed through the same low pass and high pass filters for further
decomposition.
41
The output of the second low pass filter followed by sub sampling has 128
samples spanning a frequency band of 0 to /4 rod/s, and the output of the second
high pass filter followed by sub sampling has 128 samples spanning a frequency band
of /4 to /2 rad/s. The second high pass filtered signal constitutes the second level
of DWT coefficients. This signal has half the time resolution, but twice the frequency
resolution of the first level signal. In other words, time resolution has decreased by a
factor of 4, and frequency resolution has increased by a factor of 4 compared to the
original signal. The low pass filter output is then filtered once again for further
decomposition. This process continues until two samples are left. For this specific
example there would be 8 levels of decomposition, each having half the number of
samples of the previous level. The DWT of the original signal is then obtained by
concatenating all coefficients starting from the last level of decomposition (remaining
two samples, in this case). The DWT will then have the same number of coefficients
as the original signal.
The frequencies that are most prominent in the original signal will appear as
high amplitudes in that region of the DWT signal that includes those particular
frequencies. The difference of this transform from the Fourier transform is that the
time localization of these frequencies will not be lost. However, the time localization
will have a resolution that depends on which level they appear. If the main
information of the signal lies in the high frequencies, as happens most often, the time
localization of these frequencies will be more precise, since they are characterized by
more number of samples. If the main information lies only at very low frequencies,
the time localization will not be very precise, since few samples are used to express
signal at these frequencies. This procedure in effect offers a good time resolution at
high frequencies, and good frequency resolution at low frequencies. Most practical
signals encountered are of this type.
The frequency bands that are not very prominent in the original signal will
have very low amplitudes, and that part of the DWT signal can be discarded without
any major loss of information, allowing data reduction. Figure 4.2 illustrates an
42
example of how DWT signals look like and how data reduction is provided. Figure
4.2a shows a typical 512-sample signal that is normalized to unit amplitude. The
horizontal axis is the number of samples, whereas the vertical axis is the normalized
amplitude. Figure 4.2b shows the 8 level DWT of the signal in Figure 4.2a. The last
256 samples in this signal correspond to the highest frequency band in the signal, the
previous 128 samples correspond to the second highest frequency band and so on. It
should be noted that only the first 64 samples, which correspond to lower frequencies
of the analysis, carry relevant information and the rest of this signal has virtually no
information. Therefore, all but the first 64 samples can be discarded without any loss
of information. This is how DWT provides a very effective data reduction scheme.
FIGURE 4.5 DWT WAVEFORMS
We will revisit this example, since it provides important insight to how DWT should
be interpreted. Before that, however, we need to conclude our mathematical analysis
of the DWT.
43
One important property of the discrete wavelet transform is the relationship
between the impulse responses of the high pass and low pass filters. The high pass
and low pass filters are not independent of each other, and they are related by
where g[n] is the high pass, h[n] is the low pass filter, and L is the filter length
(in number of points). Note that the two filters are odd index alternated reversed
versions of each other. Low pass to high pass conversion is provided by the (-1)n
term. Filters satisfying this condition are commonly used in signal processing, and
they are known as the Quadrature Mirror Filters (QMF). The two filtering and sub
sampling operations can be expressed by
The reconstruction in this case is very easy since half band filters form
orthonormal bases. The above procedure is followed in reverse order for the
reconstruction. The signals at every level are up sampled by two, passed through the
synthesis filters g’[n], and h’[n] (high pass and low pass, respectively), and then
added. The interesting point here is that the analysis and synthesis filters are identical
to each other, except for a time reversal. Therefore, the reconstruction formula
becomes (for each layer)
However, if the filters are not ideal half band, then perfect reconstruction
cannot be achieved. Although it is not possible to realize ideal filters, under certain
conditions it is possible to find filters that provide perfect reconstruction. The most
44
famous ones are the ones developed by Ingrid Daubechies, and they are known as
Daubechies’ wavelets.
Note that due to successive sub sampling by 2, the signal length must be a
power of 2, or at least a multiple of power of 2, in order this scheme to be efficient.
The length of the signal determines the number of levels that the signal can be
decomposed to. For example, if the signal length is 1024, ten levels of decomposition
are possible.
Interpreting the DWT coefficients can sometimes be rather difficult because
the way DWT coefficients are presented is rather peculiar. To make a real long story
real short, DWT coefficients of each level are concatenated, starting with the last
level. An example is in order to make this concept clear.
Suppose we have a 256-sample long signal sampled at 10 MHZ and we wish
to obtain its DWT coefficients. Since the signal is sampled at 10 MHz, the highest
frequency component that exists in the signal is 5 MHz. At the first level, the signal is
passed through the low pass filter h[n], and the high pass filter g[n], the outputs of
which are sub sampled by two. The high pass filter output is the first level DWT
coefficients. There are 128 of them, and they represent the signal in the [2.5 5] MHz
range. These 128 samples are the last 128 samples plotted. The low pass filter output,
which also has 128 samples, but spanning the frequency band of [0 2.5] MHz, are
further decomposed by passing them through the same h[n] and g[n]. The output of
the second high pass filter is the level 2 DWT coefficients and these 64 samples
precede the 128 level 1 coefficients in the plot. The output of the second low pass
filter is further decomposed, once again by passing it through the filters h[n] and g[n].
The output of the third high pass filter is the level 3 DWT coefficients. These 32
samples precede the level 2 DWT coefficients in the plot.
The procedure continues until only 1 DWT coefficient can be computed at
level 9. This on coefficient is the first to be plotted in the DWT plot. This is
45
followed by 2 level 8 coefficients, 4 level 7 coefficients, 8 level 6 coefficients, 16
level 5 coefficients, 32 level 4 coefficients, 64 level 3 coefficients, 128 level 2
coefficients and finally 256 level 1 coefficients. Note that less and less number of
samples is used at lower frequencies, therefore, the time resolution decreases as
frequency decreases, but since the frequency interval also decreases at low
frequencies, the frequency resolution increases. Obviously, the first few coefficients
would not carry a whole lot of information, simply due to greatly reduced time
resolution.
To illustrate this richly bizarre DWT representation let us take a look at a real
world signal. Our original signal is a 256-sample long ultrasonic signal, which was
sampled at 25 MHz. This signal was originally generated by using a 2.25 MHz
transducer, therefore the main spectral component of the signal is at 2.25 MHz. The
last 128 samples correspond to [6.25 12.5] MHz range. As seen from the plot, no
information is available here, hence these samples can be discarded without any loss
of information. The preceding 64 samples represent the signal in the [3.12 6.25] MHz
range, which also does not carry any significant information. The little glitches
probably correspond to the high frequency noise in the signal. The preceding 32
samples represent the signal in the [1.5 3.1] MHz range. As you can see, the majority
of the signal’s energy is focused in these 32 samples, as we expected to see. The
previous 16 samples correspond to [0.75 1.5] MHz and the peaks that are seen at this
level probably represent the lower frequency envelope of the signal. The previous
samples probably do not carry any other significant information. It is safe to say that
we can get by with the 3rd and 4th level coefficients, that is we can represent this 256
sample long signal with 16+32=48 samples, a significant data reduction which would
make your computer quite happy.
One area that has benefited the most from this particular property of the
wavelet transforms is image processing. As you may well know, images, particularly
high-resolution images, claim a lot of disk space. As a matter of fact, if this tutorial is
46
taking a long time to download, that is mostly because of the images. DWT can be
used to reduce the image size without losing much of the resolution. Here is how:
For a given image, you can compute the DWT of, say each row, and discard
all values in the DWT that are less then a certain threshold. We then save only those
DWT coefficients that are above the threshold for each row, and when we need to
reconstruct the original image, we simply pad each row with as many zeros as the
number of discarded coefficients, and use the inverse DWT to reconstruct each row of
the original image. We can also analyze the image at different frequency bands, and
reconstruct the original image by using only the coefficients that are of a particular
band. I will try to put sample images hopefully soon, to illustrate this point.
Another issue that is receiving more and more attention is carrying out the
decomposition (sub band coding) not only on the low pass side but on both sides. In
other words, zooming into both low and high frequency bands of the signal
separately. This can be visualized as having both sides of the tree structure of Figure
4.1. What result is what is known as the wavelet packages. We will not discuss
wavelet packages in this here, since it is beyond the scope of this tutorial. Anyone
who is interested in wavelet packages, or more information on DWT can find this
information in any of the numerous texts available in the market.
And this concludes our mini series of wavelet tutorial. If I could be of any
assistance to anyone struggling to understand the wavelets, I would consider the time
and the effort that went into this tutorial well spent. I would like to remind that this
tutorial is neither a complete nor a through coverage of the wavelet transforms. It is
merely an overview of the concept of wavelets and it was intended to serve as a first
reference for those who find the available texts on wavelets rather complicated. There
might be many structural and/or technical mistakes, and I would appreciate if you
could point those out to me. Your feedback is of utmost importance for the success of
this tutorial.
47
4.3 ALGORITHM
The proposed enhancement algorithm consists of three stages: the first and
the third stage are applied in the spatial domain and the second one in the discrete
wavelet domain.
4.3.1 Histogram Adjustment
Our motivation in making an histogram adjustment for minimizing the
illumination effect is based on some assumptions about image formation and human
vision behavior. The sensor signal S(x, y) incident upon an imaging system can be
approximated as the product[8],[26]
S(x,y) = L(x,y)R(x,y), (1)
Where R(x, y) is the reflectance and L(x, y) is the illuminance at each point (x,
y). In lightness algorithms, assuming that the sensors and filters used in artificial
visual systems possess the same nonlinear property as human photoreceptors, i.e.,
logarithmic responses to physical intensities incident on the their photoreceptors [8],
Equation 1 can be decomposed into
a sum of two components by using the transformation
I(x,y) =log(S(x,y)):
I(x, y) = log (L(x,y)) + log(R(x,y)), (2)
Where I(x,y) is the intensity of the image at pixel location (x,y).Equation 2
implies that illumination has an effect on the image histogram as a linear shift. This
shift, intrinsically, is not same in different spectral bands.
Another assumption of the lightness algorithms is the gray world
assumption stating that the average surface reflectance of each scene in each
wavelength band is the same: gray [8].
48
From an image processing stance, this assumption indicates that images of natural
scenes should contain pixels having almost equal average gray levels in each spectral
band.
Combining Equation 2 with the gray-world assumption, we perform
histogram adjustment as follows:
1. The amount of shift corresponding to illuminance is determined from the beginning
of the lower tail of the histogram such that a predefined amount (typically
0.5%) of image pixels is clipped
2. The shift is subtracted from each pixel value
3. This process is repeated separately for each color Channel
4.4 WAVELET BASED DYNAMIC RANGE
COMPRESSION AND CONTRAST ENHANCEMENT
4.4.1 Dynamic Range Compression
Dynamic range compression and the local contrast enhancement in WDRC are
performed on the luminance channel. For input color images, the intensity image
I(x,y) can
be obtained with the following equation:
I(x, y) = max [Ii (x, y)], i Î {R,G,B}. (3)
The enhancement algorithm is applied on this intensity image. The luminance values
are decomposed using orthonormal wavelet transform as shown in (4):
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Where aJ,k,l are the approximation coefficients at scale J with corresponding scaling functions FJ,k,l (x, y) , and d j,k,l are the detail coefficients at each scale with corresponding
Wavelet functions Yj,k,l (x, y) . A raised hyperbolic sinefunction given by Equation 5
maps the normalized range [0,1] of aJ,k,l to the same range, and is used for
compressing the dynamic range represented by the coefficients. The compressed
coefficients at level J can be obtained by
where a ¢ J,k,l are normalized coefficients given by
and r is the curvature parameter which adjusts the shape of the hyperbolic sine
function. Applying the mapping operator to the coefficients and taking the inverse
wavelet transform would result in a compressed dynamic range with a significant loss
of contrast. Thus, a center/surround procedure that preserves/enhances the local
contrast is applied to those
mapped coefficients.
4.4.2 Local Contrast Enhancement
The local contrast enhancement which employs a center/surround approach is
carried out as follows
The surrounding intensity information related to each coefficient is obtained
by filtering the normalized approximation coefficients with a Gaussian kernel.
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Where s is the surround space constant, and k is determined under the constraint that
Local average image representing the surround is obtained by 2D convolution
of (7) with image A ¢, the elements of which are the normalized approximation
coefficients a ¢ J,k,l and given
by (6) :
The contrast enhanced coefficients matrix Anew which will replace the original
approximation coefficients aJ,k,l is given by
where, R is the centre/surround ratio given by d is the
enhancement strength constant with a default value of 1; A is the matrix whose
elements are the output of the hyperbolic sine function in (5).
A linear combination of three kernels with three different scales, combined-
scale-Gaussian (Gc ), is used for improved rendition is given by
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4.4.3 Detail Coefficient Modification
The detail coefficients are modified using the ratio between the enhanced and
original approximation coefficients. This ratio is applied as an adaptive gain mask
such as:
where A and Anew are the original and the enhanced approximation
coefficient matrices at level 1; Dh , Dv , Dd are the detail coefficient matrices for
horizontal, vertical and diagonal details at the same level, and Dnew h , Dnew v ,
Dnew d are the corresponding modified matrices, respectively. If the wavelet
decomposition is carried out for more than one level, this procedure is repeated for
each level.
4.4.4 Color Restoration
A linear color restoration process is used to obtain the final color image in our
previous work .For WDRC with color restoration a non-linear approach is employed.
The
RGB values of the enhanced color image ( , ) , I x y enh i along with the CR factor
are given as:
52
where Ii(x, y)is the RGB values of the input color image at the corresponding pixel
location and Ienh (x, y) is the resulting enhanced intensity image derived from the
inverse wavelet transform of the modified coefficients. Here _ is the non-linear gain
factor corresponding. This factor has a canonical value and increases the color
saturation resulting in more appealing color rendition. Since the coefficients are
normalized during the enhancement process, the enhanced intensity image obtained
by the inverse transform of enhanced coefficients, along with the enhanced color
image given by (15) span almost only the lower half of the full range of the
histogram. For the final display domain output enh i I , ’s in (15) are stretched to
represent the full dynamic range. Histogram clipping from the upper tail of
histograms in each channel give the best results in
converting the output to display domain.
53
CHAPTER 5
RESULTS ANALYSIS
5.1 RESULTS
Figure. 5.1 Histogram adjusted image
Figure 5.2 orthogonal wavelet decomposition
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Figure 5.3 WDRC Approximation
Figure 5.4 WDRC Reconstucted spatial domain image
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Figure 5.5 Final result
5.3 CONCLUSION
In this project application of the WDRC algorithm in aerial imagery is
presented. The results obtained from large variety of aerial images show strong
robustness, high image quality, and improved visibility indicating promise for aerial
imagery during poor visibility flight conditions. This algorithm can further be applied
to real time video streaming and the enhanced video can be projected to the pilot’s
heads-up display for aviation safety.
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5.2 FUTURE SCOPE
As future work,
This work can be extended in order to increase the accuracy by increasing the
level of transformation.
This can be used as a part of the block in the full fledged applications ,i.e, by
using these DWT,the applications can be developed such as
compression,watermarking etc.
57
REFERENCES
[1] D. J. Jobson, Z. Rahman, G. A. Woodell, G.D.Hines, “A Comparison of Visual
Statistics for the Image Enhancement of FORESITE Aerial Images with Those of
Major Image Classes,” Visual Information Processing XV, Proc. SPIE 6246, (2006)
[2] S. M. Pizer, J. B. Zimmerman, and E. Staab, “Adaptive grey level assignment in
CT scan display,” Journal of Computer Assistant Tomography, vol. 8, pp. 300-305 ,
(1984).
[3] J. B. Zimmerman, S. B. Cousins, K. M. Hartzell, M. E. Frisse, and M. G. Kahn,
“A psychophysical comparison of two methods for adaptive histogram equalization,”
Journal of Digital Imaging, vol. 2, pp. 82-91(1989).
[4] S. M. Pizer and E. P. Amburn, “Adaptive histogram equalization and its
variations,” Computer Vision, Graphics, and Image Processing, vol. 39, pp. 355-368,
(1987).
[5] K. Rehm and W. J. Dallas, “Artifact suppression in digital chest radiographs
enhanced with adaptive histogram equalization,” SPIE: Medical Imaging III, (1989).
58
APPENDIXSOURCE CODE
%%% this is the main program for the implementation of Aerial image
%%% enhancement using DWT
clear all;
close all;
clc;
I=uigetfile('.jpg','select the aerial image');
a=imread(I);
s1=size(a);
% Stage 1: Histogram Adjustment
figure('Name','Stage 1: Histogram Adjustment','NumberTitle','off'); subplot(2,2,1);
imshow(a); title('Original image');
ag=rgb2gray(a);
subplot(2,2,2); imhist(ag);title('Original image Histogram');
a1=a;
a1(:,:,1)=histeq(a(:,:,1));
a1(:,:,2)=histeq(a(:,:,2));
a1(:,:,3)=histeq(a(:,:,3));
subplot(2,2,3); imshow(a1);title('Histogram Adjusted image');
ag1=rgb2gray(a1);
subplot(2,2,4);imhist(ag1);title('Histogram Adjusted image Histogram');
% Stage 2: Wavelet Based Dynamic Range Compression and Contrast Enhancement
% 2.1: Dynamic Range Compression
aI=max(a1,[],3);
[ai,aih,aiv,aid]=dwt2(double(aI),'bior1.1');
s2=size(ai);
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figure('Name','Stage 2.1: Orthogonal Wavelet Decomposition','NumberTitle','off');
subplot(2,2,1); imshow(ai,[]);
subplot(2,2,2); imshow(aih);
subplot(2,2,3); imshow(aiv);
subplot(2,2,4); imshow(aid);
%Mapping operator
r=2;
j=1;
aim=ai;
aivm=aiv;
aidm=aid;
aihm=aih;
for n=1:s2(2)
for m=1:s2(1)
aim(m,n)=((sinh(4.6248*((ai(m,n)/(255*(2^j))))-2.3124)+5)/10).^r;
aivm(m,n)=((sinh(4.6248*((aiv(m,n)/(255*(2^j))))-2.3124)+5)/10).^r;
aihm(m,n)=((sinh(4.6248*((aih(m,n)/(255*(2^j))))-2.3124)+5)/10).^r;
aidm(m,n)=((sinh(4.6248*((aid(m,n)/(255*(2^j))))-2.3124)+5)/10).^r;
end
end
% 2.2,2.3: Local Contrast Enhancement and Detail Coefficient modification
aimd = histeq(aim);
ai=ai+0.000001; % to avoid divided by zero
aivmd=imadjust(aivm); avn=(aimd./ai).*aivm;
aidmd=imadjust(aidm);adn=(aimd./ai).*aidm;
aihmd=imadjust(aihm);ahn=(aimd./ai).*aihm;
figure;imshow(aimd), title('WDRC Approximation image')
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a=double(a);
aId=idwt2(aimd,avn,ahn,adn,'bior1.1');
figure;imshow(aId,[]); title('WDRC Reconstructed Spatial Domain
image')
I=double(a1);
B=3;
% Step 3: Colour Restoration
for n=1:s1(2)
for m=1:s1(1)
Ai=((a(m,n,:))./max(a(m,n,:))).^B;
I(m,n,:)=Ai.*aId(m,n).*2.5;
end
end
figure('Name','Final Result','NumberTitle','off');
subplot(2,1,1); imshow(uint8(a)); title('Original Image')
subplot(2,1,2); imshow(I); title('Enhanced Image')
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