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Detection and Assessment of Abnormality in Medical Images MS Thesis Presentation Candidate: K Sai Deepak Adviser: Prof. Jayanthi Sivaswamy Center for Visual Information Technology IIIT Hyderabad India 31-March-2012

Detection and Assessment of Abnormality in Medical Images

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Detection and Assessment of Abnormality in Medical Images. MS Thesis Presentation Candidate: K Sai Deepak Adviser: Prof. Jayanthi Sivaswamy. Center for Visual Information Technology IIIT Hyderabad India. 31-March-2012. Computer Aided Diagnosis. Disease Screening. Proposed Methodology. - PowerPoint PPT Presentation

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Page 1: Detection and Assessment of Abnormality in Medical Images

Detection and Assessment of Abnormality in Medical Images

MS Thesis PresentationCandidate: K Sai Deepak

Adviser: Prof. Jayanthi Sivaswamy

Center for Visual Information TechnologyIIIT Hyderabad

India

31-March-2012

Page 2: Detection and Assessment of Abnormality in Medical Images

Agenda

• Computer Aided Diagnosis– Modes of Healthcare– CAD in Primary Care (examples)

• Disease Screening– CAD in Disease Screening– Challenges for existing CAD

• Proposed Methodology– Detecting Abnormality Instead of Disease– Detection of Lesions using Motion Patterns

• Detection and Assessment of Retinopathy– Diabetic Macular Edema– Method– Experiments and Results– Detection of Multiple Lesions

• Classification of Lesions in Mammograms– Mammographic Lesions– Experiments and Results

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Source of all the figures are explicitly mentioned in the MS Thesis

Page 3: Detection and Assessment of Abnormality in Medical Images

PART I – Computer Aided Diagnosis

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 4: Detection and Assessment of Abnormality in Medical Images

Computer Aided Diagnosis (CAD)

• Aid of computers in the process of diagnosis

• Computer aided diagnosis (CAD) has become one of the major support systems assisting medical experts in diagnosis through images

• CAD tools are used for measurement, display and analysis of both the structural and functional aspects of the body from images

Computer Aided Diagnosis

Computer Aided Diagnosis

Page 5: Detection and Assessment of Abnormality in Medical Images

CAD with Images

Computer Aided Diagnosis

Computer Aided Diagnosis

• Visualization – enhancement for visual analysis (Ex. Windowing, MIP, MAP, AIP, Zoom, Contrast Inversion etc.)

• Detection – detect the presence of disease manifestation

• Localization and Segmentation – Localize or segment the spatial regions containing disease manifestation

• Other utilities can be used for measurement of various structures from images (length, volume etc. )

Page 6: Detection and Assessment of Abnormality in Medical Images

Healthcare – Primary Care and Disease Screening

Computer Aided Diagnosis

Computer Aided Diagnosis

Secondary and Tertiary Care Centers – are where patients usually visit on referral for advanced care

Point of Consultation in basic healthcarePatients with Symptoms arrive

Undergo specialized tests if required for DiagnosisTreatment is planned based on Diagnosis

Performed on Public health initiativeMost patients have no disease symptoms

Detection is performed by a trained professionalReferred to expert on positive detection

Page 7: Detection and Assessment of Abnormality in Medical Images

CAD in Primary Care

Computer Aided Diagnosis

Computer Aided Diagnosis

• Traditionally CAD has been used in Primary Care

Page 8: Detection and Assessment of Abnormality in Medical Images

CAD in Primary Care

• Patient visits the doctor with a complaint

• If required, the patient is then referred by the doctor for specific imaging in order to diagnose the problem

• Acquired images are analyzed by the experts (Ophthalmologist, Radiologist) to arrive at a diagnosis

• The diagnosis report is used by doctor for planning treatment

Computer Aided Diagnosis

Computer Aided Diagnosis

Page 9: Detection and Assessment of Abnormality in Medical Images

PART II – Disease Screening

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 10: Detection and Assessment of Abnormality in Medical Images

Disease Screening

• Disease screening is performed at specific community healthcare centers to prevent ensuing mortality and suffering from chronic ailments

• Challenges: Geographical reach, Disease awareness and Social barriers and Availability of experts are common in screening

• Tele-radiology provides significant help but the work load of a medical expert increases significantly due to large number of patients participating in population screening

• Diabetic Retinopathy and Breast Cancer screening are already conducted or being adopted in several countries and is the focus of this work

Disease ScreeningDisease Screening

Page 11: Detection and Assessment of Abnormality in Medical Images

CAD in Disease Screening

• Existing CAD tools use a disease centric approach for disease detection

• It requires application of several methods/tools for detecting all the possible lesions in a disease– Multiple CAD tools are used for identifying different Diabetic

Retinopathy (DR) manifestations

• Existing CAD systems are not able to meet the needs of disease screening in Diabetic Retinopathy [1]– Poor sensitivity of disease detection – Large number of normal patients are detected as abnormal

Disease ScreeningDisease Screening

[1] M. D. Abramoff, M. Niemeijer, M. S. Suttorp-Schulten, M. A. Viergever, S. R. Russell, and B. van Ginneken. Evaluation of a system for automatic detection of diabetic retinopathy from color fundus photographs in a large population of patients with diabetes. Journal of Diabetes Care, 31:193–198, 2007.

Page 12: Detection and Assessment of Abnormality in Medical Images

Summary of Challenges

• Existing CAD tools use a disease centric approach for detection and segmentation of disease– In Screening most of the patients are normal (80-90% for DR & BC)

• Multiple tools result in cascading effect of detected FPs• Doctors spend a lot of time in rejecting normal patients

– Other challenges in disease centric approach• Illumination and Contrast• Tissue Pigmentation

• A disease centric CAD system has to robustly learn all possible manifestations of a disease which is challenging

• Patients with diseases outside the purview of screening are ignored – referral could be useful for a patient suffering non DR disease detected in DR screening

Disease ScreeningDisease Screening

Page 13: Detection and Assessment of Abnormality in Medical Images

Other Challenges – Disease Vs Normal Background

Disease ScreeningDisease Screening

Page 14: Detection and Assessment of Abnormality in Medical Images

PART III – Proposed Methodology

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 15: Detection and Assessment of Abnormality in Medical Images

• Non conformance to expected behaviour (normal) in the data is considered as abnormality

• Features of normal medical images can be used to model expected normal behaviour

• Abnormality detection is relevant in disease screening where detecting the presence of abnormality is of initial interest:– Retinal image screening for detecting Diabetic

Retinopathy– Mammographic screening for detecting

malignancy of lesions Normal CFI Abnormal CFI with lesions

Proposed MethodologyProposed Methodology

Detecting Abnormality instead of Disease

X

Y

Normal

Abnormal

Feature Space

Abnormal

Page 16: Detection and Assessment of Abnormality in Medical Images

Two Stage Methodology for CAD

Proposed MethodologyProposed Methodology

• Stage 1- Detection of abnormality – Derive motion pattern for detection of

lesions– Extract relevant features to represent

normal sub-space– Detect outliers as abnormal

• Stage2-Assessment of abnormality– Derive relevant features based on

domain knowledge from abnormal cases

– Determine the severity of disease

Page 17: Detection and Assessment of Abnormality in Medical Images

Two Stage Methodology for CAD

Proposed MethodologyProposed Methodology

• Stage 1- Detection of abnormality – Only normal cases are required for

disease detection– Variations observed in the normal

cases are captured by the normal feature sub-space

– Single point of control on the permitted figure of false alarms

• Stage2-Assessment of abnormality– Fewer normal cases to be examined

by experts

Page 18: Detection and Assessment of Abnormality in Medical Images

• Motivation - Effect of motion on human visual system and detectors in camera– Spatial/temporal averaging of intensities in retina– Smearing of intensities corresponding to moving

object is observed in images acquired with camera

• Inducing motion in images– Lesions can be observed as a set of localized pixels

with contrast against background– A smear of pixel along the direction of motion can

be observed in motion pattern– Spread and extent of lesions in motion pattern

depends on the sampling rate at each location and duration of motion

– Contrast of the spatially enhanced lesions in motion pattern relies on the coalescing function

• Motion pattern on Background– Uniformity in motion pattern for textured

background can be observed

Orig

inal

Imag

e (U

nifo

rm B

ackg

roun

d)Ro

tatio

nal M

otion

Patt

ern

Motion Pattern – Detecting Localized Lesions

Proposed MethodologyProposed MethodologyO

riginal Image

(Textured Background)Rotational M

otion Pattern

Page 19: Detection and Assessment of Abnormality in Medical Images

PART IV – Detection and Assessment of Macular Edema

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 20: Detection and Assessment of Abnormality in Medical Images

Macular Edema Detection and Assessment• Diabetic Macular Edema (DME) is a sight threatening condition that

occurs due to diabetic retinopathy• DME requires immediate referral to Ophthalmologists• Presence of Hard Exudates is used as an indicator of DME during retinal

disease screening

Severe and moderate cases of DMEColor Retinal Image

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 21: Detection and Assessment of Abnormality in Medical Images

Existing Approaches in DME Detection• Several local and global schemes have been proposed for DME

detection

• Local Schemes– local schemes try to successfully segment or localize the exudate clusters– Techniques including adaptive intensity thresholding, background suppression

(median filtering, morphology), color and edge detection have been proposed – several normal pixels are also detected as candidates in normal images increasing the

number of false alarms in the system

• Global Schemes– global schemes try to ensure that at least the brightest pixels corresponding to HE in

the image are detected– Techniques based on intensity thresholding, edge strength, and visual words using

features on SIFT keypoints have been used to classify images

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 22: Detection and Assessment of Abnormality in Medical Images

Proposed Workflow

Steps• Landmark Detection and Region of Interest Extraction• Generation of Motion Patterns• Feature Selection• Abnormality Detection• Abnormality Assessment

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 23: Detection and Assessment of Abnormality in Medical Images

Detection of Landmarks in CFI-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Singh, J. and Joshi, G. D. and Sivaswamy, J. Appearance-based object detection in colour retinal images. In ICIP, pages 1432–1435, 2008.G. D. Joshi and J. Sivaswamy and K Karan and S. R. Krishnadas. Optic disk and cup boundary detection using regional information. ISBI, pp. 948–951, 2010.

Page 24: Detection and Assessment of Abnormality in Medical Images

Selection of ROI

ROI around center of macula

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 25: Detection and Assessment of Abnormality in Medical Images

Motion Pattern – Rotational Motion

Effect of sampling rate on motion pattern (decreasing rotation steps)-

Coalescing Function• Mean - Arithmetic mean of all samples were taken

• Extrema – Maximum or Minimum of all samples are taken at each pixel location

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 26: Detection and Assessment of Abnormality in Medical Images

Selection of Motion Pattern

“effect of abnormality (lesion) on retinal background can be observed as change in local information with respect to the motion pattern of normal retina”

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

normal abnormal• A normal retinal image was created by averaging the green channel of 400 retinal images• The abnormal retina is modeled by adding a bright lesion to emulate HE

- motion pattern - Gradient magnitude of motion pattern - Shannon’s entropy

Page 27: Detection and Assessment of Abnormality in Medical Images

Selection of Parameters – Class Discriminability-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Size of normal retina – 150*150Neighborhood size – 7*7

Page 28: Detection and Assessment of Abnormality in Medical Images

Motion Pattern for Edema Detection• A circular ROI is determined around macula and the Optic disc is masked to

avoid false positives• Rotational motion is induced in the green channel image• Maxima is used as the coalescing function• Features derived on motion pattern are used for learning the normal sub-

space and detecting abnormality

Sample ROI and Motion Pattern (S- Subtle Hard Exudates)

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 29: Detection and Assessment of Abnormality in Medical Images

More Motion PatternsSample ROIs and Motion Pattern (S- Subtle Hard Exudates)

Nor

mal

RO

IAb

norm

al R

OI

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 30: Detection and Assessment of Abnormality in Medical Images

Feature Extraction-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

• To effectively describe motion pattern, we use a descriptor derived from the Radon space

• The desired feature vector is obtained by concatenating 6 projections (0-180 degrees) • Each projection has 6 bins resulting in a feature vector of length 36

Integral of motion pattern along a line

Page 31: Detection and Assessment of Abnormality in Medical Images

Abnormality DetectionPCA Data Description• The eigenvectors corresponding to the covariance matrix of the training set is used to describe the normal subspace• Feature vector for a new case is projected to this subspace (first 6 eigen vectors)

Residual e is defined as,

• Classification between normal and abnormal cases is then performed using an empirically determined threshold on e

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

FNTP

TPySensitivit

FPTN

TNySpecificit

Page 32: Detection and Assessment of Abnormality in Medical Images

Detection Performance (ROC Curves)• DMED - 122 images

o Normal - 68o Abnormal – 54o Normal images used for training - 18

• MESSIDOR – 400 imageso Normal - 274o Abnormal – 126o Immediate referral - 85o Normal images used for training – 74

• Diaretdb0 & db1 – 122 imageso Normal – 25o Abnormal - 97

• Combined Dataset – 644 imageso Normal – 367o Abnormal - 277

DM

EDM

ESSI

DO

R

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Receiver Operating Characteristic curve

Page 33: Detection and Assessment of Abnormality in Medical Images

Comparison against Disease Centric MethodsDMED

Normal - 68Abnormal – 54Normal images used for training - 18

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

MESSIDORNormal - 274Abnormal – 126Normal images used for training – 74

[23] L. Giancardo, F. Meriaudeau, T. P. Karnowski, Y. Li, K. W. Tobin Jr, and E. Chaum. Automatic retina exudates segmentation without a manually labelled training set. IEEE ISBI, pages 1396 – 1400, April 2011.

[2] C. Agurto, V. Murray, E. Barriga, S. Murillo, M. Pattichis, H. Davis, S. Russell, M. Abramoff, and P. Soliz. Multiscale am-fm methods for diabetic retinopathy lesion detection. IEEE TMI, 29(2):502 –512, feb. 2010.

Page 34: Detection and Assessment of Abnormality in Medical Images

Detection of subtle hard exudates

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Page 35: Detection and Assessment of Abnormality in Medical Images

Assessment of Severity

• Macula is devoid of significant vasculature • It is characterized by rough rotationally symmetry

-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

- Abnormal image

- Symmetry measure on abnormal macula

and are the minimum and maximum symmetry values for normal cases

Page 36: Detection and Assessment of Abnormality in Medical Images

Assessment of Severity-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Dataset: MESSIDOR

The threshold is expressed as a percentage (p) of the symmetry measure S of normal ROIs used in the abnormality detection task

Page 37: Detection and Assessment of Abnormality in Medical Images

Detection of Multiple Abnormalities-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Normal Cases - 362 Abnormal Cases - 302

Dataset: DMED,MESSIDOR and Diaretdb0

Abnormalities: Hemorrhage, Hard Exudates, Drusen

Page 38: Detection and Assessment of Abnormality in Medical Images

PART V – Classification of Lesions in Mammograms

Computer Aided Diagnosis

Computer Aided Diagnosis Disease ScreeningDisease Screening Proposed MethodologyProposed Methodology -Showcase 1-

Retinopathy-Showcase 1- Retinopathy

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 39: Detection and Assessment of Abnormality in Medical Images

Assessment of Mammographic Lesions• Breast cancer is responsible for about 30 percent of all new cancer cases

with a high mortality rate in women• Screening for its early detection with mammograms has been explored for

more than 3 decades now with moderate success• Correct classification of anomalous areas in the mammograms through

visual examination is challenging even for experts

Sample Benign and Malignant lesions in Mammograms

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 40: Detection and Assessment of Abnormality in Medical Images

Existing Approaches in Mammogram Analysis• 1- Lesions are first detected from mammograms• 2- Malignancy of detected lesions are identified using several texture

and shape features

• Typical features used– size– shape– density– Smoothness of borders– Brightness and contrast– local intensity distribution

• The feature space is very large and complex due to the wide diversity of the normal tissues and the variety of the abnormalities

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 41: Detection and Assessment of Abnormality in Medical Images

Classification of Mammographic Lesions• Given a lesion, its malignancy is of question• Features derived over motion pattern is used for learning the behavior of

benign class• Any deviation in lesion property is identified as a sign of malignancy

Benign lesions

Malignant lesions

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 42: Detection and Assessment of Abnormality in Medical Images

Motion Pattern – Class Discriminability• Three sample benign and malignant lesions were selected • Motion pattern was applied using rotation and translation to analyze class discriminability between benign and malignant class

• Maximum and Mean are the coalescing functions used

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 43: Detection and Assessment of Abnormality in Medical Images

Classification Performance (ROC Curve)

• An evaluation of the proposed scheme for learning normal subspace was conducted using KNN classifier

• The value of K was considered as 3 for computing the sensitivity and specificity values in the classification tasks

• An ROC curve is drawn by varying the normalized Euclidean distance from [0-1]

Mini-MIAS

Benign - 68Malignant – 51Benign lesions for training - 20

-Showcase 2- Breast Cancer-Showcase 2- Breast Cancer

Page 44: Detection and Assessment of Abnormality in Medical Images

• We identified and listed the challenges in image based disease screening for diabetic retinopathy and breast cancer

• We proposed and evaluated a method for abnormality detection and assessment– a hierarchical approach to the problem of abnormality detection

• Evaluation of the proposed hierarchical approach has been performed – on several publicly image datasets of CFI and mammograms– improvement in the disease detection performance over methods in literature

Conclusion

Page 45: Detection and Assessment of Abnormality in Medical Images

Acknowledgement

• This work is dedicated to my Parents and Teachers

• Extremely grateful to Prof. Jayanthi Sivaswamy for giving me the opportunity to pursue MS by research

• Thankful to all lab mates in CVIT for their support• Guidance of Gopal and Mayank was extremely valuable • Debates and discussion with Sandeep, Kartheek and Saurabh were always

insightful

Page 46: Detection and Assessment of Abnormality in Medical Images

Publications1. Patents

(a) Jayanthi Sivaswamy, N V Kartheek Medathati, K Sai Deepak, A System for generating Generalized Moment Patterns, Submitted to Indian Patent Office, 2010 (Application Number 3939-CHE-2010)

2. Papers

Conference(a) K Sai Deepak, Gopal Datt Joshi, Jayanthi Sivaswamy, Content-Based Retrieval of Retinal Images for Maculopathy, ACM International Health Informatics Symposium, November, 2010

Journal(a) K Sai Deepak, N V Kartheek Medathati and Jayanthi Sivaswamy, Detection and Discrimination of disease related abnormalities, Elsevier Pattern Recognition 2011 (In Press)(b) K Sai Deepak, Jayanthi Sivaswamy, Automatic Assessment of Macular Edema from Color Retinal Images, IEEE Transactions on Medical Imaging 2011

Page 47: Detection and Assessment of Abnormality in Medical Images

Supplementary Slides

Page 48: Detection and Assessment of Abnormality in Medical Images

Imaging Modalities

Computer Aided Diagnosis

Computer Aided Diagnosis

Optical Imaging - Ophthalmology X-ray Imaging - Mammography

• High resolution optical camera• Pupil may be dilated before imaging• Pixel resolutions typically range from 0.5K to ~2K*2K• Radiometric resolution is typically 8 bits per channel

• Low energy X-ray scanner• Displays change of density among tissues• Pixel resolutions can range from 1K2 to 3K2

• Radiometric resolution 8-12 bits

Page 49: Detection and Assessment of Abnormality in Medical Images

CAD in Disease Screening – Diabetic Retinopathy

Disease ScreeningDisease Screening

Hemorrhage Detection

Exudate Detection

Neovascularization Detection

MicroaneurysmsDetection

FP1

FP2

FP3

FP4

Maximum False alarms in disease centric approach – FP1 + FP2 + FP3 + FP4

Page 50: Detection and Assessment of Abnormality in Medical Images

CAD – Retinopathy (Color Fundus Image)

Disease ScreeningDisease Screening

Page 51: Detection and Assessment of Abnormality in Medical Images

CAD – Breast Lesions (Mammograms)

Benign Lesion Malignant Lesion

Disease ScreeningDisease Screening

Page 52: Detection and Assessment of Abnormality in Medical Images

Illumination and Contrast

Disease ScreeningDisease Screening

• Presence of one or more of additive bias, multiplicative bias and difference in brightness

• These variations often increases the complexity of modeling the normal background especially when there can be several other structures present in the normal image

Page 53: Detection and Assessment of Abnormality in Medical Images

Tissue Variation (Pigmentation & Density)

Disease ScreeningDisease Screening

• Tissue characteristics for the same structure can vary across race and often across patients, within a race.

• This variation manifests as differences in intensity, hue and/or pigmentation• These variations can be significant enough for an automated disease detection

technique to classify an image as abnormal

Page 54: Detection and Assessment of Abnormality in Medical Images

CAD with Images - Visualization

Computer Aided Diagnosis

Computer Aided Diagnosis

MAP of Sagittal view Bones appear bright in X-ray

52 year old Patient with Back Pain

WindowingTissues of varying densities can be examined

Page 55: Detection and Assessment of Abnormality in Medical Images

CAD with Images - Detection

Computer Aided Diagnosis

Computer Aided Diagnosis

Normal Retina Abnormal Retina

Page 56: Detection and Assessment of Abnormality in Medical Images

CAD with Images – Segmentation

Computer Aided Diagnosis

Computer Aided Diagnosis

Original Image Vessels Segmented

Page 57: Detection and Assessment of Abnormality in Medical Images

Feature Extraction-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

• To effectively describe motion pattern, we use a descriptor derived from the Radon space

- is the integral of motion pattern along a line oriented at and distance from the origin

The desired feature vector is obtained by concatenating projections from each bin at different orientations

Page 58: Detection and Assessment of Abnormality in Medical Images

PCA DD-Showcase 1- Retinopathy

-Showcase 1- Retinopathy

Wd*k is a matrix of first k eigen vectors

Xproj = W(WTW)-1 WX

Vector X is projected on the new sub-space

Re-construction error e(X) is computed as,e(X) = || X - Xproj||2