pattern recognition in medical images

Pattern Recognition in Medical Images

Dr.S.SridharAnna University

Introduction

•“One picture is worth more than ten thousand words”

•Anonymous

Contents

•This lecture will cover:– Overview of Medical Imaging – Pattern Recognition Tasks – Case Studies in Pattern Recognition

What is Medical Image Processing?

• MI focuses on two major tasks– Improvement of pictorial information for human

interpretation– Processing of image data for storage, transmission

and representation for autonomous machine perception

•Some argument about where image processing ends and fields such as image analysis and computer vision start

Examples: Medicine

•Take slice from MRI scan of canine heart, and find boundaries between types of tissue

– Image with gray levels representing tissue density– Use a suitable filter to highlight edges

Original MRI Image of a Dog Heart Edge Detection Image

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Key Stages in Digital Image Processing

Image Acquisition

Image Restoration

Morphological Processing

Segmentation

Representation & Description

Image Enhancement

Object Recognition

Problem Domain

Colour Image Processing

Image Compression

Dr V.F. Ruiz SE1CA5 Medical Image Analysis 7

Medical Image Systems• The last few decades of the 20th century has seen the development of:

– Computed Tomography (CT)– Magnetic Resonance Imaging (MRI)– Digital Subtraction Angiography– Doppler Ultrasound Imaging– Other techniques based on nuclear emission e.g:

• PET: Positron Emission Tomography• SPECT: Single Photon Emission Computed Tomography

• Provide a valuable addition to radiologists imaging tools towards ever more reliable detection and diagnosis of diseases.

• More recently conventional x-ray imaging is challenged by the emerging flat panel x-ray detectors.


• General image processing whether it is applied to:– Robotics– Computer vision– Medicine– etc.

will treat:– imaging geometry– linear transforms– shift invariance– frequency domain– digital vs continuous domains– segmentation– histogram analysis– etc

that apply to any image modality and any application


• General image analysis regardless of its application area encompasses:– incorporation of prior knowledge– classification of features– matching of model to sub-images– description of shape– many other problems and approaches of AI...

• While these classic approaches to general images and to general applications are important, the special nature of medical images and medical applications requires special treatments.


Special nature of medical images• Derived from

– method of acquisition– the subject whose images are being acquired

• Ability to provide information about the volume beneath the surface– though surface imaging is used in some applications

• Image obtained for medical purposes almost exclusively probe the otherwise invisible anatomy below the skin.

• Information may be from:– 2D projection acquired by conventional radiography– 2D slices of B-mode ultrasound– full 3D mapping from CT, MRI, SPECT, PET and 3D

ultrasound.


difficulties/specificities• Radiology: perspective projection maps physical points into image

space– but, detection and classification of objects is confounded to over- and

underlying tissue (not the case in general image processing).• Tomography: 3D images bring both complication and simplifications

– 3D topography is more complex than 2D one.– problem associated with perspective and occlusion are gone.

• Additional limitation to image quality:– distortion and burring associated with relatively long acquisition time

(due to anatomical motion).– reconstruction errors associated with noise, beam hardening etc.

• All these and others account for the differences between medical and non medical approaches to processing and analysis.


• Advantage of dealing with medical images:– knowledge of what is and what is not normal human

anatomy.– selective enhancement of specific organs or objects via

injection of contrast-enhancing material.

• All these differences affect the way in which images are processed and analysed.

• Validation of medical image processing and analysis techniques is also a major part of medical application– validating results is always important– the scarcity of accurate and reliable independent standards

create another challenge for medical imaging field.


Processing and Analysis• Medical image processing

– Deals with the development of problem specific approaches to enhancement of raw medical data for the purposes of selective visualisation as well as further analysis.

• Medical image analysis– Concentrates on the development of techniques to

supplement the mostly qualitative and frequently subjective assessment of medical images by human experts.

– Provides a variety of new information that is quantitative, objective and reproducible

MIPR Lecture 1Copyright Oleh Tretiak, 2004 14

Examples of Medical Images


Questions

• What does the image show?• What good is it?• How is it made?


X-ray Image


X-ray Image of Hand


What is it?

• Two X-ray views of the same hand are formed on an single film by exposing the hand onto half of the film while the other half is blocked by an opaque screen.


What good is it?

• A fracture of the middle finger is seen on both views, though it is clearer on the view on the left. This image can be used for diagnosis - to distinguish between a sprain and a fracture, and to choose a course of treatment.


X-ray Imaging: How it works.

X-ray shadow cast by an object Strength of shadow depends on composition and thickness.


Summary: X-ray Imaging

• Oldest non-invasive imaging of internal structures• Rapid, short exposure time, inexpensive• Unable to distinguish between soft tissues in head,

abdomen• Real time X-ray imaging is possible and used during

interventional procedures.• Ionizing radiation: risk of cancer.


CT (Computed Tomography)

CT Image of plane throughliver and stomach Projection image

from CT scans


What Is It?

• Computer Tomography image of section through upper abdomen of patient prior to abdominal surgery.

• Section shows ribs, vertebra, aorta, liver (image left), stomach (image right) partially filled with liquid (bottom).


What Good Is It?

• The set of CT images, from the heart down to the coccyx, was used in planning surgery for the alleviation of intestinal blockage.

• The surgery was successful (I’m still here).


Computer Tomography:How It Works

Only one plane is illuminated. Source-subject motion provides added information.


Fan-Beam Computer Tomography


Summary of X-Ray CT

• Images of sectional planes (tomography) are harder to interpret

• CT can visualize small density differences, e.g. grey matter, white matter, and CSF. CT can detect and diagnose disease that cannot be seen with X-ray.

• More expensive than X-ray, lower resolution.• Ionizing radiation.


Functional Magnetic Resonance Imaging

From http://www.fmri.org/Picture naming task

Plane 3

Plane 6

http://www.fmri.org/


What Is It?

• Two of sixteen planes through brain of subject participating in an image-naming experiment.

• Images are superposition of anatomical scans (gray) and functional scans (colored).

• Plane 3 shows functional activity in the visual cortex (bottom)

• Plane 5 shows activity in the speech area ( image right).


What Good Is It?

• This set of images is part of research on brain function (good for publication).

• Functional imaging is used prior to brain surgery, to identify structures such as the motor areas that should be avoided, and focal areas for epilepsy, that should be resectioned.


MRI Signal Source

0 H0

When a nuclear magnet is tilted away from the external magnetic field it rotates (precesses) at the Larmour frequency. For hydrogen, the Larmour frequency is 42.6 MHz per Tesla.

H0

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Detected Signal in MRI

Spinning magnetization induces a voltage in external coils, proportional to the size of magnetic moment and to the frequency.

H0

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s(t)


MRI Image Formation

• Magnetic field gradients cause signals from different parts of the body to have different frequencies.

• Signals collected with multiple gradients are processed by computer to produce an image, typically of a section through the body.


Features of MRI

• No ionizing radiation – expected to not have any long-term or short-term harmful effects

• Many contrast mechanisms: contrast between tissues is determined by pulse sequences

• Can produce sectional as well as projection images.• Slower and more expensive than X-ray


Magnetic Resonance Summary

• No ionizing radiation (safe)• Tomography at arbitrary angle• Many imaging modes (water, T1, T2, flow,

neural activity)• Slow• Expensive


Ultrasound Imaging

Twin pregnancy during week 10


What Is It?

• Ultrasound image of a woman’s abdomen• Image shows a section through the uterus.

Two embryos in their amniotic sacs can be seen.


What Good Is It?

• This image allows a safe means for early identification of a twin pregnancy.

• Obstetric ultrasonography can be used to monitor high-risk pregnancies to allow optimal treatment.

• Pre-natal scans are part of baby picture albums.


Ultrasound Scanner• A picture is built up

from scanned lines. • Echosonography is

intrinsically tomographic.

• An image is acquired in milliseconds, so that real time imaging is the norm.

Transducer travel

Object

Image


Ultrasound Imaging Overview

• Imaging is in real time - used for interventional procedures.

• Moving structures and flow (Doppler) can be seen. Used for heart imaging.

• Ultrasound has no known harmful effects (at levels used in clinical imaging)

• Ultrasound equipment is inexpensive• Many anatomical regions (for example, Head) cannot

be visualized with ultrasound.


Single Photon Computed Tomography

Images on left show three sections through the heart.A radioactive tracer, Tc99m MIBI (2-methoxy isobutyl isonitride) is injected and goes to healthy heart tissue.


What Is It?

• Three sectional (tomographic) images of a living heart. Colored areas are measures of metabolic activity of left ventricle muscle. Areas damaged by an infarct appear dark. This seems to be a normal heart.


What Good Is It?

• Used for staging (choosing treatment before or after a heart attack), and monitoring the effectiveness of treatment.


Radionuclide Imaging

• Basic Idea• Collimator• Tomography

Basic idea: A substance (drug) labeled with a radioactive isotope is ingested. The drug goes to selective sites.


Collimator

Only rays that are normal to the camera surface are detected.


SPECT

Single Photon Emission Computed Tomography. Shown here is a three-headed tomography system. The cameras rotate around the patient. A three-dimensional volume is imaged.

Gamma camera

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Features of Radionuclide Imaging

• The image is produced from an agent that is designed to monitor a physiological or pathological process– Blood flow– Profusion– Metabolic activity– Tumor– Brain receptor concentration


Fluorescence Microscopy

Image of living tissue culture cells. Three agents are used to form this image. They bond to the nucleus (blue), cytoskeleton (green) and membrane (red).


What Is It?

• Optical microscope image of tissue culture.• Image is formed with fluorescent light.• Tree agents are used. They bond to

– DNA in nucleus, blue– Cytoskeleton, green– Lipid membranes, red


What Good Is It?

• This image seems to be a demonstration of fluorescent agents.

• Tissue culture is used in pharmaceutical and physiological research, to monitor the effect of drugs at the cellular level.

• Fluorescent labeling and imaging allows in-vivo evaluation of the location and mechanism of a drug’s activity.


Optical Imaging

• Optical imaging (visible and near infrared) is undergoing very rapid development.

• Like radionuclide imaging, agents can be designed to bind to almost any substrate.

• Intrinsic contrast, such as oxy- vs. deoxy-hemoglobin differential absorption are also exploited.

• There has been a growth in new optical imaging methods.


Thoughts on Imaging

• Three entities in imaging– Object– Image– Observer


Image vs. Object

• Images (and vision) are two-dimensional– Surface images– Projection images– Sectional images (tomograms)

• Image eliminates data– 3D object - 2D image– Moving object - still image


Creative Imaging

• Imaging procedures create information– Functional MRI for the first time allows non-

invasive study of the brain– Doppler ultrasound for the study of flow– Agents for the study of gene expression, in-vivo

biochemistry


CT scan MRI

Same patient


MRI PET


MRI angiogram

X-ray angiograms


ultrasound

Kidney

Breast


fMRI

UCLA Brain Mapping DivisionLos Angeles, CA 90095


Virtual sinus endoscopy of chronic sinusitis. The red structure means inflammatory portion.The trip starts from right nasal cavity and goes through right maxillary sinus and ends at right frontal sinus.


This demonstrates planning of a stereotactic procedure using computerized simulation.

This shows three alternative approaches for a surgical removal of the tumor.

This demonstrates registration of vessels derived from a phase contrast angiogram and anatomy derived from double-echo MR scans.

NeuroSurgeryThis animation is derived from MRI data of a patient with a glioma


Here is an example using Visage on a data source totally different than its original design had anticipated. In this case the data comes from an MR scanner

Flow Analysis

Mammogram 1 Mammogram 2

Mammogram 1

Mammogram 2


• Contrast StretchingTo enhance low-contrast images

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300x180x8: x-tomography of orbital eye slice

256x228xfloat: MRI spine


– Thresholding: special case of clipping,• and the output becomes binary

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Thresholding transformations

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128 138 64x64x8: nuclear medicine image, axial slice of heart


• Logarithmic contrast enhancement– to brighten dark images, apply a logarithmic colour-

table.

– map the pixel values of original:

OriginalLogarithmic colour table


• Exponential contrast enhancement

Original Image Exponential Map


Original Laplacian filtered:high-pass

Sharpened: original added to laplacian


Original Original with a grey-ramp

Rainbow colour table SApseudo colour table


Original image

Increase the image contrast

Subtract the backround image from the original image

Thresholded image


Labelled object in the image


original image

Image courtesy of Alan PartinJohns Hopkins University

binary gradient mask dilated gradient mask binary image with filled holes

cleared border image segmented image outlined original image

© Copyright 2006, Natasha Balac 79

Data Mining Tasks

• Exploratory Data Analysis• Predictive Modeling: Classification and Regression• Descriptive Modeling

– Cluster analysis/segmentation• Discovering Patterns and Rules

– Association/Dependency rules– Sequential patterns– Temporal sequences

• Deviation detection


Data Mining Tasks

Concept/Class description: Characterization and discrimination Generalize, summarize, and contrast data

characteristics, e.g., dry vs. wet regions

Association (correlation and causality) Multi-dimensional or single-dimensional association

age(X, “20-29”) ^ income(X, “60-90K”) buys(X, “TV”)


Data Mining Tasks

Classification and Prediction

Finding models (functions) that describe and distinguish classes or concepts for future prediction

Example: classify countries based on climate, or classify cars based on gas mileage

Presentation: If-THEN rules, decision-tree, classification rule,

neural network Prediction: Predict some unknown or missing

numerical values


• Cluster analysis– Class label is unknown: Group data to form new

classes, • Example: cluster houses to find distribution patterns

– Clustering based on the principle: maximizing the intra-class similarity and minimizing the interclass similarity

Data Mining Tasks


Data Mining Tasks

Outlier analysis Outlier: a data object that does not comply with the

general behavior of the data

Mostly considered as noise or exception, but is

quite useful in fraud detection, rare events analysis

Trend and evolution analysis Trend and deviation: regression analysis

Sequential pattern mining, periodicity analysis


KDD Process

Database

Selection Transformation

Data Preparation

Data Data MiningMining

Training Data

Evaluation, Verification

Model, Patterns

Data Miningin Medicine

Medicine revolves on Pattern Recognition, Classification, and Prediction

Diagnosis: Recognize and classify patterns in multivariate patient attributes

Therapy: Select from available treatment methods; based on effectiveness, suitability to patient, etc.

Prognosis: Predict future outcomes based on previous experience and present conditions

Medical Applications

• Screening• Diagnosis• Therapy• Prognosis• Monitoring• Biomedical/Biological Analysis• Epidemiological Studies• Hospital Management• Medical Instruction and Training

Medical Screening

• Effective low-cost screening using disease models that require easily-obtained attributes:

(historical, questionnaires, simple measurements)• Reduces demand for costly specialized tests (Good for

patients, medical staff, facilities, …) • Examples:

- Prostate cancer using blood tests- Hepatitis, Diabetes, Sleep apnea, etc.

Diagnosis and Classification

• Assist in decision making with a large number of inputs and in stressful situations

• Can perform automated analysis of: - Pathological signals (ECG, EEG, EMG) - Medical images (mammograms, ultrasound, X-ray,

CT, and MRI)• Examples:

- Heart attacks, Chest pains, Rheumatic disorders- Myocardial ischemia using the ST-T ECG complex- Coronary artery disease using SPECT images

Diagnosis and Classification ECG Interpretation

R-R interval

S-T elevation

P-R interval

QRS duration

AVF lead

QRS amplitude SV tachycardia

Ventricular tachycardia

LV hypertrophy

RV hypertrophy

Myocardial infarction

Therapy

• Based on modeled historical performance, select best intervention course: e.g. best treatment plans in radiotherapy

• Using patient model, predict optimum medication dosage: e.g. for diabetics

• Data fusion from various sensing modalities in ICUs to assist overburdened medical staff

Prognosis

• Accurate prognosis and risk assessment are essential for improved disease management and outcome

Examples:– Survival analysis for AIDS patients– Predict pre-term birth risk– Determine cardiac surgical risk– Predict ambulation following spinal cord injury– Breast cancer prognosis

Biochemical/Biological Analysis

• Automate analytical tasks for:- Analyzing blood and urine- Tracking glucose levels- Determining ion levels in body fluids- Detecting pathological conditions

Epidemiological Studies

Study of health, disease, morbidity, injuries and mortality in human communities

• Discover patterns relating outcomes to exposures• Study independence or correlation between diseases• Analyze public health survey data• Example Applications:

- Assess asthma strategies in inner-city children- Predict outbreaks in simulated populations

Hospital Management

• Optimize allocation of resources and assist in future planning for improved services

Examples:- Forecasting patient volume, ambulance run volume, etc.- Predicting length-of-stay for

incoming patients

Medical Instruction and Training

• Disease models for the instruction and assessment of undergraduate medical and nursing students

• Intelligent tutoring systems for assisting in teaching the decision making process

Benefits:

• Efficient screening tools reduce demand on costly health care resources

• Data fusion from multiple sensors• Help physicians cope with the information

overload• Optimize allocation of hospital resources • Better insight into medical survey data• Computer-based training and evaluation

The KFUPM Experience

Medical Informatics Applications

• Modeling obesity (KFU)• Modeling the educational score in school health surveys

(KFU)• Classifying urinary stones by Cluster Analysis of ionic

composition data (KSU)• Forecasting patient volume using Univariate Time-Series

Analysis (KFU)• Improving classification of multiple dermatology disorders

by Problem Decomposition (Cairo University)

Modeling Obesity Using Abductive Networks

• Waist-to-Hip Ratio (WHR) obesity risk factor modeled in terms of 13 health parameters

• 1100 cases (800 for training, 300 for evaluation)• Patients attending 9 primary health care clinics in 1995

in Al-Khobar• Modeled WHR as a categorical variable and as a

continuous variable• Analytical relationships derived from the continuous

model adequately ‘explain’ the survey data

Modeling Obesity:Categorical WHR Model

• WHR > 0.84: Abnormal (1)• Automatically selects most

relevant 8 inputs

Predicted

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Classification Accuracy: 99%

Modeling Obesity:Continuous WHR - Simplified Model

• Uses only 2 variables: Height and Diastolic Blood Pressure

• Still reasonably accurate:– 88% of cases had error within 10%

• Simple analytical input-output relationship

• Adequately explains the survey data

Modeling the Educational Score in School Health Surveys

• 2720 Albanian primary school children• Educational score modeled as an ordinal categorical variable

(1-5) in terms of 8 attributes: region, age, gender, vision acuity, nourishment level,

parasite test, family size, parents education • Model built using only 100 cases predicts output for

remaining 2620 cases with 100% accuracy• A simplified model selects 3 inputs only: - Vision acuity

- Number of children in family - Father’s education

Classifying Urinary Stones by Cluster Analysis of Ionic Composition Data

• Classified 214 non-infection kidney stones into 3 groups

• 9 chemical analysis variables: Concentrations of ions: CA, C, N, H, MG, and radicals: Urate, Oxalate, and Phosphate

• Clustering with only the 3 radicals had 94% agreement with an empirical classification scheme developed previously at KSU, with the same 3 variables

Forecasting Monthly Patient Volume at a Primary Health Care Clinic, Al-Khobar Using

Univariate Time-Series Analysis

• Used data for 9 years to forecast volume for two years ahead

Error over forecasted 2 years: Mean = 0.55%, Max = 1.17%

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Improving classification of multiple dermatology disorders by Problem Decomposition (Cairo University)

- Improved classification accuracy from 91% to 99%- About 50% reduction in the number of required input features

Level 1 Level 2Standard UCI Dataset6 classes of dermatology

disorders34 input featuresClasses split into two

categoriesClassification done

sequentially at two levels

Summary

• Data mining is set to play an important role in tackling the data overload in medical informatics

• Benefits include improved health care quality, reduced operating costs, and better insight into medical data

• Abductive networks offer advantages over neural networks, including faster model development and better explanation capabilities

Classification

Features

• Loosely stated, a feature is a value describing something about your data points (e.g. for pixels: intensity, local gradient, distance from landmark, etc)

• Multiple (n) features are put together to form a feature vector, which defines a data point’s location in n-dimensional feature space

Feature Space

• Feature Space -– The theoretical n-dimensional space occupied by n

input raster objects (features). – Each feature represents one dimension, and its

values represent positions along one of the orthogonal coordinate axes in feature space.

– The set of feature values belonging to a data point define a vector in feature space.

Statistical Notation

• Class probability distribution:

p(x,y) = p(x | y) p(y)

x: feature vector – {x1,x2,x3…,xn}

y: class p(x | y): probabilty of x given y p(x,y): probability of both x and y

Example: Binary Classification

Example: Binary Classification

• Two class-conditional distributions:

p(x | y = 0) p(x | y = 1)

• Priors:

p(y = 0) + p(y = 1) = 1

Modeling Class Densities

• In the text, they choose to concentrate on methods that use Gaussians to model class densities

Modeling Class Densities

Generative Approach to Classification

1. Represent and learn the distribution:

p(x,y)

2. Use it to define probabilistic discriminant functionse.g.

go(x) = p(y = 0 | x) g1(x) = p(y = 1 | x)

Generative Approach to Classification

Typical model:p(x,y) = p(x | y) p(y)

p(x | y) = Class-conditional distributions (densities) p(y) = Priors of classes (probability of class y)

We Want: p(y | x) = Posteriors of classes

Class Modeling• We model the class distributions as multivariate

Gaussians

x ~ N(μ0, Σ0) for y = 0 x ~ N(μ1, Σ1) for y = 1

• Priors are based on training data, or a distribution can be chosen that is expected to fit the data well (e.g. Bernoulli distribution for a coin flip)

Making a class decision

• We need to define discriminant functions ( gn(x) )

• We have two basic choices:– Likelihood of data – choose the class (Gaussian) that best

explains the input data (x):

– Posterior of class – choose the class with a better posterior probability:

Calculating Posteriors

• Use Bayes’ Rule:

• In this case,

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Linear Decision Boundary• When covariances are the same

Linear Decision Boundary

Quadratic Decision Boundary

• When covariances are different

Quadratic Decision Boundary

Clustering• Basic Clustering Problem:

– Distribute data into k different groups such that data points similar to each other are in the same group

– Similarity between points is defined in terms of some distance metric

• Clustering is useful for:– Similarity/Dissimilarity analysis

• Analyze what data point in the sample are close to each other

– Dimensionality Reduction• High dimensional data replaced with a group (cluster) label

Clustering• Cluster: a collection of data objects

– Similar to one another within the same cluster– Dissimilar to the objects in other clusters

• Cluster analysis– Grouping a set of data objects into clusters

• Clustering is unsupervised classification: no predefined classes

• Typical applications– to get insight into data – as a preprocessing step– we will use it for image segmentation

What is Clustering?

Find K clusters (or a classification that consists of K clusters) so that the objects of one cluster are similar to each other whereas objects of different clusters are dissimilar. (Bacher 1996)

The Goals of Clustering • Determine the intrinsic grouping in a set of unlabeled data.

• What constitutes a good clustering?• All clustering algorithms will produce clusters, regardless of whether the data contains them

• There is no golden standard, depends on goal:– data reduction– “natural clusters” – “useful” clusters– outlier detection

Stages in clustering

Taxonomy of Clustering Approaches

Hierarchical Clustering

Agglomerative clustering treats each data point as a singleton cluster, and then successively merges clusters until all points have been merged into a single remaining cluster. Divisive clustering works the other way around.

Single link

Agglomerative Clustering

In single-link hierarchical clustering, we merge in each step the two clusters whose two closest members have the smallest distance.

Complete link

Agglomerative Clustering

In complete-link hierarchical clustering, we merge in each step the two clusters whose merger has the smallest diameter.

Example – Single Link AC

BA FI MI NA RM TO

BA 0 662 877 255 412 996

FI 662 0 295 468 268 400

MI 877 295 0 754 564 138

NA 255 468 754 0 219 869

RM 412 268 564 219 0 669

TO 996 400 138 869 669 0

What is Cluster Analysis?• Finding groups of objects such that the objects in a group

will be similar (or related) to one another and different from (or unrelated to) the objects in other groups

Inter-cluster distances are maximized

Intra-cluster distances are

minimized

Notion of a Cluster can be Ambiguous

How many clusters?

Four Clusters Two Clusters

Six Clusters

Types of Clusters: Contiguity-Based

• Contiguous Cluster (Nearest neighbor or Transitive)– A cluster is a set of points such that a point in a cluster is closer (or

more similar) to one or more other points in the cluster than to any point not in the cluster.

8 contiguous clusters

Types of Clusters: Density-Based

• Density-based– A cluster is a dense region of points, which is separated by low-

density regions, from other regions of high density. – Used when the clusters are irregular or intertwined, and when

noise and outliers are present.

6 density-based clusters

Euclidean Density – Cell-based

• Simplest approach is to divide region into a number of rectangular cells of equal volume and define density as # of points the cell contains

Euclidean Density – Center-based

• Euclidean density is the number of points within a specified radius of the point

Data Structures in Clustering

• Data matrix– (two modes)

• Dissimilarity matrix– (one mode)

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• Standardize data

– Calculate the mean squared deviation:

where

– Calculate the standardized measurement (z-score)

• Using mean absolute deviation could be more robust than

using standard deviation

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• Also one can use weighted distance, parametric Pearson product moment correlation, or other disimilarity measures.

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Similarity and Dissimilarity Between Objects

The set of 5 observations, measuring 3 variables, can be described by its mean vector and covariance matrix. The three variables, from left to right are length, width, and height of a certain object, for example.Each row vector Xrow is another observation of the three variables (or components) for row=1, …, 5.

Covariance Matrix

The mean vector consists of the means of each variable. The covariance matrix consists of the variances of the variables along the main diagonal and the covariances between each pair of variables in the other matrix positions.

0.025 is the variance of the length variable, 0.0075 is the covariance between the length and the width variables, 0.00175 is the covariance between the length and the height variables, 0.007 is the variance of the width variable.

where n = 5 for this example

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Mahalanobis Distance

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Covariance Matrix:

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Mahal(A,B) = 5

Mahal(A,C) = 4

Cosine Similarity

• If x1 and x2 are two document vectors, then cos( x1, x2 ) = (x1 x2) / ||x1|| ||x2|| , where indicates vector dot product and || d || is the length of vector d.

• Example:

x1 = 3 2 0 5 0 0 0 2 0 0 x2 = 1 0 0 0 0 0 0 1 0 2

x1 x2= 3*1 + 2*0 + 0*0 + 5*0 + 0*0 + 0*0 + 0*0 + 2*1 + 0*0 + 0*2 = 5

||x1|| = (3*3+2*2+0*0+5*5+0*0+0*0+0*0+2*2+0*0+0*0)0.5 = (42) 0.5 = 6.481

||x2|| = (1*1+0*0+0*0+0*0+0*0+0*0+0*0+1*1+0*0+2*2) 0.5 = (6) 0.5 = 2.245

cos( x1, x2 ) = .3150

Correlation• Correlation measures the linear relationship

between objects• To compute correlation, we standardize data

objects, p and q, and then take their dot product

)(/))(( pstdpmeanpp kk

)(/))(( qstdqmeanqq kk

qpqpncorrelatio ),(

Visually Evaluating Correlation

Scatter plots showing the similarity from –1 to 1.

K-means Clustering

• Partitional clustering approach • Each cluster is associated with a centroid (center point) • Each point is assigned to the cluster with the closest centroid• Number of clusters, K, must be specified• The basic algorithm is very simple

k-means Clustering

• An algorithm for partitioning (or clustering) N data points into K disjoint subsets Sj containing Nj data points so as to minimize the sum-of-squares criterion

2

1

|| j

K

j Snn

j

xJ

where xn is a vector representing the nth data point and j is the

geometric centroid of the data points in SSjj

K-means Clustering – Details• Initial centroids are often chosen randomly.

– Clusters produced vary from one run to another.• The centroid is (typically) the mean of the points in the cluster.• ‘Closeness’ is measured by Euclidean distance, cosine similarity, correlation, etc.• K-means will converge for common distance functions.• Most of the convergence happens in the first few iterations.

– Often the stopping condition is changed to ‘Until relatively few points change clusters’• Complexity is O( n * K * I * d )

– n = number of points, K = number of clusters, I = number of iterations, d = number of attributes

Two different K-means Clusterings

-2 -1.5 -1 -0.5 0 0.5 1 1.5 2

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y

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Sub-optimal Clustering

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y

Optimal Clustering

Original Points

• Importance of choosing initial centroids

Solutions to Initial Centroids Problem• Multiple runs

– Helps, but probability is not on your side• Sample and use hierarchical clustering to determine initial

centroids• Select more than k initial centroids and then select among

these initial centroids– Select most widely separated

• Postprocessing• Bisecting K-means

– Not as susceptible to initialization issues

Basic K-means algorithm can yield empty clusters

Handling Empty Clusters

Pre-processing and Post-processing

• Pre-processing– Normalize the data– Eliminate outliers

• Post-processing– Eliminate small clusters that may represent outliers– Split ‘loose’ clusters, i.e., clusters with relatively high SSE– Merge clusters that are ‘close’ and that have relatively low

SSE

Bisecting K-means

• Bisecting K-means algorithm– Variant of K-means that can produce a partitional or a hierarchical

clustering

Bisecting K-means Example

Limitations of K-means

• K-means has problems when clusters are of differing – Sizes– Densities– Non-globular shapes

• K-means has problems when the data contains outliers.

Limitations of K-means: Differing Sizes

Original Points K-means (3 Clusters)

Limitations of K-means: Differing Density


Limitations of K-means: Non-globular Shapes


Overcoming K-means Limitations

Original Points K-means Clusters

One solution is to use many clusters.Find parts of clusters, but need to put together.

Overcoming K-means Limitations

Original Points K-means Clusters

Variations of the K-Means Method

• A few variants of the k-means which differ in– Selection of the initial k means– Dissimilarity calculations– Strategies to calculate cluster means

• Handling categorical data: k-modes (Huang’98)– Replacing means of clusters with modes– Using new dissimilarity measures to deal with categorical objects– Using a frequency-based method to update modes of clusters

• Handling a mixture of categorical and numerical data: k-prototype method

The K-Medoids Clustering Method

• Find representative objects, called medoids, in clusters• PAM (Partitioning Around Medoids, 1987)

– starts from an initial set of medoids and iteratively replaces one of the medoids by one of the non-medoids if it improves the total distance of the resulting clustering

– PAM works effectively for small data sets, but does not scale well for large data sets

• CLARA (Kaufmann & Rousseeuw, 1990)– draws multiple samples of the data set, applies PAM on each sample,

and gives the best clustering as the output

• CLARANS (Ng & Han, 1994): Randomized sampling• Focusing + spatial data structure (Ester et al., 1995)

Hierarchical Clustering

• Produces a set of nested clusters organized as a hierarchical tree

• Can be visualized as a dendrogram– A tree like diagram that records the sequences of merges

or splits

1 3 2 5 4 60

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Strengths of Hierarchical Clustering

• Do not have to assume any particular number of clusters– Any desired number of clusters can be obtained by

‘cutting’ the dendogram at the proper level

• They may correspond to meaningful taxonomies– Example in biological sciences (e.g., animal kingdom,

phylogeny reconstruction, …)

Hierarchical Clustering• Two main types of hierarchical clustering

– Agglomerative: • Start with the points as individual clusters• At each step, merge the closest pair of clusters until only one cluster (or k clusters) leftMatlab: Statistics Toolbox: clusterdata, which performs all these steps: pdist, linkage, cluster

– Divisive: • Start with one, all-inclusive cluster • At each step, split a cluster until each cluster contains a point (or there are k clusters)

• Traditional hierarchical algorithms use a similarity or distance matrix– Merge or split one cluster at a time– Image segmentation mostly uses simultaneous merge/split

Agglomerative Clustering Algorithm

• More popular hierarchical clustering technique

• Basic algorithm is straightforward1. Compute the proximity matrix2. Let each data point be a cluster3. Repeat4. Merge the two closest clusters5. Update the proximity matrix6. Until only a single cluster remains

• Key operation is the computation of the proximity of two clusters

– Different approaches to defining the distance between clusters distinguish the different algorithms

Starting Situation

• Start with clusters of individual points and a proximity matrix

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

. Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Intermediate Situation

• After some merging steps, we have some clusters

C1

C4

C2 C5

C3

C2C1

C1

C3

C5

C4

C2

C3 C4 C5

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

Intermediate Situation

• We want to merge the two closest clusters (C2 and C5) and update the proximity matrix.

C1

C4

C2 C5

C3

C2C1

C1

C3

C5

C4

C2

C3 C4 C5

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

After Merging• The question is “How do we update the proximity matrix?”

C1

C4

C2 U C5

C3? ? ? ?

?

?

?

C2 U C5

C1

C1

C3

C4

C2 U C5

C3 C4

Proximity Matrix

...p1 p2 p3 p4 p9 p10 p11 p12

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

.

Similarity?

• MIN• MAX• Group Average• Distance Between Centroids• Other methods driven by an

objective function– Ward’s Method uses squared error

Proximity Matrix

How to Define Inter-Cluster Similarity

p1

p3

p5

p4

p2

p1 p2 p3 p4 p5 . . .

.

.

. Proximity Matrix

• MIN• MAX• Group Average• Distance Between Centroids• Other methods driven by an

objective function– Ward’s Method uses squared error

Hierarchical Clustering: Comparison

Group Average

Ward’s Method

1

2

3

4

5

61

2

5

3

4

MIN MAX

1

2

3

4

5

61

2

5

34

1

2

3

4

5

61

2 5

3

41

2

3

4

5

6

12

3

4

5

Hierarchical Clustering: Time and Space requirements

• O(N2) space since it uses the proximity matrix. – N is the number of points.

• O(N3) time in many cases– There are N steps and at each step the size, N2, proximity

matrix must be updated and searched– Complexity can be reduced to O(N2 log(N) ) time for some

approaches

Hierarchical Clustering: Problems and Limitations

• Once a decision is made to combine two clusters, it cannot be undone

Therefore, we use merge/split to segment images!

• No objective function is directly minimized• Different schemes have problems with one or more

of the following:– Sensitivity to noise and outliers– Difficulty handling different sized clusters and convex

shapes– Breaking large clusters

MST: Divisive Hierarchical Clustering

• Build MST (Minimum Spanning Tree)– Start with a tree that consists of any point– In successive steps, look for the closest pair of points (p, q) such that

one point (p) is in the current tree but the other (q) is not– Add q to the tree and put an edge between p and q

MST: Divisive Hierarchical Clustering

• Use MST for constructing hierarchy of clusters

More on Hierarchical Clustering Methods

• Major weakness of agglomerative clustering methods– do not scale well: time complexity of at least O(n2), where n is the

number of total objects– can never undo what was done previously

• Integration of hierarchical with distance-based clustering– BIRCH (1996): uses CF-tree and incrementally adjusts the quality of sub-

clusters– CURE (1998): selects well-scattered points from the cluster and then

shrinks them towards the center of the cluster by a specified fraction– CHAMELEON (1999): hierarchical clustering using dynamic modeling

Density-Based Clustering Methods

• Clustering based on density (local cluster criterion), such as density-connected points

• Major features:– Discover clusters of arbitrary shape– Handle noise– One scan– Need density parameters as termination condition

• Several interesting studies:– DBSCAN: Ester, et al. (KDD’96)– OPTICS: Ankerst, et al (SIGMOD’99).– DENCLUE: Hinneburg & D. Keim (KDD’98)– CLIQUE: Agrawal, et al. (SIGMOD’98)

Graph-Based Clustering

• Graph-Based clustering uses the proximity graph– Start with the proximity matrix– Consider each point as a node in a graph– Each edge between two nodes has a weight which is the

proximity between the two points– Initially the proximity graph is fully connected – MIN (single-link) and MAX (complete-link) can be viewed

as starting with this graph

• In the simplest case, clusters are connected components in the graph.

Graph-Based Clustering: Sparsification

• Clustering may work better– Sparsification techniques keep the connections to the most

similar (nearest) neighbors of a point while breaking the connections to less similar points.

– The nearest neighbors of a point tend to belong to the same class as the point itself.

– This reduces the impact of noise and outliers and sharpens the distinction between clusters.

• Sparsification facilitates the use of graph partitioning algorithms (or algorithms based on graph partitioning algorithms.

– Chameleon and Hypergraph-based Clustering

Sparsification in the Clustering Process

Cluster Validity

• For supervised classification we have a variety of measures to evaluate how good our model is– Accuracy, precision, recall

• For cluster analysis, the analogous question is how to evaluate the “goodness” of the resulting clusters?

• Then why do we want to evaluate them?– To avoid finding patterns in noise– To compare clustering algorithms– To compare two sets of clusters– To compare two clusters

Clusters found in Random Data

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DBSCAN

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Complete Link

• Numerical measures that are applied to judge various aspects of cluster validity, are classified into the following three types.– External Index: Used to measure the extent to which cluster labels

match externally supplied class labels.• Entropy

– Internal Index: Used to measure the goodness of a clustering structure without respect to external information.

• Sum of Squared Error (SSE)

– Relative Index: Used to compare two different clusterings or clusters. • Often an external or internal index is used for this function, e.g., SSE or entropy

• Sometimes these are referred to as criteria instead of indices– However, sometimes criterion is the general strategy and index is the numerical

measure that implements the criterion.

Measures of Cluster Validity

• Cluster Cohesion: Measures how closely related are objects in a cluster– Example: SSE

• Cluster Separation: Measure how distinct or well-separated a cluster is from other clusters

• Example: Squared Error– Cohesion is measured by the within cluster sum of squares (SSE)

– Separation is measured by the between cluster sum of squares

• Where |Ci| is the size of cluster i

Internal Measures: Cohesion and Separation

i Cx

ii

mxWSS 2)(

i

ii mmCBSS 2)(


• Example:

1 2 3 4 5 m1 m2

m

1091

9)35.4(2)5.13(2

1)5.45()5.44()5.12()5.11(22

2222

Total

BSS

WSSK=2 clusters:

10010

0)33(4

10)35()34()32()31(2

2222

Total

BSS

WSSK=1 cluster:

• A proximity graph based approach can also be used for cohesion and separation.– Cluster cohesion is the sum of the weight of all links within a cluster.– Cluster separation is the sum of the weights between nodes in the

cluster and nodes outside the cluster.


cohesion separation

Clustering

Distance Metrics• Euclidean Distance, in some space (for our purposes,

probably a feature space)

• Must fulfill three properties:

Distance Metrics

• Common simple metrics:

– Euclidean:

– Manhattan:

• Both work for an arbitrary k-dimensional space

Clustering Algorithms

• k-Nearest Neighbor• k-Means• Parzen Windows

k-Nearest Neighbor

• In essence, a classifier• Requires input parameter k

– In this algorithm, k indicates the number of neighboring points to take into account when classifying a data point

• Requires training data

k-Nearest Neighbor Algorithm

• For each data point xn, choose its class by finding the most prominent class among the k nearest data points in the training set

• Use any distance measure (usually a Euclidean distance measure)

k-Nearest Neighbor Algorithm

++

++

-

--

-

-

-e1

1-nearest neighbor:the concept represented by e1

5-nearest neighbors:q1 is classified as negative

q1

k-Nearest Neighbor• Advantages:

– Simple– General (can work for any distance measure you want)

• Disadvantages:– Requires well classified training data– Can be sensitive to k value chosen– All attributes are used in classification, even ones that may

be irrelevant– Inductive bias: we assume that a data point should be

classified the same as points near it

k-Means

• Suitable only when data points have continuous values

• Groups are defined in terms of cluster centers (means)

• Requires input parameter k– In this algorithm, k indicates the number of

clusters to be created• Guaranteed to converge to at least a local

optima

k-Means Algorithm

• Algorithm:1. Randomly initialize k mean values2. Repeat next two steps until no change in

means:1. Partition the data using a similarity measure

according to the current means2. Move the means to the center of the data in the

current partition

3. Stop when no change in the means

k-Means

k-Means• Advantages:

– Simple– General (can work for any distance measure you want)– Requires no training phase

• Disadvantages:– Result is very sensitive to initial mean placement– Can perform poorly on overlapping regions– Doesn’t work on features with non-continuous values (can’t compute

cluster means)– Inductive bias: we assume that a data point should be classified the

same as points near it

Parzen Windows

• Similar to k-Nearest Neighbor, but instead of using the k closest training data points, its uses all points within a kernel (window), weighting their contribution to the classification based on the kernel

• As with our classification algorithms, we will consider a gaussian kernel as the window

Parzen Windows• Assume a region defined by a d-dimensional

Gaussian of scale σ • We can define a window density function:

• Note that we consider all points in the training set, but if a point is outside of the kernel, its weight will be 0, negating its influence

S

j

jSxGS

xp1

2),)((

1),(

Parzen Windows

Parzen Windows

• Advantages:– More robust than k-nearest neighbor– Excellent accuracy and consistency

• Disadvantages:– How to choose the size of the window?– Alone, kernel density estimation techniques

provide little insight into data or problems

Case study: polyp detection

• Step 1: CT scan of patient• Step 2: Segmentation of colon

Paik, et al.


• Step 3: detection of polyp candidates – Hough transform (looking for spheres)

Paik, et al.


• Step 4: feature extraction

• Step 5: classification– Take your pick of algorithms (SVM, ANN, etc.)

Gokturk, et al.


• Step 6: Flythrough colon giving information to physician for final diagnosis (not yet realized)

Paik, et al.


Paik, et al.

Future…

Two categories of interest

• Applications of standard computer vision techniques into the medical domain– Segmentation– Computer-Aided Detection

• New techniques from medical image analysis added to the vision toolbox– Multi-modal registration

Registration

• “The process of establishing a common, geometric reference frame between two data sets.”

• Previously used in vision to align satellite images, generate image mosaics, etc.

Image 1 Image 2 Registered

+ =

Registration in medicine

• Explosion of data, both 2D and 3D from many different imaging modalities have made registration a very important and challenging problem in medicine

© L. Joskowicz (HUJI)Ref_MRI Ref_NMR

Multi-modal registration

Data Set#1

FeatureSelection

FeatureSelection

T

SimilarityMeasure

Optimizer

Transform

Data Set#2


Registration

Preoperative Intraoperative

X-rays

US NMR

CT MRI Fluoro

CAD

Tracking

US

Open MR

Special sensors Video

Combined Data© L. Joskowicz (HUJI)


Data Set#1

FeatureSelection

FeatureSelection

T

SimilarityMeasure

Optimizer

Transform

Data Set#2

Feature selection

• Points-based– 3D points calculated using an

optical tracker

• Surfaces– Extracted from images using

segmentation algorithms

• Intensities– Uses the raw voxel data itself


Data Set#1

FeatureSelection

FeatureSelection

T

SimilarityMeasure

Optimizer

Transform

Data Set#2

Optimization

• Gradients– Gradient descent– Conjugate-gradient– Levenburg-Marquardt

• No gradients– Finite-difference gradient + above– Best-neighbor search– Nelder-Mead– Simulated annealing


Data Set#1

FeatureSelection

FeatureSelection

T

SimilarityMeasure

Optimizer

Transform

Data Set#2

Transformations

• Rigid (6 DOF)– 3 rotation– 3 translation

• Affine (12 DOF)– 6 from before– 3 scale– 3 skew

• Non-rigid (? DOF)– As many control points as

your favorite supercomputer can handle

© T. Rohlfing (Stanford)


Data Set#1

FeatureSelection

FeatureSelection

T

SimilarityMeasure

Optimizer

Transform

Data Set#2

Similarity measures

• Intra-modality– normalized cross-correlation– gradient correlation– pattern intensity– sum of squared differences

• Inter-modality– mutual information (the industry standard)

Example: CT-DSA

Native CT image Post-contrast CT image


Example: CT-DSA

After affine registration B-spline with 10mm c.p.g.


Example: liver motion


Irradiate tumor (T) with a series of directed beams avoiding critical structures (C)

Example: CyberKnife

T

C

RDRDXX

YY

ZZ

The crux of the problem is to match up the coordinate frames of the CT and the radiation delivery device

Example: CyberKnife

XX22

YY22

ZZ22

CTCTXX 22YY 22

ZZ 22

CT

RDRDXX

YY

ZZ

CTCTXX 22YY 22

ZZ 22

Using only 2D projection images!

Example: CyberKnife

RD

CTX 2Y 2

Z 2

X

Y

Z

CT

T1

Example: CyberKnife

DigitallyReconstructedRadiograph

virtual source

RDRDXX

YY

ZZ

RDRDXX

YY

ZZ

CT

T*

DRR

virtual source

RDRDXX

YY

ZZ

RDRDXX

YY

ZZ

Example: CyberKnife

Conclusions

• Medicine is a fertile and active area for computer vision research

• Application of existing vision tools to new, challenging domains

• Development of new vision tools to assist in the practice of medicine

Nov. 25 - 28 257

ObjectivesObjectives

To evaluate the tissue characteristic of kidney To evaluate the tissue characteristic of kidney for implementing unbiased diagnosis procedure for implementing unbiased diagnosis procedure and to classify important kidney orders and to classify important kidney orders

To establish a set of unconstraint features that To establish a set of unconstraint features that are independent to kidney area variations are independent to kidney area variations

Nov. 25 - 28 258

Sample US kidney ImagesSample US kidney Images

Fig.1 a. Normal image of male with age 38 years, b. Medical renal diseases image of male Fig.1 a. Normal image of male with age 38 years, b. Medical renal diseases image of male with age 45 years and c. Cortical polycystic disease image of female with age 51 years.with age 45 years and c. Cortical polycystic disease image of female with age 51 years.

(a) (b) (c)

Nov. 25 - 28 259

Material and MethodsMaterial and Methods • Image Data CollectionImage Data Collection

• Two types of scanning systems namely ATL HDI 5000 Two types of scanning systems namely ATL HDI 5000 curvilinear probe with transducer frequency of 5 – 6 MHz and curvilinear probe with transducer frequency of 5 – 6 MHz and WiproGE LOGIC 400 curvilinear probe with transducer WiproGE LOGIC 400 curvilinear probe with transducer frequency of 3 – 5 MHz.frequency of 3 – 5 MHz.

• The longitudinal cross section of the kidney is taken by fixing The longitudinal cross section of the kidney is taken by fixing the transducer frequency at 4 MHz.the transducer frequency at 4 MHz.

• In each class 50 images are obtained. In total 150 images are In each class 50 images are obtained. In total 150 images are pre-processed before feature extraction.pre-processed before feature extraction.

• The necessary care has been taken to preserve the shape, The necessary care has been taken to preserve the shape, size and gray-level distribution as it obliterates the size and gray-level distribution as it obliterates the sonographic content of information.sonographic content of information.

Nov. 25 - 28 260

Material and MethodsMaterial and Methods• Image Pre-processingImage Pre-processing

Segmentation by higher order Segmentation by higher order spline interpolation after up-spline interpolation after up-sampling of distributed sampling of distributed coordinate coordinate

Rotation to zero degree axisRotation to zero degree axis

Retaining the pixel of interestRetaining the pixel of interest

Estimation of Content Estimation of Content Descriptive FeaturesDescriptive FeaturesKidney CharacterizationKidney Characterization

261

Material and MethodsMaterial and Methods• Image Pre-processingImage Pre-processing

Input US Input US kidney imagekidney image

ii-HSIC -HSIC segmentationsegmentation

Image rotation Image rotation to zero degree to zero degree reference axisreference axis

Unbounded pixel Unbounded pixel eliminationelimination

Nov. 25 - 28

Nov. 25 - 28 262

Material and MethodsMaterial and Methods• Feature ExtractionFeature Extraction

• First order gray level statistical featuresFirst order gray level statistical features

• Second order gray level statistical featuresSecond order gray level statistical features

• Algebraic moment invariants featuresAlgebraic moment invariants features

• Multi-scale differential featuresMulti-scale differential features

• Power spectral features Power spectral features

• Dominant Gabor wavelet featuresDominant Gabor wavelet features

263


• First order gray level statistical featuresFirst order gray level statistical features

– mean (M1), dispersion (M2), variance (M3), average energy mean (M1), dispersion (M2), variance (M3), average energy (M4), skewness (M5), kurtosis (M6), median (M7) and mode (M4), skewness (M5), kurtosis (M6), median (M7) and mode (M8)(M8)

• Second order gray level statistical featuresSecond order gray level statistical features

– energy (E), entropy (H), correlation (C), inertia (In) and energy (E), entropy (H), correlation (C), inertia (In) and homogeneity (L) homogeneity (L)

• Algebraic moment invariants featuresAlgebraic moment invariants features

– eight RST invariant features фeight RST invariant features ф11, ф, ф22, ф, ф33, ф, ф44, ф, ф55, ф, ф66, ф, ф77 and ф and ф55/ф/ф11

Nov. 25 - 28

264


• Multi-scale differential featuresMulti-scale differential features

– two principal curvature features namely isophote (N) and two principal curvature features namely isophote (N) and flowline (T) are computed. From these values of N and T, a set flowline (T) are computed. From these values of N and T, a set of MSDF’s are then determined, namely, the mean (Nmean; of MSDF’s are then determined, namely, the mean (Nmean; Tmean), maximum (Nmax; Tmax) and minimum (Nmin; Tmin) Tmean), maximum (Nmax; Tmax) and minimum (Nmin; Tmin)

• Power spectral featuresPower spectral features

– six power spectral features denoted by six power spectral features denoted by and are estimated at the specific cut-off frequencies and are estimated at the specific cut-off frequencies in the spectrum and by considering global mean total power. in the spectrum and by considering global mean total power.

• Dominant Gabor wavelet featuresDominant Gabor wavelet features

– Out of 30 Gabor wavelets, a unique Dominant Gabor Wavelet Out of 30 Gabor wavelets, a unique Dominant Gabor Wavelet is determined by estimating the similarity metrics between is determined by estimating the similarity metrics between original and reconstructed Gabor image. The Gabor features original and reconstructed Gabor image. The Gabor features ‘μ‘μmnmn’, ‘σ’, ‘σmnmn’ and ‘AAD’ and ‘AADmnmn’ are then evaluated using Dominant ’ are then evaluated using Dominant

Gabor WaveletGabor Wavelet

1WT 2W

T 1

12

RWT 2

12

RWT

3

1

RWT d 4

1

RWT d

Nov. 25 - 28

265

Decision Support System For Kidney ClassificationDecision Support System For Kidney Classification

.

.

.

.

Input feature Input feature vectorvector

IIjj

Fuzzification Fuzzification ffjj

All 36All 36If If

X≥n/X≥n/22

YesYesNRNR

NoNo

Initiate Initiate Optimized Optimized

MBPNMBPN

MRDMRD

CCCCFuzzy rulesFuzzy rules

FISFIS

Hybrid fuzzy-neural systemHybrid fuzzy-neural system

Nov. 25 - 28

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