Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques, 1st Edition (Hardback) book cover

Medical Image Processing

Advanced Fuzzy Set Theoretic Techniques, 1st Edition

By Tamalika Chaira

CRC Press

236 pages | 182 B/W Illus.

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Medical image analysis using advanced fuzzy set theoretic techniques is an exciting and dynamic branch of image processing. Since the introduction of fuzzy set theory, there has been an explosion of interest in advanced fuzzy set theories—such as intuitionistic fuzzy and Type II fuzzy set—that represent uncertainty in a better way.

Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques deals with the application of intuitionistic fuzzy and Type II fuzzy set theories for medical image analysis. Designed for graduate and doctorate students, this higher-level text:

  • Provides a brief introduction to advanced fuzzy set theory, fuzzy/intuitionistic fuzzy aggregation operators, and distance/similarity measures
  • Covers medical image enhancement using advanced fuzzy sets, including MATLAB®-based examples to increase contrast of the images
  • Describes intuitionistic fuzzy and Type II fuzzy thresholding techniques that separate different regions/leukocyte types/abnormal lesions
  • Demonstrates the clustering of unwanted lesions/regions even in the presence of noise by applying intuitionistic fuzzy clustering
  • Highlights the edges of poorly illuminated images and uses intuitionistic fuzzy edge detection to find the edges of different regions
  • Defines fuzzy mathematical morphology and explores its application using the Lukasiewicz operator, t-norms, and t-conorms

Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques is useful not only for students, but also for teachers, engineers, scientists, and those interested in the field of medical image analysis. A basic knowledge of fuzzy set is required, along with a solid understanding of mathematics and image processing.


"The book treats the most commonly used fuzzy methods in medical image analysis. It does focus on widely used approaches and refrains from methods, which are still under investigations. This increases its value for practitioners, senior students and young researchers… Clearly. The book has been written by a dedicated professional (I do not know the author and have never met her). It should be on the desk of everybody who works on medical image analysis and researching the potentials of fuzzy systems."

—Hamid R. Tizhoosh, Affiliation: University of Waterloo, Canada

"This book focuses on the application of clustering algorithms based on intuitionistic fuzzy set model [s]and their application in segmenting and analyzing medical images. …I would like to keep a copy of the book on my shelf.

—Dr.B.K.Tripathy, VIT University, India

"Among the characteristics that make the book Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques a valuable addition to the library of both the medical image processing student and the experienced practitioner, is the detailed and self-contained nature of the subjects treated in each one of the chapters of the book. Moreover, the examples that accompany the theoretical notions of the book, as well as the MATLAB code supporting the applications of fuzzy sets in the area of medical image processing, are of paramount importance for both the novice and the experienced reader.

—Ioannis K. Vlachos, School of Electrical and Computer Engineering National Technical University of Athens

Table of Contents


Organization of the Book


Intuitionistic Fuzzy Set and Type II Fuzzy Set


Intuitionistic Fuzzy Set

Some Operations on Intuitionistic Fuzzy Sets

Fuzzy Complement and Intuitionistic Fuzzy Generator

Intuitionistic Fuzzy Generator

Intuitionistic Fuzzy Relations

Composition of Intuitionistic Fuzzy Relation (Supremum–Infimum)

Composition of Intuitionistic Fuzzy Relation Using Fuzzy t-Norm and t-Conorm



Reflexive Property

Symmetric Property

Transitive Property

Interval-Valued Intuitionistic Fuzzy Set

Type II Fuzzy Set



Medical Image Processing


Image Contrast Enhancement

Image Segmentation

Boundary Detection


Image Registration

Image Fusion

Image Retrieval

Fuzzy Processing of Medical Images

Advanced Fuzzy Processing of Medical Images

Intuitionistic Fuzzy Set

Type II Fuzzy Set

Some Applications of Advanced Fuzzy Set in Medical Image Processing



Fuzzy and Intuitionistic Fuzzy Operators with Application in Decision-Making


Fuzzy Operators

Fuzzy Operators Induced by Fuzzy t-Norm and t-Conorm




Fuzzy Aggregating Operators

Weighted Averaging Operator

Ordered Weighted Averaging Operator

Intuitionistic Fuzzy Weighted Averaging Operator

Generalized Intuitionistic Fuzzy Weighted Averaging Operator

Generalized Intuitionistic Fuzzy Ordered Weighted Averaging Operator

Generalized Intuitionistic Fuzzy Hybrid Averaging Operator

Application of Intuitionistic Fuzzy Operators to Multi-Attribute Decision-Making

Intuitionistic Fuzzy Triangular Norms and Triangular Conorms



Similarity, Distance Measures, and Entropy


Similarity Measure

Similarity/Distance Measure

Distance Measures

Different Types of Distance and Similarity Measures

Intuitionistic Fuzzy Measure

Intuitionistic Fuzzy Information Measure

Intuitionistic Fuzzy Entropy

Different Types of Entropies

Entropy of Interval-Valued Intuitionistic Fuzzy Set

Similarity Measure and Distance Measures of IVIFS



Image Enhancement


Fuzzy Image Contrast Enhancement

Fuzzy Methods in Contrast Enhancement

Contrast Enhancement Using the Intensification Operator

Contrast Improvement Using Fuzzy Histogram Hyperbolization

Contrast Enhancement Using IF-THEN Rules

Contrast Improvement Using the Fuzzy Expected Value

Intuitionistic Fuzzy Enhancement Methods

Entropy-Based Enhancement Methods

Two-Dimensional Entropy–Based Intuitionistic Fuzzy Enhancement (Method II)

Entropy-Based Enhancement Method by Chaira (Method III)

Contrast Enhancement by Chaira (Method IV)

Hesitancy Histogram Equalization

Image Enhancement Using Type II Fuzzy Set

Type II Fuzzy Enhancement (Method I)

Enhancement Using Hamacher t-Conorm

Enhancement Using Type II Fuzzy Set

Introduction to MATLAB®

Examples Using MATLAB®



Thresholding of Medical Images


Threshold Detection Methods

Global Thresholding

Iterative Thresholding

Optimal Thresholding

Locally Adaptive Thresholding

Locally Adaptive and Optimal Thresholding

Fuzzy Methods

Fuzzy Divergence Method

Fuzzy Geometry Method

Fuzzy Clustering Method

Intuitionistic Fuzzy Threshold Detection Methods

Intuitionistic Fuzzy Entropy–Based Method

Intuitionistic Fuzzy Divergence–Based Method

Window-Based Thresholding

Calculation of Membership Function

Thresholding Using Type II Fuzzy Set Theory

Segmentation Using Type II Fuzzy Set Theory

Segmenting Leucocyte Images in Blood Cells

Cauchy Distribution

Examples Using MATLAB®

Type II Fuzzy Thresholding

Intuitionistic Windowed Thresholding Method



Clustering of Medical Images


Fuzzy c Means Clustering

Hierarchical Clustering

Kernel Clustering

Kernel Clustering Methods

Intuitionistic Fuzzy c Means Clustering

Kernel-Based Intuitionistic Fuzzy Clustering

Colour Clustering

Colour Model

Type II Fuzzy Clustering



Edge Detection


Thresholding Method

Hough Transform Method

Boundary-Based Method

Fuzzy Methods

Intuitionistic Fuzzy Edge Detection Method

Template-Based Edge Detection

Edge Detection Using the Median Filter

Fuzzy Edge Image Using Interval-Valued Fuzzy Relation

Construction of Enhanced Fuzzy Edge Using Type II Fuzzy Set

Accurate Edge Detection Technique

Implementation Using MATLAB®

An Example to Find the Edge Image

An Example to Find the Fuzzy Edge Image



Fuzzy Mathematical Morphology


Preliminaries on Morphology

Greyscale Mathematical Morphology

Fuzzy Mathematical Morphology

Different Definitions of Fuzzy Morphology

Fuzzy Morphology Using Lukasiewicz Operator

Fuzzy Morphology Using t-Norms and t-Conorms by De Baets and Kerre and Bloch and Maitre

Opening and Closing Operations

Fuzzy Morphology in Image Processing

Edge Detection

Intuitionistic Fuzzy Approach

Implementation in MATLAB®




About the Author

Tamalika Chaira is a research scientist in the Department of Biotechnology, Government of India, and the Indian Institute of Technology Delhi, New Delhi. Previously, she was a research associate at the National Research Council (CNR), Pisa, Italy. She holds a bachelor’s degree from Bihar Institute of Technology, Sindri, Jharkhand, India; a master’s degree from Bengal Engineering and Science University, Shibpur, Howrah, India; and a Ph.D from the Indian Institute of Technology, Kharagpur, West Bengal. She is an author of the book Fuzzy Image Processing and Applications with MATLAB, as well as numerous papers. She also received the prestigious National Award (Innovative Young Biotechnologist Award, 2010) from the Government of India.

Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Machine Theory