Digital Geometry in Image Processing: 1st Edition (Hardback) book cover

Digital Geometry in Image Processing

1st Edition

By Jayanta Mukhopadhyay, Partha Pratim Das, Samiran Chattopadhyay, Partha Bhowmick, Biswa Nath Chatterji

Chapman and Hall/CRC

318 pages | 105 B/W Illus.

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Hardback: 9781466505674
pub: 2013-04-05

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Exploring theories and applications developed during the last 30 years, Digital Geometry in Image Processing presents a mathematical treatment of the properties of digital metric spaces and their relevance in analyzing shapes in two and three dimensions. Unlike similar books, this one connects the two areas of image processing and digital geometry, highlighting important results of digital geometry that are currently used in image analysis and processing.

The book discusses different digital geometries in multi-dimensional integral coordinate spaces. It also describes interesting properties of the geometries, including metric and topological properties, shapes of circles and spheres, proximity to Euclidean norms, and number theoretic representations of geometric objects such as straight lines and circles. The authors—all active researchers in image processing and digital geometry—demonstrate how these concepts and properties are useful in various techniques for image processing and analysis. In particular, the book covers applications in object representation and shape analysis.

With many figures (some in color) and end-of-chapter exercises, this book provides an in-depth, unified account of digital metrics, the characterization of digital curves and straight lines, and their uses in shape analysis. It gives you insight on the latest two- and three-dimensional image processing applications.


" … there is a lot in this book to like: it covers a great deal of material … . I hope to see a second edition--this book deserves one, and the material deserves plenty of readers."

--Alasdair McAndrew, Computing Reviews, December 2013

Table of Contents

Digital Topology: Fundamentals

Tessellation of a Continuous Space

Digital Grid

Grid Topology

Topology Preserving Operations

The Euler Characteristics

Distance Functions in Digital Geometry

Mathematical Definitions and Notation

Neighborhoods, Paths and Distances

Neighborhood Distances

Path-Dependent Neighborhoods and Distances

Hyperspheres of Digital Distances

Error Estimation and Approximation of Euclidean Distance

Digitization of Straight Lines and Planes

2-D Discrete Straight Line Segments

Iterative Refinement: An Algebraic Characterization

3-D Digital Straight Line Segments

Digital Plane Segments

Digital Straightness and Polygonal Approximation

Digital Straightness

Approximate Straightness

Polygonal Approximation

Approximation on Gray-Scale Images


Parametric Curve Estimation and Reconstruction

Digital Conics in Canonical Form

Circles and Parabolas in Canonical Form

Estimation of Major and Minor Axes of an Ellipse in Canonical Form

Reconstruction of Hyperbola in Canonical Form

A Restricted Class of Digitized Planar Curves

Medial Axis Transform

Distance Transform

Medial Axis Transform (MAT)

Skeletonization using MAT

Geometric Transformation

Computation of Normals at Boundary Points of 2-D Objects

Computation of Cross-Sections of 3-D Objects

Shading of 3D Objects

Modeling of Voxelated Surface

Voxelation and Approximation of 3-D Surface

Voxelation of Surface of Revolution



A Summary appears at the end of each chapter.

About the Authors

Jayanta Mukhopadhyay is a professor in the Department of Computer Science and Engineering at the Indian Institute of Technology (IIT) Kharagpur, where he is currently head of the Department of Computer Science and Engineering and the School of Information and Technology. Dr. Mukhopadhyay was a Humboldt Research Fellow at the Technical University of Munich and has held visiting positions at the University of California-Santa Barbara, University of Southern California, and the National University of Singapore. He is a senior member of the IEEE and a fellow of the Indian National Academy of Engineering (INAE). His research interests include image processing, pattern recognition, computer graphics, multimedia systems, and medical informatics. He has published more than 170 journal articles and conference proceedings in these areas. He received his B.Tech., M.Tech., and Ph.D. in electronics and electrical communication engineering from IIT Kharagpur.

Partha Pratim Das is a professor in the Department of Computer Science and Engineering at IIT Kharagpur. He is also a visiting professor in the Institute of Radio Physics and Electronics at Calcutta University. Dr. Das is a member of the Association for Computing Machinery (ACM) and the VLSI Society of India and a reviewer for ACM Computing Surveys and Pattern Recognition Letters. He has published over 40 technical papers in digital geometry, image processing, parallel computing, and knowledge-based systems and has co-authored a book Digital Geometry in Image Processing. His research interests include object tracking and interpretation in videos, medical information processing, and debugging automation for multi-threaded programs. He obtained his B.Tech., M.Tech., and Ph.D. in electronics and electrical communication from IIT Kharagpur.

Samiran Chattopadhyay is a professor in the Department of Information Technology at Jadavpur University. Dr. Chattopadhyay has authored two textbooks and more than 70 papers in journals and conferences. His research interests include discrete geometry, distributed computing, security, and mobile computing. He received his B.Tech. and M.Tech. from IIT Kharagpur and his Ph.D. from Jadavpur University.

Partha Bhowmick is an assistant professor in the Department of Computer Science and Engineering at IIT Kharagpur. He holds 4 U.S. patents and has published more than 70 research papers in international journals, edited volumes, and refereed conference proceedings. His primary research area is digital geometry with applications to low-level image processing, approximate pattern matching, document image processing and analysis, shape analysis, and biometrics. Dr. Bhowmick earned his B.Tech. from IIT Kharagpur and his M.S. and Ph.D. from the Indian Statistical Institute, Kolkata.

B.N. Chatterji is a professor of electronics and communication engineering and computer science and engineering at the B.P. Poddar Institute of Management & Technology in Kolkata. He was previously a professor of electronics and electrical communication engineering at IIT Kharagpur for more than 38 years. He has authored four textbooks, chapters of several edited books, and more than 200 papers. He is also the recipient of ten national awards. His areas of interest include image processing and pattern recognition.

About the Series

IIT Kharagpur Research Monograph Series

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Subject Categories

BISAC Subject Codes/Headings:
COMPUTERS / Computer Graphics