CRC Press, 2013. — 316 p. — (IIT Kharagpur Research Monograph Series). — ISBN: 1466505672, ISBN-13: 9781466505674
Authors: Jayanta Mukhopadhyay, Partha Pratim Das, Samiran Chattopadhyay, Partha Bhowmick, Biswa Nath Chatterji.In a digital image, each element has an integral coordinate position and has a finite set of points in its neighborhood. On the other hand, a point in a Euclidean space has an infinite number of neighboring points. This indicates that the geometry in the digital image space is non-Euclidean. One must study this geometry and its approximation to the Euclidean world, to correlate the measurements and shape of geometric objects with our common notion of Euclidean geometry. The geometry in the digital space is called digital geometry. However, one should note that this geometry is not unique. In different ways, digital geometry may be defined depending upon the neighborhood definition of a point in the space or the distance functions used for the same purpose. In this book, we discuss different digital geometries in multi-dimensional integral coordinate spaces, and also study some of their interesting properties, including their metric and topological properties, shapes of circles (for 2-D space) and spheres (for 3-D space), proximity to Euclidean norms, and a number of theoretic representations of different geometric objects such as straight lines, circles, etc. We will demonstrate how these concepts and properties are useful in different techniques for image processing and analysis. In particular, their applications in object representation and shape analysis are extensively covered in different chapters of this book.
At IIT Kharagpur, there has always been a strong research group working in this area for about the last three decades. Though there exist some good texts and reference books covering the topics of image processing and digital geometry in general, it is felt by this group of authors that there is a need to connect these two topics highlighting the important results of digital geometry which are used in image analysis and processing. This book is the outcome of that endeavor. The project was also initiated in the diamond jubilee year of this prestigious institute as a part of publishing a series of monographs highlighting the continuing research and development activities in different areas. However, while writing this book we treated all the topics comprehensively elucidating the important and significant results of other researchers. Nevertheless in all the topics, as there is a significant research contribution by the authors themselves, it adds more depth and clarity in their presentation. We hope the book will be useful to the researchers in these areas, and also in teaching advanced topics in image processing and digital geometry to graduate and research students.Digital Topology: Fundamentals
Distance Functions in Digital Geometry
Digitization of Straight Lines and Planes
Digital Straightness and Polygonal Approximation
Parametric Curve Estimation and Reconstruction
Medial Axis Transform
Modeling of a Voxelated Surface
