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

IIT Kharagpur Research Monograph Series. Boca Raton, FL: CRC Press (ISBN 978-1-4665-0567-4/hbk; 978-1-4665-0568-1/ebook). xxvii, 274 p. (2013).

We live in the real world, to which Euclidean geometry is applied. However, when we deal with digital images or 3D objects digital geometry has to be used. This book treats different digital geometries in 2D and 3D spaces. It presents interesting properties of these geometries and their practical applications to image processing, especially to object representation and shape analysis.
The book consists of seven chapters. In the first chapter the digital topology fundamentals are presented. Chapter 2 is related to neighborhoods and paths in a metric space. Chapter 3 presents methods of straight lines and planes digitization followed by Chapter 4 with digital straightness and polygonal approximation methods. Next chapter describes methods of parametric, mainly conic, curves estimation and reconstruction. Chapter 6 treats medial axis transform computation. Finally, Chapter 7 ends the book with digital geometric approaches for surfaces modeling.
This book presents many research results from the last three decades on digital geometry. It is written in an accessible way full of images, examples, pseudocode and exercises. It is suitable for professionals or graduate students who want to understand the theory and implement algorithms of digital image analysis. It can be used for a self study as well as a course book.

Keywords:

digital geometry;image processing;digital topology;digital distance;line digitization;surface digitization;medial axis transform