Bézier and Splines in

Image Processing and

Machine Vision


by Sambhunath Biswas and Brian C. Lovell

Springer, December 2007


Reviewed by:  Mark Sugrue


Splines, those piece-wise polynomial functions that take their name from an old shipwright's tool, are becoming the Swiss army knife of the image processing world, used in applications as diverse as image compression and object tracking in video.  Biswas and Lovell's new book, Bézier and Splines in Image Processing and Machine Vision, therefore promises to be a useful addition to the bookshelf.

When I opened it, I was hoping for a book that would bring some order to the smorgasbord of various algorithms and terms that have multiplied under the banner of "splines". I was also hoping to come away with a clear understanding of which splines should be used for what applications, and why. This book does go some way towards satisfying my perhaps excessive demands, but it doesn't quite succeed on every score.

While it does contain a large amount of excellent information and useful derivations, I found the layout and organization were not ideal for quickly finding what I was looking for. 

The book opens with a highly detailed and well written chapter on the Bézier-Bernstein spline. This is followed by a chapter on image segmentation and one on splines and graylevel coding. Both of these chapters contain sections on image compression, and these lead in to Chapter 4, titled "Image Compression".

Based on the title “Image Compression”, I expected a general treatment of the use of spline in compression.  The chapter discusses a single algorithm called Subimage based Lossy Image Compression or SLIC. This algorithm uses the Bézier-Bernstein polynomial and aims to extract regions of common texture within the image. While this is interesting, I believe the layout would have been greatly improved if the image compression content from Chapters 2 and 3 were moved to Chapter 4 to make this chapter more rounded.

The next lengthy chapter comprehensively covers the area of B-splines and their application in machine vision. Also excellent are the chapters on discrete splines and wavelet splines, which provide a strong mathematical foundation for these topics. I question the inclusion of a whole chapter on the area of Beta-splines, even though, as that chapter concludes, theses have not been used in image processing and machine vision.

The final two chapters are by far the most accessible to the novice. Chapter 9 deals with snakes and active contours and begins with a well written guide to using energy minimisation functions to direct a snake. Dynamic programming techniques and the famous Viterbi algorithm are then well explained, with reference to numerous example images. Chapter 10, the final chapter, presents techniques using Global Optimal Energy Minimization Techniques and reads like a case study for the application of snakes  to the field of medical imagery.  I would recommend that the novice reader consider starting with these chapters before moving onto the heavier early chapters.

In general, this book scores highly for content but could improve in organisation and presentation in my opinion. The preface describes splines as "effective, efficient, easy to implement, and [with] a strong and elegant mathematical background." I was hoping for a less mathematical and more ‘hands-on’ approach to the material with practical coding and implementation examples.  A second edition could include more pseudo-code segments, which would clarify the practicality of the sometimes lengthy derivations sections. In summary, this is a mathematics book for the machine vision practitioner.

Click above to go to the publisher’s web page where there is a description of the book and a link to the Table of Contents.

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