This book is the first in a series of perception engineering books from Springer-Verlag. As such, it shows great promise for the series.

The book describes in detail the author’s approach to segmenting range images, which has application to images formed using other sensing modalities. The approach is general because it is based simply on the three-dimensional properties of mathematical surfaces and assumes only that desirable regions are piecewise smooth. The approach is data-driven rather than model- or hypothesis-driven.

The author describes the main steps of the segmentation algorithm chapter-by-chapter. Where appropriate, each chapter begins with general theory and progresses to the author’s approach and particular implementation decisions.

Chapter 1 gives an overview of the problem, describes the basic approach used, and presents a too-brief and slightly outdated literature review of surface characterization and image segmentation research. Chapter 2 provides a mathematical description of the problem of recognizing objects in range images and, in particular, the subproblem of digital surface segmentation. Such a segmentation produces three main items: (1) a list of two-dimensional image regions, each corresponding to the projection of a piecewise-smooth portion of the input image, (2) a list of the approximating smooth surface functions, one for each region, and (3) a list of the approximation errors for each region.

Chapter 3 first reviews the differential geometry concepts that will be needed later and then discusses potential mathematical invariants to characterize surfaces. The author chooses the mean and Gaussian curvature measures and provides support for that choice. He presents techniques to estimate the chosen invariants along with experimental results.

In chapter 4, region growing based on variable-order function fitting is used to obtain the required symbolic representations of the original image. This forms the heart of the author’s technique. The region-growing algorithm begins with seed regions, which are found via a novel method requiring repeated applications of the erosion (dilation) operator on sign maps of the invariant features chosen above. Regions are grown about the seeds by first fitting the simplest function in a fixed set of totally ordered functions via a least-squares technique. A “large” RMS error triggers the fitting of the next, more complex, function from the ordered set of fitting functions. The RMS error threshold and final triggering are performed by the application of two novel tests. Finally, pixels compatible with the current functional fit are added to the current region and the process is repeated until no further pixels can be added. The chapter contains an excellent discussion of the termination conditions of this process.

Chapter 5 discusses the formation of a region adjacency graph and considers the final region segmentation output. Chapter 6 discusses converting the nonparametric representation of region edges into a parametric representation, utilizing a technique similar to the above fitting technique for surfaces, here called variable-order edge fitting.

Chapter 7 discusses in detail the results of applying the author’s algorithms to 22 test images. Chapter 8 provides conclusions and suggestions for future research. Finally, various appendices cover special topics, such as least squares surface fitting.

From an image understanding point of view, the author’s presentation is delightfully rigorous. He has described all of his algorithms in a precise mathematical style and all decision, when not rigorous, are well justified.

While the test database described in chapter 7 is rather small (22 items), the segmentation results appear very good, especially considering the wide range of quality and types of images used. A comparison study to other methods of image segmentation still needs to be made, however.

The book is a revised version of the author’s Ph.D. dissertation. As such, it has the strengths and weaknesses implied by its origin. It treats certain predilections of the author in too much depth, but it does give precise details on the methods and techniques used in segmentation. The presentation is mathematically rigorous and, though it tends to be long-winded in spots, it is not tutorial.

As the author presents his work with a good deal of mathematical sophistication, the manuscript would be strengthened by a table of notations used. Also, an index of terms would prove very useful. I recommend this book to all researchers in machine vision, as well as those interested in beginning such research.