Given a pure image *I* from some ensemble observed by some technology that produces a noisy version of it, say a deformed image *I*^{D}, can we construct an algorithm that restores *I* from *I*^{D} so well that we judge the restored picture *I*^{*} to be a reasonably faithful copy of *I*? For the same problem, but given a subset , can we design a test that discovers when with accuracy comparable to that of human judgment and that locates the pathology in the shape? This book reports the results of an experiment dealing with these problems.

The first chapter is a concise description of a pattern-theoretic approach to image understanding based on structural restoration, which was developed by Grenander in the beginning of the 1980s. Chapters 2 and 3 contain the mathematical results necessary to overcome the computational obstacles to pattern synthesis and pattern analysis. These theoretical results are incorporated in some APL programs. The next two chapters persuasively present the experiment of applying Grenander’s approach for real patterns (digital pictures of hands with many sorts of visual noise); these chapters include more than 40 full-color illustrations. When the noise is made successively more severe, the algorithms are pushed to the point at which they start to perform poorly. The book ends with a pertinent model critique and four appendices containing, among other things, the experimental APL software sources.

The experiment’s basic purpose was to answer the question of whether it is possible to mechanize human intuitive understanding of biological patterns that typically exhibit a lot of variability but also possess characteristic structure. The result of the experiment led to an encouraging answer and thus the book fulfills its basic purpose. To master the mathematical framework you must read Grenander’s earlier book [1]. This book is good, especially because of the practical results. I appreciate the theoretical framework as well and, for those who want to study it further, this book contains a complete reference list. The book is suitable for an advanced graduate seminar in pattern recognition or as an accompanying book for a course in applied probability, computer vision, or pattern recognition.