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**Recognizing planar objects using invariant image features.**
*(English)*
Zbl 0789.68120

Lecture Notes in Computer Science 676. Berlin: Springer-Verlag (ISBN 3-540-56713-5). X, 180 p. (1993).

This book deals with the question of how computers recognize an object irrespective of its size, position and its orientation. The basic approach is to find mathematical functions of an object’s image, or of an object’s \(3-D\) description, that are invariant under the transformations caused by the object’s motion. The book introduces the notion of image invariants for planar objects.

Major sections are as follows. The first chapter introduces features that are invariant under translation, rotation and changes in size and in contrast, with particular attention paid to the effect of using discrete images as opposed to continuous ones. Next, a tutorial introduction to the theory of algebraic invariants is presented with emphasis on moment invariants for affine transformations, and projective invariants for perspective transformations. The next two chapters are devoted entirely to affine and perspective invariants, summarizing work on both differential and global invariants. The main contribution (Chapter 6) shows how invariant features can be used to recognize objects that have been partially occluded. A treatment of the so called geometric hashing is given, followed by some methods of back projection which allow one to verify whether the hypothesized object really is in the image. Finally, a number of schemes for the use of moment invariants are presented to allow recognition under partial occlusion. A summary and conclusions close the book.

Major sections are as follows. The first chapter introduces features that are invariant under translation, rotation and changes in size and in contrast, with particular attention paid to the effect of using discrete images as opposed to continuous ones. Next, a tutorial introduction to the theory of algebraic invariants is presented with emphasis on moment invariants for affine transformations, and projective invariants for perspective transformations. The next two chapters are devoted entirely to affine and perspective invariants, summarizing work on both differential and global invariants. The main contribution (Chapter 6) shows how invariant features can be used to recognize objects that have been partially occluded. A treatment of the so called geometric hashing is given, followed by some methods of back projection which allow one to verify whether the hypothesized object really is in the image. Finally, a number of schemes for the use of moment invariants are presented to allow recognition under partial occlusion. A summary and conclusions close the book.

Reviewer: A. Leitsch (Wien)