Refereed full papers (journals, book chapters, international conferences)

1993

Given a familiar object extracted from its surroundings, we humans have little difficulty in recognizing it irrespective of its size, position and orientation in our field of view. Changes in lighting and the effects of perspective also pose no problems. How do we achieve this, and more importantly, how can we get a computer to do this? One very promising approach is to find mathematical functions of an object's image, or of an object's 3D description, that are invariant to the transformations caused by the object's motion. This book is devoted to the theory and practice of such invariant image features, so-called image invariants, for planar objects. Following the introduction in chapter 1, the book discusses features that are invariant to image translations, rotations, to changes in size and contrast, with particular attention being paid to the effect of using discrete images rather than continuous ones. The next chapter presents a tutorial introduction to the theory of algebraic invariants which lies at the heart of two important types of invariant features: moment invariants for affine transformations, and projective invariants for perspective transformations. Chapter 4 is devoted entirely to features invariant to affine transformations: the theory behind moment-based invariants, Fourier descriptors and differential techniques is presented, along with a novel technique based on correlations, and results of experiments on the stability of coarsely sampled images are discussed. Chapter 5 goes one step further and covers features invariant to perspective transformations, summarizing work on both differential and global invariants. The penultimate chapter, chapter 6, shows how invariant features can be used to recognize objects that have been partially occluded. A thorough treatment of the `geometric hashing' method is given, followed by some novel methods of `back-projection' which allows one to verify whether the hypothesized object really is in the image. Many authors claim that moment invariants cannot be used under partial occlusion; this is not so, and a number of schemes for their use are presented. Not only can they be used, but they have some significant advantages over other invariant features, a fact that is backed up by experiments. The final chapter contains a summary and conclusions.