A Theory of Shape Identification

What are shapes? Although shape recognition has long been one of the most important topics in computer vision, it is still hard to answer this question in a few words. In this book, shapes are defined as curves that can be recognized up to a given group of transformations. This definition, though tautological in appearance, has a very strong implication: how is it possible to identify two curves as being one and the same? The adopted point of view in this book is that no a priori model is necessary to take such a decision. A perceptual principle, the Helmholtz principle, will be the cornerstone of the decision. It asserts that two shapes should be identified if the probability that their resemblance may be due to chance is very small. Not only this principle may be useful in this identification step, but it will be also used throughout the complete system that will be presented: from the extraction of meaningful pieces of curves in digital images, to the grouping of invariant parts of shapes