Gaussian scale-space theory. Workshop, Copenhagen, Denmark, May 1996
[The articles of this volume will not be indexed individually.] This book consists in a collection of 16 articles entirely devoted to Gaussian scale space theory. A quite ``lyrical'' introduction is given by J. Koenderink and the book himself is split in four parts. The Application part gives hints on how the theory can be exploited in practice. The first article is fairly general and demonstrate how the theory allows to compute more robust differential invariants. The two other chapters are more task specific. One about finger prints, the other about optical flow and stereo. The Foundation part presents the theory and its historical development at various levels of mathematical abstraction. The chapter 4 is about historical precursors. Chapters 5, 6 and 7 are mainly about axiomatics of the theory. Chapters 8 and 9 respectively deal with Euclidean invariants and relations between image stochastic analysis and scale space smoothing. The Structure part is about classification of singularities: what kind of phenomena can appear or disappear along the scale. This is treated using codimension, Morse theory, critical points topological numbers and watershed segmentation in the chapters 10 to 14. The two last chapters are the Nonlinear extensions part. Chapter 15 is devoted to the morphological equivalent of the Gaussian scale space and chapter 16 treats of the Perona-Malik model which is one of the schemes allowing edge preservation in the scale space at the price of linearity. The main difficulty of this publication is the wide mathematical prerequisite necessary to encompass all the articles, especially in the two central parts.
scientific article; zbMATH DE number 1120272