Variational methods in image segmentation with 7 image processing experiments
This book contains synthesis and mathematical analysis of a set of algorithms and theories whose aim is the automatic segmentation of digital images as well as the understanding of visual perception. A variational form is used to obtain a common formalism for these theories and algorithms. Perception theory has to deal with the complex interaction between regions and edges in an image: in the variational segmentation energies, edge terms compete with region terms in a way which is supposed to impose regularity on both regions and boundaries. The second part of the book provides a presentation of the classical theory of rectifiable sets and unrectifiable sets. In the third part of the book it is proven that the competition of 1-D and 2-D energy terms in a variational formulation cannot create fractal-like behavior for the edges.
automatic segmentation of digital images
scientific article; zbMATH DE number 699376