Discrete topological transformations for image processing

Abstract

Topology-based image processing operators usually aim at transforming an image while preserving its topological characteristics. This chapter reviews some approaches which lead to efficient and exact algorithms for topological transformations in 2D, 3D and grayscale images. Some transformations that modify topology in a controlled manner are also described. Finally, based on the framework of critical kernels, we show how to design a topologically sound parallel thinning algorithm guided by a priority function.