Homological Spanning Forest framework for 2D image processing

A 2D topology-based digital image processing framework is presentedhere. This framework consists of the computation of a flexible geometric graphbasedstructure, starting from a raster representation of a digital image I. Thisstructure is called Homological Spanning Forest (HSF for short), and it is builton a cell complex associated to I. The HSF framework allows an efficient andaccurate topological analysis of regions of interest (ROIs) by using a four-levelarchitecture. By topological analysis, we mean not only the computation of Eulercharacteristic, genus or Betti numbers, but also advanced computational algebraictopological information derived from homological classification of cycles. An initialHSF representation can be modified to obtain a different one, in which ROIs arealmost isolated and ready to be topologically analyzed. The HSF framework issusceptible of being parallelized and generalized to higher dimensions.