A Topologically Consistent Color Digital Image Representation by a Single Tree

Abstract

A novel, flexible (non-unique) and topologically consistent representation called CRIT (Contour-Region incidence Tree) for a color 2D digital image I is defined here. The CRIT is a tree containing all the inter and intra connectivity information of the constant-color regions. Considering I as an abstract cell complex (ACC), its topological infor mation can be packed as a smaller (in terms of cells) ACC, whose 2-cells are the different constant-color regions of I. This modus operandi over comes the classical connectivity paradoxes of digital images by working with lower-dimensional cells such as 0-cells, 1-cells, and 2-cells. The CRIT structure allows to describe this smaller ACC in a non-redundant way. The proposed technique is based on the previous construction of the Homological Spanning Forest (HSF) structures for encoding homological information of the ACCs canonically associated to I, in terms of rooted trees connecting digital object elements without redundancy