Building the Topological Tree by recursive FCM color clustering

In this paper we define a Topological Tree (TT) as a knowledge representation method that aims to describe important visual and spatial features of image regions, namely the color similarity, the inclusion and the spatial adjacency. The topological tree exhibits some interesting properties that can be exploited to extract knowledge from images for information retrieval, image understanding and diagnosis purposes. Examples of applications in dermatology are described. The TT can be constructed after segmentation, by computing the spatial relationships of regions or can be generated directly during the segmentation: to this aim we present a novel recursive fuzzy c-means (FCM) clustering algorithm based on the Principal Component Analysis of the color space. The recursive FCM proves to be effective for underlining the adjacency and inclusion property of regions.