Entropy Quad-Trees for High Complexity Regions Detection

Abstract

This paper introduces entropy quad-trees, which are structures derived from quad-trees by allowing nodes to split only when those correspond to sufficiently complex sub-domains of a data domain. Complexity is evaluated using an information-theoretic measure based on the analysis of the entropy associated to sets of objects designated by nodes. An alternative measure related to the concept of box-counting dimension is also explored. Experimental results demonstrate the efficiency of entropy quad-trees to mine complex regions. As an application, the proposed technique is used in the initial stage of a crater detection algorithm using digital images taken from the surface of Mars. Additional experimental results are provided that demonstrate the crater detection performance and analyze the effectiveness of entropy quad-trees for high-complexity regions detection in the pixel space with significant presence of noise. This work focuses on 2-dimensional image domains, but can be generalized to higher dimensional data.