16 International Journal of Software Science and Computational Intelligence, 3(1), 16-33, January-March 2011 Copyright © 2011, IGI Global. Copying or distributing in print or electronic forms without written permission of IGI Global is prohibited. Keywords: Box-Counting Dimension, Circular Hough Transform, Entropy, Nodes, Quad-Trees INTRODUCTION The concept of complexity relates to the pres- ence of variation. In science there are many ap- proaches that characterize complexity. A variety of scientific fields have dealt with complex mechanisms, simulations, systems, behavior and data complexity as those have always been a part of our environment. In this work, we focus on the topic of data complexity which is studied in information theory. While randomness is not considered complexity in certain areas such as those related to the study of complex systems, Entropy Quad-Trees for High Complexity Regions Detection Rosanne Vetro, University of Massachusetts Boston, USA Dan A. Simovici, University of Massachusetts Boston, USA Wei Ding, University of Massachusetts Boston, USA ABSTRACT This paper introduces entropy quad-trees, which are structures derived from quad-trees by allowing nodes to split only when those correspond to suffciently 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 effciency 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 signifcant presence of noise. This work focuses on 2-dimensional image domains, but can be generalized to higher dimensional data. information theory tends to assign high values of complexity to random noise. Many fields benefit from the identification of content or noise related complex areas. In data hiding, adaptive steganography takes advantage of high concen- tration of self-information on high complexity areas originated from both content and noise to embed data. Solanki, Dabeer, Madhow, Man- junath, and Chandrasekaran (2003) describe the benefits of selective embedding related to the reduction of perceptual degradation for transform domain steganographic techniques. Bio diversity is another area where complexity can be used for identification and localization of different species. In this case, the complexity DOI: 10.4018/jssci.2011010102