Entropy Quad-Trees for High Complexity Regions Detection

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.

[1]  Tomasz F. Stepinski,et al.  Automatic detection of sub-km craters in high resolution planetary images , 2009 .

[2]  Hon Fung Li,et al.  Shapes Recognition Using the Straight Line Hough Transform: Theory and Generalization , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[3]  Yongyi Yang,et al.  Relevance Feedback as New Tool for Computer-Aided Diagnosis in Image Databases , 2012 .

[4]  Tomás Pevný,et al.  Benchmarking for Steganography , 2008, Information Hiding.

[5]  Du Zhang,et al.  Machine Learning and Value-Based Software Engineering , 2009, Int. J. Softw. Sci. Comput. Intell..

[6]  Kenji Suzuki.  Machine Learning in Computer-Aided Diagnosis: Medical Imaging Intelligence and Analysis , 2012 .

[7]  Brian D. Bue,et al.  Machine Detection of Martian Impact Craters From Digital Topography Data , 2007, IEEE Transactions on Geoscience and Remote Sensing.

[8]  Yucong Duan,et al.  A dualism based semantics formalization mechanism for model driven engineering , 2008, 2008 7th IEEE International Conference on Cognitive Informatics.

[9]  Fumio Mizoguchi,et al.  Design and Implementation of a Cognitive User-Support System for Skin Progress Analysis Using a Smart Phone , 2013, Int. J. Softw. Sci. Comput. Intell..

[10]  E. R. Davies,et al.  A modified Hough scheme for general circle location , 1988, Pattern Recognit. Lett..

[11]  V. F. Leavers,et al.  Which Hough transform , 1993 .

[12]  Josef Kittler,et al.  A survey of the hough transform , 1988, Comput. Vis. Graph. Image Process..

[13]  Emilio Soria-Olivas,et al.  Medical Applications of Intelligent Data Analysis: Research Advancements , 2012 .

[14]  Peter Kwong-Shun Tam,et al.  Modification of hough transform for circles and ellipses detection using a 2-dimensional array , 1992, Pattern Recognit..

[15]  Szymon Jaroszewicz,et al.  An axiomatization of partition entropy , 2002, IEEE Trans. Inf. Theory.

[16]  Xiangfeng Luo,et al.  Measuring Textual Context Based on Cognitive Principles , 2009, Int. J. Softw. Sci. Comput. Intell..

[17]  Claudius Gros,et al.  Emotions, Diffusive Emotional Control and the Motivational Problem for Autonomous Cognitive Systems , 2009, 0901.3025.

[18]  Jordi Vallverdú,et al.  Embodying Cognition: A Morphological Perspective , 2010 .

[19]  D. P. Acharjya,et al.  Global Trends in Intelligent Computing Research and Development , 2013 .

[20]  B. S. Manjunath,et al.  Robust Image-Adaptive Data Hiding : Modeling , Source Coding and Channel Coding ∗ , 2003 .

[21]  Richard O. Duda,et al.  Use of the Hough transformation to detect lines and curves in pictures , 1972, CACM.

[22]  Witold Kinsner,et al.  Challenges in the Design of Adaptive, Intelligent and Cognitive Systems , 2007, 6th IEEE International Conference on Cognitive Informatics.

[23]  Szymon Jaroszewicz,et al.  Generalized Conditional Entropy and Decision Trees , 2003, EGC.

[24]  Sven Lončarić,et al.  GT-57633 catalogue of Martian impact craters developed for evaluation of crater detection algorithms , 2008 .

[25]  Toyoaki Nishida,et al.  Modeling Agent Interactions using Common Ground Knowledge from a Joint Activity Theory Perspective , 2013, Int. J. Softw. Sci. Comput. Intell..

[26]  Eva Armengol,et al.  Building a Lazy Domain Theory for Characterizing Malignant Melanoma , 2012 .

[27]  Tomasz F. Stepinski,et al.  Automatic Detection of Sub-Kilometer Craters in High Resolution Planetary Images , 2008 .

[28]  Chabane Djeraba,et al.  Mathematical Tools for Data Mining: Set Theory, Partial Orders, Combinatorics , 2008, Advanced Information and Knowledge Processing.