Nonextensive information-theoretic measure for image edge detection

We propose a nonextensive information-theoretic measure called Jensen-Tsallis divergence, which may be defined between any arbitrary number of probability distributions, and we analyze its main theoretical properties. Using the theory of majorization, we also derive its upper bounds performance. To gain further insight into the robustness and the application of the Jensen-Tsallis divergence measure in imaging, we provide some numerical experiments to show the power of this entopic measure in image edge detection.

[1]  David J. Brady,et al.  Information theory in optoelectronic systems: introduction to the feature , 2000 .

[2]  C. Tsallis Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[3]  Alfred O. Hero,et al.  Applications of entropic spanning graphs , 2002, IEEE Signal Process. Mag..

[4]  Josiane Zerubia,et al.  Image retrieval and indexing: a hierarchical approach in computing the distance between textured images , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[5]  S. M. Ali,et al.  A General Class of Coefficients of Divergence of One Distribution from Another , 1966 .

[6]  Jan Havrda,et al.  Quantification method of classification processes. Concept of structural a-entropy , 1967, Kybernetika.

[7]  I. Olkin,et al.  Inequalities: Theory of Majorization and Its Applications , 1980 .

[8]  Jianhua Lin,et al.  Divergence measures based on the Shannon entropy , 1991, IEEE Trans. Inf. Theory.

[9]  C. R. Rao,et al.  On the convexity of some divergence measures based on entropy functions , 1982, IEEE Trans. Inf. Theory.

[10]  J. Astola,et al.  Information divergence measures-for detection of borders between coding and noncoding DNA regions using recursive entropic segmentation , 2003, IEEE Workshop on Statistical Signal Processing, 2003.

[11]  Huaiyu Zhu On Information and Sufficiency , 1997 .

[12]  Anuj Srivastava,et al.  Stochastic models for capturing image variability , 2002, IEEE Signal Process. Mag..

[13]  José Martínez-Aroza,et al.  An Analysis of Edge Detection by Using the Jensen-Shannon Divergence , 2000, Journal of Mathematical Imaging and Vision.

[14]  Lyndon S. Hibbard Region segmentation using information divergence measures , 2004, Medical Image Anal..

[15]  Paul A. Viola,et al.  Alignment by Maximization of Mutual Information , 1997, International Journal of Computer Vision.

[16]  Yun He,et al.  A generalized divergence measure for robust image registration , 2003, IEEE Trans. Signal Process..

[17]  Guy Marchal,et al.  Multimodality image registration by maximization of mutual information , 1997, IEEE Transactions on Medical Imaging.