Applications of entropic spanning graphs

This article presents applications of entropic spanning graphs to imaging and feature clustering applications. Entropic spanning graphs span a set of feature vectors in such a way that the normalized spanning length of the graph converges to the entropy of the feature distribution as the number of random feature vectors increases. This property makes these graphs naturally suited to applications where entropy and information divergence are used as discriminants: texture classification, feature clustering, image indexing, and image registration. Among other areas, these problems arise in geographical information systems, digital libraries, medical information processing, video indexing, multisensor fusion, and content-based retrieval.

[1]  Nuno Vasconcelos,et al.  Feature representations for image retrieval: beyond the color histogram , 2000, 2000 IEEE International Conference on Multimedia and Expo. ICME2000. Proceedings. Latest Advances in the Fast Changing World of Multimedia (Cat. No.00TH8532).

[2]  P. Hall,et al.  On the estimation of entropy , 1993 .

[3]  Alfred O. Hero,et al.  Feature coincidence trees for registration of ultrasound breast images , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[4]  D. N. Geary Mixture Models: Inference and Applications to Clustering , 1989 .

[5]  Alfred O. Hero,et al.  Image registration with minimum spanning tree algorithm , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[6]  Anne Condon,et al.  Parallel implementation of Bouvka's minimum spanning tree algorithm , 1996, Proceedings of International Conference on Parallel Processing.

[7]  Alfred O. Hero,et al.  Robust entropy estimation strategies based on edge weighted random graphs , 1998, Optics & Photonics.

[8]  Max A. Viergever,et al.  f-information measures in medical image registration , 2004, IEEE Transactions on Medical Imaging.

[9]  R. Prim Shortest connection networks and some generalizations , 1957 .

[10]  Oldrich A Vasicek,et al.  A Test for Normality Based on Sample Entropy , 1976 .

[11]  B. Ripley,et al.  Robust Statistics , 2018, Wiley Series in Probability and Statistics.

[12]  J. Beardwood,et al.  The shortest path through many points , 1959, Mathematical Proceedings of the Cambridge Philosophical Society.

[13]  L. Györfi,et al.  Nonparametric entropy estimation. An overview , 1997 .

[14]  Abdelkader Mokkadem,et al.  Estimation of the entropy and information of absolutely continuous random variables , 1989, IEEE Trans. Inf. Theory.

[15]  Yun He,et al.  Information divergence measure for ISAR image registration , 2001, SPIE Defense + Commercial Sensing.

[16]  D. Donoho One-sided inference about functionals of a density , 1988 .

[17]  David L. Neuhoff,et al.  On the asymptotic distribution of the errors in vector quantization , 1996, IEEE Trans. Inf. Theory.

[18]  Bing Ma,et al.  Parametric and nonparametric approaches for multisensor data fusion. , 2001 .

[19]  Minh N. Do,et al.  Texture similarity measurement using Kullback-Leibler distance on wavelet subbands , 2000, Proceedings 2000 International Conference on Image Processing (Cat. No.00CH37101).

[20]  Joseph A. O'Sullivan Divergence penalty for image regularization , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[21]  Anil K. Jain,et al.  A test of randomness based on the minimal spanning tree , 1983, Pattern Recognit. Lett..

[22]  J. Yukich Probability theory of classical Euclidean optimization problems , 1998 .

[23]  Alfred O. Hero,et al.  Comparison of GLR and invariant detectors under structured clutter covariance , 2001, IEEE Trans. Image Process..

[24]  M. Basseville Distance measures for signal processing and pattern recognition , 1989 .

[25]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[26]  J. Steele Probability theory and combinatorial optimization , 1987 .

[27]  Alfred O. Hero,et al.  Asymptotic theory of greedy approximations to minimal k-point random graphs , 1999, IEEE Trans. Inf. Theory.

[28]  Allen Gersho,et al.  Asymptotically optimal block quantization , 1979, IEEE Trans. Inf. Theory.

[29]  Ibrahim A. Ahmad,et al.  A nonparametric estimation of the entropy for absolutely continuous distributions (Corresp.) , 1976, IEEE Trans. Inf. Theory.

[30]  Sanjeev Arora,et al.  Nearly Linear Time Approximation Schemes for Euclidean TSP and Other Geometric Problems , 1997, RANDOM.

[31]  A. Hero,et al.  Estimation of Renyi information divergence via pruned minimal spanning trees , 1999, Proceedings of the IEEE Signal Processing Workshop on Higher-Order Statistics. SPW-HOS '99.

[32]  Josiane Zerubia,et al.  The two-dimensional Wold decomposition for segmentation and indexing in image libraries , 1998, Proceedings of the 1998 IEEE International Conference on Acoustics, Speech and Signal Processing, ICASSP '98 (Cat. No.98CH36181).

[33]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[34]  Kannan Ramchandran,et al.  Information-Theoretic Bounds on Target Recognition Performance Based on Degraded Image Data , 2002, IEEE Trans. Pattern Anal. Mach. Intell..

[35]  H. Krim,et al.  An information divergence measure for ISAR image registration , 2001, Proceedings of the 11th IEEE Signal Processing Workshop on Statistical Signal Processing (Cat. No.01TH8563).

[36]  Harry L. Van Trees,et al.  Detection, Estimation, and Modulation Theory, Part I , 1968 .

[37]  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).

[38]  R. Z. Khasʹminskiĭ,et al.  Statistical estimation : asymptotic theory , 1981 .

[39]  R. Ravi,et al.  Spanning trees short or small , 1994, SODA '94.

[40]  H. Joe Estimation of entropy and other functionals of a multivariate density , 1989 .

[41]  Nuno Vasconcelos,et al.  A Bayesian framework for content-based indexing and retrieval , 1998, Proceedings DCC '98 Data Compression Conference (Cat. No.98TB100225).

[42]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

[43]  L. L. Cam,et al.  Asymptotic Methods In Statistical Decision Theory , 1986 .

[44]  Richard Baraniuk,et al.  Time-frequency based distance and divergence measures , 1994, Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis.

[45]  Alfred O. Hero,et al.  Automatic extraction of time-frequency skeletons with minimal spanning trees , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

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

[47]  P. Massart,et al.  Estimation of Integral Functionals of a Density , 1995 .

[48]  A. Rényi On Measures of Entropy and Information , 1961 .