# American Institute of Mathematical Sciences

November  2008, 2(4): 485-525. doi: 10.3934/ipi.2008.2.485

## Two dimensional histogram analysis using the Helmholtz principle

 1 NAWCWD - Physics and Computational Sciences, China Lake, CA 93555, United States, United States 2 University of California, ECE Department, Santa Barbara, CA 93555, United States

Received  May 2007 Revised  September 2008 Published  November 2008

An algorithm for two dimensional histogram modal analysis is presented. A major challenge in two dimensional histogram analysis is to provide an accurate location and description of the extended modal shape. The approach presented in this paper combines the Fast Level Set Transform of the histogram and the Helmholtz principle to find the location and shape of the modes. Furthermore, the algorithm is devoid of any a priori assumptions about the underlying density or the number of modes. At the core, this approach is a new way to manage and search the number of regions that must be examined to identify meaningful sets. Computational issues required a new tail sum bound on the multinomial distribution to be stated and proven. This bound reduces to the Höeffding inequality for the binomial distribution. The histogram segmentation procedure was applied to the two problems of image color segmentation and correlation pattern recognition. With no a priori knowledge about the color image assumed, the two dimensional modal analysis is applied to the CIELAB color space to find perceptually uniform dominant colors. The modal analysis is also extended to correlation pattern recognition to find multiple targets in a single correlation plane.
Citation: Arjuna Flenner, Gary A. Hewer, Charles S. Kenney. Two dimensional histogram analysis using the Helmholtz principle. Inverse Problems & Imaging, 2008, 2 (4) : 485-525. doi: 10.3934/ipi.2008.2.485
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