Elliptic Algebra and Integrable Models for Solitons on Noncummutative Torus T{\cal T}

We study the algebra ${\cal A}_n$ and the basis of the Hilbert space ${\cal H}_n$ in terms of the $\theta$ functions of the positions of $n$ solitons. Then we embed the Heisenberg group as the quantum operator factors in the representation of the transfer matrice of various integrable models. Finally we generalize our result to the generic $\theta$ case.Comment: Talk given by Bo-Yu Hou at the Joint APCTP-Nankai Symposium. Tianjin (PRC), Oct. 2001. To appear in the proceedings, to be published by Int. J. Mod. Phys. B. 7 pages, latex, no figure

Automatic Image Segmentation by Dynamic Region Merging

This paper addresses the automatic image segmentation problem in a region merging style. With an initially over-segmented image, in which the many regions (or super-pixels) with homogeneous color are detected, image segmentation is performed by iteratively merging the regions according to a statistical test. There are two essential issues in a region merging algorithm: order of merging and the stopping criterion. In the proposed algorithm, these two issues are solved by a novel predicate, which is defined by the sequential probability ratio test (SPRT) and the maximum likelihood criterion. Starting from an over-segmented image, neighboring regions are progressively merged if there is an evidence for merging according to this predicate. We show that the merging order follows the principle of dynamic programming. This formulates image segmentation as an inference problem, where the final segmentation is established based on the observed image. We also prove that the produced segmentation satisfies certain global properties. In addition, a faster algorithm is developed to accelerate the region merging process, which maintains a nearest neighbor graph in each iteration. Experiments on real natural images are conducted to demonstrate the performance of the proposed dynamic region merging algorithm.Comment: 28 pages. This paper is under review in IEEE TI