A Newton method for simultaneous reconstruction of an interface and a buried obstacle from far-field data

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves from a penetrable and buried obstacles. By introducing a related transmission scattering problem, a Newton iteration method is proposed to simultaneously reconstruct both the penetrable interface and the buried obstacle inside from far-field data. A main feature of our method is that we do not need to know the type of boundary conditions on the buried obstacle. In particular, the boundary condition on the buried obstacle can also be determined simultaneously by the method. Finally, numerical examples using multi-frequency data are carried out to illustrate the effectiveness of our method.Comment: 25 pages, 8 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