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This paper addresses the automatic image segmentation problem in a region merging style. With an initially oversegmented image, in which many regions (or superpixels) with homogeneous color are detected, an 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 and the minimal cost criterion. Starting from an oversegmented 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 the 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.