Superpixel-Segmentation Based on Energy Minimization and Convolution with the Geodesic Distance Kernel

Abstract—The energy minimization or maximum a posteriori probability (MAP) method is the basis for solving many computer vision problems, including the segmentation problem. However, it is assumed that the number of regions during segmentation is quite small. At the same time, in the problem of superpixel segmentation or otherwise excessive segmentation, the number of such areas exceeds 1000, which makes the computational optimization problem by the MAP method practically impossible. In this paper, we propose a solution that reduces segmentation with any number of areas to the problem of marking only nine labels. In addition, convolution with the geodesic distance kernel is used to enhance the robustness of optimization. This makes it possible to obtain single-linked superpixels at the output of the algorithm, unlike many other methods that require additional adjustments. The effectiveness of the proposed method is compared and measured by the precision-recall criteria, as well as by visual illustration.