A Multiscale Algorithm for Image Segmentation by Variational Method

Abstract

Most segmentation algorithms are composed of several procedures: split and merge, small region elimination, boundary smoothing,..., each depending on several parameters. The introduction of an energy to minimize leads to a drastic reduction of these parameters. The authors prove that the most simple segmentation tool, the “region merging” algorithm, made according to the simplest energy, is enough to compute a local energy minimum belonging to a compact class and to achieve the job of most of the tools mentioned above. The authors explain why “merging” in a variational framework leads to a fast multiscale, multichannel algorithm, with a pyramidal structure. The obtained algorithm is $O(n\ln n)$, where n is the number of pixels of the picture. This fast algorithm is applied to make grey level and texture segmentation and experimental results are shown.