Fast algorithm for MDL-based multi-band image segmentation

Abstract

We consider the problem of image segmentation and describe an algorithm that is based on the Minimum Description Length (MDL) principle, is fast, is applicable to multi-band images, and guarantees closed regions. We construct an objective function that, when minimized, yields a partitioning of the image into regions where the pixel values in each band of each region are described by a polynomial surface plus noise. The polynomial orders and their coefficients are determined by the algorithm. The minimization is difficult because (1) it involves a search over a very large space and (2) there is extensive computation required at each stage of the search. To address the first of these problems we use a region-merging minimization algorithm. To address the second we use an incremental polynomial regression that uses computations from the previous stage to compute results in the current stage, resulting in a significant speed up over the non-incremental technique. The segmentation result obtained is suboptimal in general but of high quality. Results on real images are shown.