A 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 €unction 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.

A comprehensive survey of traditional, merge-split and evolutionary approaches proposed for determination of cluster number

“…To reject or accept each assignment, the Minimum Length [Encoding] (MML) scheme is computed. Kanungo et al [105] introduced the Minimum Description Length (MDL) based method for multi-band image segmentation. Another MDL based method was proposed by Bischof et al [106].…”

Smooth contour coding with minimal description length active grid segmentation techniques

“…Let us first consider the standard nearest neighbor chain-code representation (Jain, 1989, Section 9.6) classically used in MDL based segmentation techniques (Leclerc, 1989;Kanungo et al, 1994;Lee, 2000;Martin et al, 2004). In that case, the contour is a polygon with nodes that are neighbors to each other with neighborhood regions defined with the 8-connectivity on the square node grid.…”

“…In general, segmentation algorithms require the determination by the user of different parameter values and may also lead to large computational times. Efficient segmentation techniques based on minimum description length (MDL) principle (Rissanen, 1978(Rissanen, , 1989 have been proposed (Leclerc, 1989;Kanungo et al, 1994;Pan, 1994;Nohre, 1995;Zhu and Yuille, 1996;Lee, 2000;Figueiredo et al, 2000;Ruch and Réfrégier, 2001;Galland et al, 2003;Martin et al, 2004) so that the optimal partition is the minimizer of a criterion with a reduced number of undetermined parameters. Furthermore, it has been shown in (Galland et al, 2003) that a MDL segmentation technique based on a polygonal active grid (i.e.…”

“…The first ones are based on contour description with parametric techniques such as spline descriptors (Figueiredo et al, 2000). The second ones are based on a non-parametric or chain code description of the contours (Leclerc, 1989;Kanungo et al, 1994;Lee, 2000), such as in the region competition approach (Zhu and Yuille, 1996), in level set based segmentation techniques (Martin et al, 2004), or in other domains such as Markov Random Fields (Figueiredo and Leitao, 1997). However, up to now, no general solution has been implemented for segmentation techniques based on the MDL-AG (Galland et al, 2003) with a contour description adapted to regions with smooth boundaries, although such a possibility may be applied to a large class of application domains.…”

Two-Phase Compression of Histological Images with MDL Ranking of Segmentation Images

“…Minimum description length (MDL) principle was earlier used in image segmentation as a decision device for comparing two competing segmentations [2]- [4]. In [4] the segmentation scheme starts by calling the mean-shift algorithm with a small bandwidth parameter, so that the obtained segmentation has high number of regions, and then a region merging process is carried on, where MDL is used to decide the pair of regions to merge at each new iteration.…”