Segmentation via NCuts and Lossy Minimum Description Length: A Unified Approach

Abstract

We investigate a fundamental problem in computer vision: unsupervised image segmentation. During the last decade, the Normalized Cuts has become very popular for image segmentation. NCuts guarantees a globally optimal solution in the continuous solution space, however, how to automatically select the number of segments for a given image is left as an open problem. Recently, the lossy minimum description length (LMDL) criterion has been proposed for segmentation of images. This criterion can adaptively determine the number of segments, however, as the optimization is combinatorial, only a suboptimal solution can be achieved by a greedy algorithm. The complementarity of both criteria motivates us to combine NCuts and LMDL into a unified fashion, to achieve a better segmentation: given the NCuts segmentations under different numbers of segments, we choose the optimal segmentation to be the one that minimizes the overall coding length, subject to a given distortion. We then develop a new way to use the coding length decrement as the similarity measure for NCuts, so that our algorithm is able to seek both the optimal NCuts solution under fixed number of segments, and the optimal LMDL solution among different numbers of segments. Extensive experiments demonstrate the effectiveness of our algorithm.