A Minimum Entropy Approach to

This paper introduces a novel adaptive image seg- mentation algorithm which represents images by polygonal seg- ments. The algorithm is based on an intuitive generative model for pixel intensities and its associated cost function which can be effectively optimized by a hierarchical triangulation algorithm. A triangular mesh is iteratively refined and reorganized to extract a compact description of the essential image structure. After an- alyzing fundamental convexity properties of our cost function, we adapt an information-theoretic bound to assess the statistical sig- nificance of a given triangulation step. The bound effectively de- fines a stopping criterion to limit the number of triangles in the mesh, thereby avoiding undesirable overfitting phenomena. It also facilitates the development of a multiscale variant of the triangula- tion algorithm, which substantially improves its computational de- mands. The algorithm has various applications in contextual clas- sification, remote sensing, and visual object recognition. It is par- ticularly suitable for the segmentation of noisy imagery. segments with piecewise linear boundaries dominate the image interpretation. In contrast to heuristic approaches, our algorithm minimizes a cost function which is derived from an intuitive generative model of images. It encodes the assumption that images con- sist of nonoverlapping segments, which feature a specific pixel- value distribution. Due to its generality, the model can be ap- plied to a wide range of image types and it is suited particularly well for the segmentation of noisy imagery with a rough, dis- torted appearance of segments, e.g., textured images and syn- thetic aperture radar images. The validation of segmentation results is another important issue: it is necessary to distinguish the reliable structure (signal) in images from the noise to avoid overfitting. We develop an in- formation-theoretic concept to terminate the model refinement at an appropriate level of granularity. The optimization process is stopped (or, in a multiscale scenario, it steps to a finer res- olution) when further progress can be explained by noise ef- fects and the statistical confidence drops below a pre-defined threshold. These confidence values are estimated by Sanov's theorem (2).