Unforced Image Partitioning by Weighted Pyramid Linking

This paper describes a method of image segmentation that creates a partition of the image into compact, homogeneous regions using a parallel, iterative approach that does not require immediate forced choices. The approach makes use of a "pyramid" of successively reduced-resolution ' ersions of the image. It defines link strengths between pairs of pixels at successive levels of this pyramid, based on proximity and similarity, and iteratively recomputes the pixel values and adjusts the link strengths. After a fev iterations, the link strengths stabilize, and the links that remain strong define a set of subtrees of the pyramid. Each such tree represents a compact (piece of a) homogeneous region in the image; the leaves of the subtree are the pixels in the region, and the size of the region depends on how high the root of the tree lies in the pyramid. Thus the trees define a partition of the image into (pieces of) homogeneous regions. Introduction K Most of the existing methods of image segmentation [1,2] are based on forced-choice decisions. In methods that classify pixels into subpopulntlons, we must decide to which class each pixel belongs. In methods that partition the image into homogeneous regions using splitting and merging processes, we must decide, for each current region, whether to split it, or whether to merge it with a neighboring region (and If so, with which one). This forced-choice aspect of segmentation is undesirable, since many of the decisions may be wrong, particularly when they are made on the basis of very little information, and it is difficult to undo the effects of wrong decisions. In segmentation by pixel classification, a "relaxation" approach [3] can be used to defer the classification decisions until more information is available. In this approach we compute a degree cf membership for each pixel in each class, or a "probability" that it belongs to each class; and we then Iteratively adjust these membership values. The support of the Defense Advanced Research Projects Agency and the U.S. Army Night Vision Laboratory under Contract DAAG-53-76C-0138 (DARPA Order 3206) is gratefully acknowledged, as is the help of Clara Robertson in preparing this paper. based on the values at neighboring pixels and the compatibilities of the various possible combinations of class memberships of pairs of neighbors. After a few iterations, the mombership values stabilize, with some values becoming or remaining relatively high and others becoming very low, so that it becomes easy to make th,^ final classification decisions. Segmentation by partitioning into homogeneous regions e.g., regions of approximately constant value is generally more powerful than segmentation by pixel classification, becauoe the information on which it is based is computed over regions rather than ("myopically") over small neighborhoods of pixels. Thus it would be desirable to develop a region-based segmentation scheme in which decisions are not made immediately. This paper defines such a scheme and gives examples of the results obtained when it is applied to various types of images. Section 2 describes the general principles of this scheme and compares it with some related approaches; Section 3 discusses the algorithm; and Section 4 presents experimental results. 2. Weighted pyramid linking Our approach to unforced image partitioning makes use of a "pyramid" of successively reducedresolution versions of the given image, say of sizes 2 by 2, 2by 2"l,..., 2x2. The bast of the pyramid (level 0) is the input image, and each successive level is constructed by avera^'ng 4 by 4 blocks of pixels on the level below, where the blocks overlap 50% in x and in y. (For convenience, each level is regarded as cyclically closed, so that its top row is adjacent to its bottom row and its left column to its right column.) Thus each pixel on a given level has 16 "sons" on the level below (if any) that contribute to its average, and 4 "fathers" on the level above (if any) to whose average it contributes. This type of pyramid has also been used for segmentation purposes by other investigators; e.g., see the work of Hanson and Riseman described in [4]. The basic idea in our approach is to define link strengths between "neighboring" pixels (i.e., father/son pairs) on adjacent levels of the pyramid, based on the similarity (in value) and proximity (in (x,y) coordinates) of each such pair. We then recompute the pixel values (at the levels above the base) as weighted averages of their sons'