Abstract-We present a new method for automatic segmentation of heterogeneous image data that takes a step toward bridging the gap between bottom-up affinity-based segmentation methods and top-down generative model based approaches. The main contribution of the paper is a Bayesian formulation for incorporating soft model assignments into the calculation of affinities, which are conventionally model free. We integrate the resulting model-aware affinities into the multilevel segmentation by weighted aggregation algorithm, and apply the technique to the task of detecting and segmenting brain tumor and edema in multichannel MR volumes. The computationally efficient method runs orders of magnitude faster than current state-ofthe-art techniques giving comparable or improved results. Our quantitative results indicate the benefit of incorporating modelaware affinities into the segmentation process for the difficult case of brain tumor.

Abstract-We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns, for every internal point of the silhouette, a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson's equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this, we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification and retrieval.

We introduce a fast, multiscale algorithm for image segmentation. Our algorithm uses modern numeric techniques to nd an approximate solution to normalized cut measures in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into segments. The algorithm detects the segments by applying a process of recursive coarsening in which the same minimization problem is represented with fewer and fewer variables producing an irregular pyramid. During this coarsening process we may compute additional internal statistics of the emerging segments and use these statistics to facilitate the segmentation process. Once the pyramid is completed it is scanned from the top down to associate pixels close to the boundaries of segments with the appropriate segment. The algorithm is inspired by algebraic multigrid (AMG) solvers of minimization problems of heat or electric networks. We demonstrate the algorithm by applying it to real images.

Finding salient, coherent regions in images is the basis for many visual tasks, and is especially important for object recognition. Human observers perform this task with ease, relying on a system in which hierarchical processing seems to have a critical role. Despite many attempts, computerized algorithms have so far not demonstrated robust segmentation capabilities under general viewing conditions. Here we describe a new, highly efficient approach that determines all salient regions of an image and builds them into a hierarchical structure. Our algorithm, segmentation by weighted aggregation, is derived from algebraic multigrid solvers for physical systems, and consists of fine-to-coarse pixel aggregation. Aggregates of various sizes, which may or may not overlap, are revealed as salient, without predetermining their number or scale. Results using this algorithm are markedly more accurate and significantly faster (linear in data size) than previous approaches.

In this work we show how to combine bottom-up and topdown approaches into a single figure-ground