Computer sensing of hand and limb motion is an important problem for applications in humancomputer interaction and computer graphics. We describe aframework for local tracking of self-occluding motion, in which one part of an object obstructs the visibility of another. Our approach uses a kinematic model to predict occlusions and windowed templates to track partially occluded objects. We present o-line 3D tracking results for hand motion with signi cant self-occlusion. 1

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We describe an algorithm and representation level theory of illusory contour shape and salience. Unlike previous theories, our model is derived from a single assumption--- namely, that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane (i.e., the space which one can reasonably assume is represented by neurons of the mammalian visual cortex). Our model does not employ numerical relaxation or other explicit minimization, but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector-field convolutions. We show that for the random walk we define, the maximum likelihood paths are curves of least energy, that is, on average, random walks follow paths commonly assumed to model the shape of illusory co...

We present an approach to the problem of representing images that contain multiple objects or surfaces. Rather than use an edge-based approach to represent the segmentation of a scene, we propose a multi-layer estimation framework which uses support maps to represent the segmentation of the image into homogeneous chunks. This support-based approach can represent objects that are split into disjoint regions, or have surfaces that are transparently interleaved. Our framework is based on an extension of robust estimation methods which provide a theoretical basis for supportbased estimation. The Minimum Description Length principle is used to decide how many support maps to use in describing a particular image. We show results applying this framework to heterogeneous interpolation and segmentation tasks on range and motion imagery. 1 Introduction Real-world perceptual systems must deal with complicated and cluttered environments. To succeed in such environments, a system must be able to r...

A half-occluded region in a stereo pair is a set of pixels in one image representing points in svace visible to that camera or eye only, and not to ihe other. These occur typically as parts of the background immediately to the left and right sides of nearby occluding objects, and are present in most natural scenes. Previous approaches to stereo either ignored these unmatchable points or attempted to weed them out in a second pass. Our algorithm incorporates them from the start as a strong clue to depth discontinuities. Psychophysical evidence suggests that the human visual system also exploits these clues. We start by deriving a measure for goodness of fit and a prior based on a simplified model of objects in space, which leads to an energy functional depending both on the depth as measured from a central “cyclopean ” eye and on the regions of points occluded from the left and right eye perspectives. We minimize this using dynamic programming along epipolar lines followed by annealing in both dimensions. Experiments indicate that this method is very effective even in difficult scenes. 1

. We call "natural" image any photograph of an outdoor or indoor scene taken by a standard camera. We discuss the physical generation process of natural images as a combination of occlusions, transparencies and contrast changes. This description fits to the phenomenological description of Gaetano Kanizsa according to which visual perception tends to remain stable with respect to these basic operations. We define a contrast invariant presentation of the digital image, the topographic map, where the subjacent occlusion-transparency structure is put into evidence by the interplay of level lines. We prove that each topographic map represents a class of images invariant with respect to local contrast changes. Several visualization strategies of the topographic map are proposed and implemented and mathematical arguments are developed to establish stability properties of the topographic map under digitization. Keywords: topographic map, mathematical morphology, level set, junctions, contrast changes, digitization 1.

Researchers in computer vision have primarily studied the problem of visual reconstruction of environmental structure that is plainly visible. In this thesis, the conventional goals of visual reconstruction are generalized to include both visible and occluded forward facing surfaces. This larger fraction of the environment is termed the anterior surfaces. Because multiple anterior surface neighborhoods project onto a single image neighborhood wherever surfaces overlap, surface neighborhoods and image neighborhoods are not guaranteed to be in one-to-one correspondence, as conventional "shape-from" methods assume. The result is that the topology of threedimensional scene structure can no longer be taken for granted, but must be inferred from evidence...

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This paper contains a systematic analysis of a natural measure theoretic notion of connectedness for sets of finite perimeter in R^N, introduced by H. Federer in the more general framework of the theory of currents. We provide a new and simpler proof of the existence and uniqueness of the decomposition into the so-called M-connected components. Moreover, we study carefully the structure of the essential boundary of these components and give in particular a reconstruction formula of a set of finite perimeter from the family of the boundaries of its components. In the two dimensional case we show that this notion of connectedness is comparable with the topological one, modulo the choice of a suitable representative in the equivalence class. Our strong motivation for this study is a mathematical justification of all those operations in image processing that involve connectedness and boundaries. As an application, we use this weak notion of connectedness to provide a rigorous mathemati...

Computer sensing of hand and limb motion is an important problem for applications in human-computer interaction, virtual reality, and athletic performance measurement. We describe a framework for local tracking of self-occluding motion, in which parts of the mechanism obstruct each others visibility to the camera. Our approach uses a kinematic model to predict occlusion and windowed templates to track partially occluded objects. We analyze our model of self-occlusion, discuss the implementation of our algorithm, and give experimental results for 3D hand tracking under significant amounts of self-occlusion. These results extend the DigitEyes system for articulated tracking described in [22, 21] to handle self-occluding motions. Contents 1 Introduction 1 2 A Framework for Tracking Self-Occluding Objects 2 2.1 Representing Self-Occlusion with Layered Templates : : : : : : : : : : : : : : 3 2.2 Local Visibility Orders for Templates : : : : : : : : : : : : : : : : : : : : : : 4 2.3 Wind...