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This paper addresses the problem of recovering the 3D shape and motion of curves and surfaces from image sequences of apparent contours. For known viewer motion the visible surfaces can then be reconstructed by exploiting a spatio-temporal parametrization of the apparent contours and contour generators under viewer motion. A natural parametrization exploits the contour generators and the epipolar geometry between successive viewpoints. The epipolar parametrization (Cipolla & Blake 1992) leads to simplified expressions for the recovery of depth and surface curvatures from image velocities and accelerations and known viewer motion. The parametrization is, however, degenerate when the apparent contour is singular since the ray is tangent to the contour generator (Koenderink & Van Doorn 1976) and at frontier points (Giblin & Weiss 1994) when the epipolar plane is a tangent plane to the surface. At these isolated points the epipolar parametrization can no longer be used to recover the local surface geometry. This paper reviews the epipolar parametrization and shows how the degenerate cases can be used to recover surface geometry and unknown viewer motion from apparent contours of curved surfaces. Practical implementations are outlined. 1. Introduction

Approximating detailed models with coarse, texture-mapped meshes results in polygonal silhouettes. To eliminate this artifact, we introduce silhouette clipping, a framework for efficiently clipping the rendering of coarse geometry to the exact silhouette of the original model. The coarse mesh is obtained using progressive hulls, a novel representation with the nesting property required for proper clipping. We describe an improved technique for constructing texture and normal maps over this coarse mesh. Given a perspective view, silhouettes are efficiently extracted from the original mesh using a precomputed search tree. Within the tree, hierarchical culling is achieved using pairs of anchored cones. The extracted silhouette edges are used to set the hardware stencil buffer and alpha buffer, which in turn clip and antialias the rendered coarse geometry. Results demonstrate that silhouette clipping can produce renderings of similar quality to high-resolution meshes in less rendering time.

We have studied the mechanism of contour perception by recording from neurons in the visual cortex of alert rhesus monkeys. In order to assess the relationship between neural signals and perception, we compared the responses to edges and lines with the responses to patterns in which human observers perceive a contour where no line or edge is given (anomalous contour), such as the border between gratings of thin lines offset by half a cycle. With only one exception out of 60, orientation-selective neurons in area Vl did not signal the anomalous contour. Many neurons failed to re-spond to this stimulus at all, others responded according to the orientation of the grating lines. In area V2, 45 of 103 neurons (44%) signaled the orientation of the anomalous contour. Sixteen did so without signaling the orientation of the inducing lines. Some responded better to anomalous

We present an approach for recovering surface shape from the occluding contour using an active (i.e., moving) observer. It is based onarelation between the geometries of a surface inascene and its occluding contour: If the viewing direction of the observer is along a principal direction for a surface point whose projection is on the contour, surface shape (i.e., curvature) at the surfacepoint can be recovered from the contour. Unlike previous approaches for recovering shape from the occluding contour, we use an observer that purposefully changes viewpoint in order to achieve a well-de ned geometric relationship with respect to a 3D shape prior to its recognition. We show that there is a simple and e cient viewing strategy that allows the observer to align the viewing direction with one of the two principal directions for a point on the surface. Experimental results demonstrate that our method can be easily implemented and can provide reliable shape information. 1

I hereby declare that no part of this thesis has already been or is being submitted for any other degree or qualification. This dissertation is the result of my own original work carried out in the Department of Engineering at the University of Cambridge, except where explicit reference has been made to the work of others. This dissertation contains 36,194 words and 91 figures. ii “Cogito, ergo sum. ” (I think, therefore I am.)- René Descartes, Le Discours de la Méthode. iv

This paper addresses the problem of motion estimation from profiles (also known as apparent contours) of an object rotating on a turntable in front of a sin- gle camera. Its main contribution is the development of a practical and accurate technique for solving this problem from profiles alone, which is precise enough to allow the reconstruction of the shape of the object. No correspondences be- tween points or lines are necessary, although the method proposed can be used equally when these features are available, without any further adaptation. Sym- metry properties of the surface of revolution swept out by the rotating object are exploited to obtain the image of the rotation axis and the homography relating epipolar lines in 2 views, in a robust and elegant way. These, together with ge- ometric constraints for images of rotating objects, are then used to obtain first *Corresponding author the image of the horizon, which is the projection of the plane that contains the camera centers, and then the epipoles, thus fully determining the epipolar ge- ometry of the image sequence. The estimation of the epipolar geometry by this sequential approach (image of rotation axis -- homography -- image of the hori- zon -- epipoles) avoids many of the problems usually found in other algorithms for motion recovery from profiles. In particular, the search for the epipoles, by far the most critical step, is carried out as a simple one-dimensional optimization problem. The initialization of the parameters is trivial and completely automatic for all stages of the algorithm. After the estimation of the epipolar geometry, the Euclidean motion is recovered using the fixed intrinsic parameters of the cam- era, obtained either from a calibration grid or from self-calibrati...

This paper addresses the problem of computing visual hulls from image contours. We propose a new hybrid approach which overcomes the precision-complexity trade-off inherent to voxel based approaches by taking advantage of surface based approaches. To this aim, we introduce a space discretization which does not rely on a regular grid, where most cells are ineffective, but rather on an irregular grid where sample points lie on the surface of the visual hull. Such a grid is composed of tetrahedral cells obtained by applying a Delaunay triangulation on the sample points. These cells are carved afterward according to image silhouette information. The proposed approach keeps the robustness of volumetric approaches while drastically improving their precision and reducing their time and space complexities. It thus allows modeling of objects with complex geometry, and it also makes real time feasible for precise models. Preliminary results with synthetic and real data are presented. 1.

In theoretical analyses of visual form perception, it is often assumed that the 3-dimensional structures of smoothly curved surfaces are perceptually represented as point-by-point mappings of metric depth and/or orientation relative to the observer. This article describes an alternative theory in which it is argued that our visual knowledge of smoothly curved surfaces can also be denned in terms of local, nonmetric order relations. A fundamental prediction of this analysis is that relative depth judgments between any two surface regions should be dramatically influenced by the monotonicity of depth change (or lack of it) along the intervening portions of the surface through which they are separated. This prediction is confirmed in a series of experiments using surfaces depicted with either shading or texture. Additional experiments are reported, moreover, that demonstrate that smooth occlusion contours are a primary source of information about the ordinal structure of a surface and that the depth extrema in between contours can be optically specified by differences in luminance at the points of occlusion. For many higher organisms, including humans, a primary source of knowledge about objects and events in the surrounding environment is provided by vision. Because of the ecological

The systems and concepts described in this paper document the evolution of the geometric invariance approach to object recognition over the last five years. Invariance overcomes one of the fundamental difficulties in recognising objects from images: that the appearance of an object depends on viewpoint. This problem is entirely avoided if the geometric description is unaffected by the imaging transformation. Such invariant descriptions can be measured from images without any prior knowledge of the position, orientation and calibration of the camera. These invariant measurements can be used to index a library of object models for recognition and provide a principled basis for the other stages of the recognition process such as feature grouping and hypothesis verification. Object models can be acquired directly from images, allowing efficient construction of model libraries without manual intervention. A significant part of the paper is a summary of recent results on the construction of ...