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A theory of shape by space carving
 In Proceedings of the 7th IEEE International Conference on Computer Vision (ICCV99), volume I, pages 307– 314, Los Alamitos, CA
, 1999
"... In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarilyshaped scene from multiple photographs taken at known but arbitrarilydistributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a ..."
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Cited by 455 (14 self)
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In this paper we consider the problem of computing the 3D shape of an unknown, arbitrarilyshaped scene from multiple photographs taken at known but arbitrarilydistributed viewpoints. By studying the equivalence class of all 3D shapes that reproduce the input photographs, we prove the existence of a special member of this class, the photo hull, that (1) can be computed directly from photographs of the scene, and (2) subsumes all other members of this class. We then give a provablycorrect algorithm, called Space Carving, for computing this shape and present experimental results on complex realworld scenes. The approach is designed to (1) build photorealistic shapes that accurately model scene appearance from a wide range of viewpoints, and (2) account for the complex interactions between occlusion, parallax, shading, and their effects on arbitrary views of a 3D scene. 1.
The Visual Motion of Curves and Surfaces
, 1998
"... 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 spatiotemporal parametrization of the apparent contours and contour generat ..."
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Cited by 103 (16 self)
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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 spatiotemporal 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
A probabilistic framework for space carving
, 2001
"... for the degree of Doctor of Philosophy. ii This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration. This dissertation is not substantially the same as any I have submitted for a degree or diploma or other qualification at any other Unive ..."
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Cited by 66 (3 self)
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for the degree of Doctor of Philosophy. ii This dissertation is the result of my own work and includes nothing which is the outcome of work done in collaboration. This dissertation is not substantially the same as any I have submitted for a degree or diploma or other qualification at any other University. I further state that no part of my dissertation/thesis has already been, or is being concurrently submitted for any such degree, diploma or other qualification. This dissertation contains 78 figures and approximately 46000 words. This dissertation was revised December 2001. This thesis investigates the problem of reconstructing threedimensional objects from image sequences. There are two major contributions in this thesis. The first contribution is an extension to the Space Carving framework that elimi
Recovering Occlusion Boundaries from a Single Image
"... Occlusion reasoning, necessary for tasks such as navigation and object search, is an important aspect of everyday life and a fundamental problem in computer vision. We believe that the amazing ability of humans to reason about occlusions from one image is based on an intrinsically 3D interpretation. ..."
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Cited by 58 (10 self)
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Occlusion reasoning, necessary for tasks such as navigation and object search, is an important aspect of everyday life and a fundamental problem in computer vision. We believe that the amazing ability of humans to reason about occlusions from one image is based on an intrinsically 3D interpretation. In this paper, our goal is to recover the occlusion boundaries and depth ordering of freestanding structures in the scene. Our approach is to learn to identify and label occlusion boundaries using the traditional edge and region cues together with 3D surface and depth cues. Since some of these cues require good spatial support (i.e., a segmentation), we gradually create larger regions and use them to improve inference over the boundaries. Our experiments demonstrate the power of a scenebased approach to occlusion reasoning. 1.
Recovering shape by purposive viewpoint adjustment
 International Journal of Computer Vision
, 1994
"... 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 surfac ..."
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Cited by 56 (8 self)
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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 wellde 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
3D Surface Reconstruction Using Occluding Contours
 International Journal of Computer Vision
, 1995
"... This paper addresses the problem of 3D surface reconstruction using image sequences. It has been shown that shape recovery from three or more occluding contours of the surface is possible given a known camera motion. Several algorithms, which have been recently proposed, allow such a reconstruction ..."
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Cited by 54 (9 self)
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This paper addresses the problem of 3D surface reconstruction using image sequences. It has been shown that shape recovery from three or more occluding contours of the surface is possible given a known camera motion. Several algorithms, which have been recently proposed, allow such a reconstruction under the assumption of a linear camera motion. A new approach is presented which deals with the reconstruction problem directly from a discrete point of view. A correct depth formulation is derived from a local approximation of the surface up to order two. This allows the local shape to be estimated, given three consecutive contours, without any constraints on the camera motion. Moreover, the use of the epipolar correspondence constraints the reconstruction problem and leads to linear estimation of both depth and curvature. Experimental results on real data are presented. Short version of this manuscript appears in the Proceedings of 6th International Conference on Computer Analysis of Imag...
Motion From the Frontier of Curved Surfaces
, 1994
"... this paper we address the problem of recovering the viewer motion from the deformation of apparent contours. A solution can be found by considering the cases in which the epipolar parameterization is degenerate and so can not be used to recover the local surface geometry. These are: 1. Cusps or sing ..."
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Cited by 51 (11 self)
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this paper we address the problem of recovering the viewer motion from the deformation of apparent contours. A solution can be found by considering the cases in which the epipolar parameterization is degenerate and so can not be used to recover the local surface geometry. These are: 1. Cusps or singular apparent contours This occurs when viewing a hyperbolic patch along an direction. The ray is not only tangent to the surface but also to the contour generator and the eect is to generate a cusp in the apparent contour. For opaque surfaces, only one branch of the cusp is visible and the contour ends abruptly [11, 10]. Although cusps can be detected and tracked under viewer motions Cipolla and Giblin [5] 2 ##### ######## ############## ########## # have shown that they do not provide any constraints on viewer motion. They can however be used to recover the surface geometry by the image motion of the cusp to induce an alternative parameterisation of the surface in the vicinity of the locus on the surface. 2. Rigid space curves The second case of degeneracy is when the contour generator does not over the surface with viewer motion but is xed. The contour generator is not an extremal boundary but is xed to the surface or is 3D rigid space curve (surface marking or discontinuity in depth or orientation). Despite the problem { only the normal component of image velocity can be measured from local measurements of a curve { Faugeras et al [7] and Cipolla [3] have shown how in principle that the spatio{temporal image of a space curve under viewer can be used to derive a constraint on the viewer motion from second order spatio{ temporal derivatives. This has not yet been proved to be of practical use due to the diculty in accurately extracting second order spatio{temporal der...
Robust Shape Recovery from Occluding Contours Using a Linear Smoother
, 1993
"... Recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent. For three or more views, shape recovery is possible, and several algorithms have recently been developed for this purpose. We present a new approach to the ..."
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Cited by 47 (10 self)
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Recovering the shape of an object from two views fails at occluding contours of smooth objects because the extremal contours are view dependent. For three or more views, shape recovery is possible, and several algorithms have recently been developed for this purpose. We present a new approach to the multiframe stereo problem which does not depend on differential measurements in the image, which may be noise sensitive. Instead, we use a linear smoother to optimally combine all of the measurements available at the contours (and other edges) in all of the images. This allows us to extract a robust and dense estimate of surface shape, and to integrate shape information from both surface markings and occluding contours. Keywords: Computer vision, image sequence analysis, motion analysis and multiframe stereo, shape and object representation, occluding contours (profiles). c flDigital Equipment Corporation 1993. All rights reserved. 1 Computer and Information Science Department, University...
Epipolar Geometry from Profiles under Circular Motion
 IEEE Trans. on Pattern Analysis and Machine Intelligence
, 2001
"... 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, wh ..."
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Cited by 42 (13 self)
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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 onedimensional 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 selfcalibrati...