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47
Computing differential properties of 3D shapes from stereoscopic images without 3D models
, 1994
"... We are considering the problem of recovering the threedimensional geometry of a scene from binoculor stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local diferential properties of the cowesponding 30 surface such as ..."
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Cited by 82 (9 self)
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We are considering the problem of recovering the threedimensional geometry of a scene from binoculor stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local diferential properties of the cowesponding 30 surface such as orientation or curvatures. The wual approach is to build a 30 reconstruction of the surface(s) from which all shape properties will then be derived without ever going back to the original images. In this paper, we depart from this paradigm and propose to w e the images directly to compute the shape properties. We thus propose a new method extending the classical cowelation method to estimate accurately both the disparity and its derivatives directly from the image data. We then relate those derivatives to diferential properties of the surface such as orientation and curvatures.
Shapeadapted smoothing in estimation of 3D depth cues from affine distortions of local 2D brightness structure
 IN PROC. 3RD EUROPEAN CONF. ON COMPUTER VISION
, 1994
"... Rotationally symmetric operations in the image domain may give rise to shape distortions. This article describes a way of reducing this effect for a general class of methods for deriving 3D shape cues from 2D image data, which are based on the estimation of locally linearized distortion of brightn ..."
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Cited by 82 (18 self)
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Rotationally symmetric operations in the image domain may give rise to shape distortions. This article describes a way of reducing this effect for a general class of methods for deriving 3D shape cues from 2D image data, which are based on the estimation of locally linearized distortion of brightness patterns. By extending the linear scalespace concept into an affine scalespace representation and performing affine shape adaption of the smoothing kernels, the accuracy of surface orientation estimates derived from texture and disparity cues can be improved by typically one order of magnitude. The reason for this is that the image descriptors, on which the methods are based, will be relative invariant under a ne transformations, and the error will thus be confined to the higherorder terms in the locally linearized perspective mapping.
Shapeadapted smoothing in estimation of 3D shape cues from affine distortions of local 2D brightness structure
, 2001
"... This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shap ..."
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Cited by 72 (3 self)
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This article describes a method for reducing the shape distortions due to scalespace smoothing that arise in the computation of 3D shape cues using operators (derivatives) de ned from scalespace representation. More precisely, we are concerned with a general class of methods for deriving 3D shape cues from 2D image data based on the estimation of locally linearized deformations of brightness patterns. This class
What shadows reveal about object structure
 Journal of the Optical Society of America
, 1998
"... Abstract. In a scene observed from a xed viewpoint, the set of shadow curves in an image changes as a point light source (nearby or at in nity) assumes di erent locations. We show that for any nite set of point light sources illuminating an object viewed under either orthographic or perspective proj ..."
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Cited by 45 (5 self)
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Abstract. In a scene observed from a xed viewpoint, the set of shadow curves in an image changes as a point light source (nearby or at in nity) assumes di erent locations. We show that for any nite set of point light sources illuminating an object viewed under either orthographic or perspective projection, there isanequivalence class of object shapes having the same set of shadows. Members of this equivalence class di er by afourparameter family of projective transformations, and the shadows of a transformed object are identical when the same transformation is applied to the light source locations. Under orthographic projection, this family is the generalized basrelief (GBR) transformation, and we show that the GBR transformation is the only family of transformations of an object's shape for which the complete set of imaged shadows is identical. Finally, we show that given multiple images under di ering and unknown light source directions, it is possible to reconstruct an object up to these transformations from the shadows alone. 1
Stereo Matching as a NearestNeighbor Problem
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 1998
"... We propose a representation of images, called intrinsic curves, that transforms stereo matching from a search problem into a nearestneighbor problem. Intrinsic curves are the paths that a set of local image descriptors trace as an image scanline is traversed from left to right. Intrinsic curves ar ..."
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Cited by 24 (2 self)
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We propose a representation of images, called intrinsic curves, that transforms stereo matching from a search problem into a nearestneighbor problem. Intrinsic curves are the paths that a set of local image descriptors trace as an image scanline is traversed from left to right. Intrinsic curves are ideally invariant with respect to disparity. Stereo correspondence then becomes a trivial lookup problem in the ideal case. We also show how to use intrinsic curves to match real images in the presence of noise, brightness bias, contrast fluctuations, moderate geometric distortion, image ambiguity, and occlusions. In this case, matching becomes a nearestneighbor problem, even for very large disparity values.
Cyclopean Geometry of Binocular Vision
 Journal of the Optical Society of America A
, 2008
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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Cited by 18 (10 self)
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
Image Divergence and Deformation from Closed Curves
 INTERNATIONAL JOURNAL OF ROBOTICS RESEARCH
, 1997
"... This paper describes a novel method to measure the differential invariants of the image velocity field from the integral of normal image velocities around image contours. This is equivalent to measuring the temporal changes in the area of a closed contour. This avoids having to recover a dense i ..."
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Cited by 16 (3 self)
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This paper describes a novel method to measure the differential invariants of the image velocity field from the integral of normal image velocities around image contours. This is equivalent to measuring the temporal changes in the area of a closed contour. This avoids having to recover a dense image velocity field and taking partial derivatives. It also does not require point or line correspondences. Moreover integration provides some immunity to image measurement noise. It is shown
A Scale Selection Principle for Estimating Image Deformations
 Image and Vision Computing
, 1998
"... A basic functionality of a vision system concerns the ability to compute deformation fields between di#erent images of the same physical structure. This article advocates the need for incorporating an explicit mechanism for scale selection in this context, in algorithms for computing descriptors suc ..."
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Cited by 15 (5 self)
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A basic functionality of a vision system concerns the ability to compute deformation fields between di#erent images of the same physical structure. This article advocates the need for incorporating an explicit mechanism for scale selection in this context, in algorithms for computing descriptors such as optic flow and for performing stereo matching . A basic reason why such a mechanism is essential is the fact that in a coarsetofine propagation of disparity or flow information, it is not necessarily the case that the most accurate estimates are obtained at the finest scales. The existence of interfering structures at fine scales may make it impossible to accurately match the image data at fine scales. A systematic methodology for approaching this problem is proposed, by estimating the uncertainty in the computed flow estimate at each scale, and then selecting deformation estimates from the scales that minimize the (suitably normalized) uncertainty over scales . A specific implementat...
Structure from two orthographic views of rigid motion
, 1989
"... We study the inference of rigid threedimensional interpretations for the structure and motion of four or more moving points from but two orthographic views of the points. We develop an algorithm to determine whether image data are compatible with a rigid interpretation. As a corollary of this resul ..."
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Cited by 15 (2 self)
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We study the inference of rigid threedimensional interpretations for the structure and motion of four or more moving points from but two orthographic views of the points. We develop an algorithm to determine whether image data are compatible with a rigid interpretation. As a corollary of this result we find that the measure of false targets(roughly, nonrigid objects that appear rigid) is zero. We find that if the two views have at least one rigid interpretation, then in fact there is a canonical oneparameter family of rigid interpretations; we show how to compute this family, and we describe precisely how the rigid interpretations vary within it. Since only two views are used, this analysis is relevant also to stereo vision. 1.