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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 72 (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 68 (13 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 52 (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 39 (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
Applications of NonMetric Vision to Some Visual Guided Tasks
 Visual Navigation: From Biological Systems to Unmanned Ground Vehicles, chapter 5
, 1994
"... : We present a stratification of geometric information available from stereo in three levels: Euclidean, affine and projective, depending upon the kind of calibration that has been obtained for a stereo rig. We focus on the last two levels since they are mostly unexplored. We show how projective and ..."
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Cited by 34 (3 self)
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: We present a stratification of geometric information available from stereo in three levels: Euclidean, affine and projective, depending upon the kind of calibration that has been obtained for a stereo rig. We focus on the last two levels since they are mostly unexplored. We show how projective and affine calibration can be achieved from real images without the need of calibration patterns. We also show how to use this calibration to determine, for example, whether an obstacle is coming too close to the stereo rig or such useful information as the middle of a corridor or a road. Keywords: projective calibration, affine calibration, reconstruction, rectification (R'esum'e : tsvp) This work was partially supported by the EEC under Esprit Project 6448, Viva Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 93, 06902 SOPHIAANTIPOLIS Cedex (France) Telephone : (33) 93 65 77 77  Telecopie : (33) 93 65 77 65 Applications de la vision non m'etrique `a certaines ...
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 19 (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.
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 15 (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
Cyclopean geometry of binocular vision
"... The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A l ..."
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Cited by 14 (9 self)
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The geometry of binocular projection is analyzed in relation to the primate visual system. An oculomotor parameterization that includes the classical vergence and version angles is defined. It is shown that the epipolar geometry of the system is constrained by binocular coordination of the eyes. A local model of the scene is adopted in which depth is measured relative to a plane containing the fixation point. These constructions lead to an explicit parameterization of the binocular disparity field involving the gaze angles as well as the scene structure. The representation of visual direction and depth is discussed with reference to the relevant psychophysical and neurophysiological literature. © 2008 Optical Society of America OCIS codes: 330.1400, 330.2210. 1.
Stereo Without Search
 EUROPEAN CONFERENCE ON COMPUTER VISION (ECCV)
, 1996
"... In its traditional formulation, stereo correspondence involves both searching and selecting. Given a feature in one scanline, the corresponding scanline in the other image is searched for the positions of similar features. Often more than one candidate is found, and the correct one must be selec ..."
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Cited by 13 (2 self)
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In its traditional formulation, stereo correspondence involves both searching and selecting. Given a feature in one scanline, the corresponding scanline in the other image is searched for the positions of similar features. Often more than one candidate is found, and the correct one must be selected. The problem of selection is unavoidable because different features look similar to each other. Search, on the other hand, is not inherent in the correspondence problem. We propose a representation of scanlines, called intrinsic curves, that avoids search over different disparities. The idea is to represent scanlines by means of local descriptor vectors, without regard for where in the image a descriptor is computed, but without losing information about the contiguity of image points. In fact, intrinsic curves are the paths that the descriptor vector traverses as an image scanline is traversed from left to right. Because the...
Computing di erential 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 binocular stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local di erential properties of the corresponding 3D surface such as o ..."
Abstract

Cited by 13 (1 self)
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We are considering the problem of recovering the threedimensional geometry of a scene from binocular stereo disparity. Once a dense disparity map has been computed from a stereo pair of images, one often needs to calculate some local di erential properties of the corresponding 3D surface such as orientation or curvatures. The usual approach is to build a 3D 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 use the images directly to compute the shape properties. We thus propose a new method extending the classical correlation method to estimate accurately both the disparity and its derivatives directly from the image data. We then relate those derivatives to di erential properties of the surface such as orientation and curvatures.