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29
Iterative point matching for registration of freeform curves and surfaces
, 1994
"... A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in ma ..."
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Cited by 519 (6 self)
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A heuristic method has been developed for registering two sets of 3D curves obtained by using an edgebased stereo system, or two dense 3D maps obtained by using a correlationbased stereo system. Geometric matching in general is a difficult unsolved problem in computer vision. Fortunately, in many practical applications, some a priori knowledge exists which considerably simplifies the problem. In visual navigation, for example, the motion between successive positions is usually approximately known. From this initial estimate, our algorithm computes observer motion with very good precision, which is required for environment modeling (e.g., building a Digital Elevation Map). Objects are represented by a set of 3D points, which are considered as the samples of a surface. No constraint is imposed on the form of the objects. The proposed algorithm is based on iteratively matching points in one set to the closest points in the other. A statistical method based on the distance distribution is used to deal with outliers, occlusion, appearance and disappearance, which allows us to do subsetsubset matching. A leastsquares technique is used to estimate 3D motion from the point correspondences, which reduces the average distance between points in the two sets. Both synthetic and real data have been used to test the algorithm, and the results show that it is efficient and robust, and yields an accurate motion estimate.
What Can Two Images Tell Us About a Third One?
 International Journal of Computer Vision
, 1996
"... : This paper discusses the problem of predicting image features in an image from image features in two other images and the epipolar geometry between the three images. We adopt the most general camera model of perpective projection and show that a point can be predicted in the third image as a bilin ..."
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Cited by 108 (5 self)
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: This paper discusses the problem of predicting image features in an image from image features in two other images and the epipolar geometry between the three images. We adopt the most general camera model of perpective projection and show that a point can be predicted in the third image as a bilinear function of its images in the first two cameras, that the tangents to three corresponding curves are related by a trilinear function, and that the curvature of a curve in the third image is a linear function of the curvatures at the corresponding points in the other two images. Our analysis relies heavily on the use of the fundamental matrix which has been recently introduced [7] and on the properties of a special plane which we call the trifocal plane. We thus answer completely the following question: given two views of an object, what would a third view look like? the question and its answer bear upon several areas of computer vision, stereo, motion analysis, and modelbased object re...
3D Scene Representation as a Collection of Images and Fundamental Matrices
, 1994
"... : In this report, we address the problem of the prediction of new views of a given scene from existing weakly or fully calibrated views called reference views. Our method does not make use of a threedimensional model of the scene, but of the existing relations between the images. The new views are ..."
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Cited by 77 (0 self)
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: In this report, we address the problem of the prediction of new views of a given scene from existing weakly or fully calibrated views called reference views. Our method does not make use of a threedimensional model of the scene, but of the existing relations between the images. The new views are represented in the reference views by a viewpoint and a retinal plane, i.e. by four points which can be chosen interactively. From this representation and from the constraints between the images, we derive an algorithm to predict the new views. We discuss the advantages of this method compared to the commonly used scheme : 3D reconstructionprojection. We show some experimental results with synthetic and real data. Keywords: 3D scene representation, multiview stereo, image synthesis (R'esum'e : tsvp) This work was partially supported by DRET contract No 91815/DRET/EAR and by the EEC under Esprit project 6448, Viva Unite de recherche INRIA SophiaAntipolis 2004 route des Lucioles, BP 9...
Dense Disparity Map Estimation Respecting Image Discontinuities: A PDE and ScaleSpace Based Approach
 JOURNAL OF VISUAL COMMUNICATION AND IMAGE REPRESENTATION
, 2000
"... We present an energy based approach to estimate a dense disparity map between two images while preserving its discontinuities resulting from image boundaries. We first derive a simplied expression for the disparity that allows us to easily estimate it from a stereo pair of images using an energy min ..."
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Cited by 69 (10 self)
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We present an energy based approach to estimate a dense disparity map between two images while preserving its discontinuities resulting from image boundaries. We first derive a simplied expression for the disparity that allows us to easily estimate it from a stereo pair of images using an energy minimization approach. We assume that the epipolar geometry is known, and we include this information in the energy model. Discontinuities are preserved by means of a regularization term based on the NagelEnkelmann operator. We investigate the associated EulerLagrange equation of the energy functional, and we approach the solution of the underlying partial differential equation (PDE) using a gradient descent method. In order to reduce the risk to be trapped within some irrelevant local minima during the iterations, we use a focusing strategy based on a linear scalespace. We prove the existence and uniqueness of the underlying parabolic partial differential equation. Experimental results on bot...
Real time correlationbased stereo: algorithm, implementations and applications
, 1993
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The Geometry and Matching of Lines and Curves Over Multiple Views
"... This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography in ..."
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Cited by 45 (1 self)
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This paper describes the geometry of imaged curves in two and three views. Multiview relationships are developed for lines, conics and nonalgebraic curves. The new relationships focus on determining the plane of the curve in a projective reconstruction, and in particular using the homography induced by this plane for transfer from one image to another. It is shown that given the fundamental matrix between two views, and images of the curve in each view, then the plane of a conic may be determined up to a two fold ambiguity, but local curvature of a curve uniquely determines the plane. It is then shown that given the trifocal tensor between three views, this plane defines a homography map which may be used to transfer a conic or the curvature from two views to a third. Simple expressions are developed for the plane and homography in each case.
Using 3Dimensional Meshes To Combine ImageBased and GeometryBased Constraints
 IN EUROPEAN CONFERENCE ON COMPUTER VISION
, 1994
"... A unified framework for 3D shape reconstruction allows us to combine imagebased and geometrybased information sources. The image information is akin to stereo and shapefromshading, while the geometric information may be provided in the form of 3D points, 3D features or 2D silhouettes. A form ..."
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Cited by 26 (4 self)
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A unified framework for 3D shape reconstruction allows us to combine imagebased and geometrybased information sources. The image information is akin to stereo and shapefromshading, while the geometric information may be provided in the form of 3D points, 3D features or 2D silhouettes. A formal integration framework is critical in recovering complicated surfaces because the information from a single source is often insufficient to provide a unique answer. Our approach to shape recovery is to deform a generic objectcentered 3D representation of the surface so as to minimize an objective function. This objective function is a weighted sum of the contributions of the various information sources. We describe these various terms individually, our weighting scheme, and our optimization method. Finally, we present results on anumber of difficult images of real scenes for which a single source of information would have proved insufficient.
The Geometry and Matching of Curves in Multiple Views
 In Proceedings European Conference on Computer Vision
, 1998
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Camera Calibration, Scene Motion and Structure recovery from point correspondences and fundamental matrices
 IJCV
, 1997
"... We address the problem of estimating threedimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orienta ..."
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Cited by 18 (3 self)
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We address the problem of estimating threedimensional motion, and structure from motion with an uncalibrated moving camera. We show that point correspondences between three images, and the fundamental matrices computed from these point correspondences, are sufficient to recover the internal orientation of the camera (its calibration), the motion parameters, and to compute coherent perspective projection matrices which enable us to reconstruct 3D structure up to a similarity. In contrast with other methods, no calibration object with a known 3D shape is needed, and no limitations are put upon the unknown motions to be performed or the parameters to be recovered, as long as they define a projective camera. The theory of the method, which is based on the constraint that the observed points are part of a static scene, thus allowing us to link the intrinsic parameters and the fundamental matrix via the absolute conic, is first detailed. Several algorithms are then presented, and their perfo...
A Theory of the Motion Fields of Curves
 International Journal of Computer Vision
, 1993
"... This paper is a study of the motion field generated by moving 3D curves which are observed by a camera. We first discuss the relationship between optical flow and motion field and show that the assumptions made in the computation of the optical flow are a bit difficult to defend. We then go ahead to ..."
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Cited by 17 (1 self)
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This paper is a study of the motion field generated by moving 3D curves which are observed by a camera. We first discuss the relationship between optical flow and motion field and show that the assumptions made in the computation of the optical flow are a bit difficult to defend. We then go ahead to study the motion field of a general curve. We first study the general case of a curve moving nonrigidly and introduce the notion of isometric motion. In order to do this, we introduce the notion of spatiotemporal surface and study its differential properties up to the second order. We show that, contrarily to what is commonly believed, the full motion field of the curve (i.e the component tangent to the curve) cannot be recovered from this surface. We also give the equations that characterize the spatiotemporal surface completely up to a rigid transformation. Those equations are the expressions of the first and second fundamental forms and the Gauss and CodazziMainardi equations. We then...