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113
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.
Estimation of relative camera positions for uncalibrated cameras
, 1992
"... Abstract. This paper considers, the determination of internal camera parameters from two views of a point set in three dimensions. A noniterative algorithm is given for determining the focal lengths of the two cameras, as well as their relative placement, assuming all other internal camera paramete ..."
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Cited by 277 (21 self)
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Abstract. This paper considers, the determination of internal camera parameters from two views of a point set in three dimensions. A noniterative algorithm is given for determining the focal lengths of the two cameras, as well as their relative placement, assuming all other internal camera parameters to be known. It is shown that this is all the information that may be deduced from a set of image correspondences. 1
Canonic Representations for the Geometries of Multiple Projective Views
 Computer Vision and Image Understanding
, 1994
"... This work is in the context of motion and stereo analysis. It presents a new uni ed representation which will be useful when dealing with multiple views in the case of uncalibrated cameras. Several levels of information might be considered, depending on the availability of information. Among other t ..."
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Cited by 180 (8 self)
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This work is in the context of motion and stereo analysis. It presents a new uni ed representation which will be useful when dealing with multiple views in the case of uncalibrated cameras. Several levels of information might be considered, depending on the availability of information. Among other things, an algebraic description of the epipolar geometry of N views is introduced, as well as a framework for camera selfcalibration, calibration updating, and structure from motion in an image sequence taken by a camera which is zooming and moving at the same time. We show how a special decomposition of a set of two or three general projection matrices, called canonical enables us to build geometric descriptions for a system of cameras which are invariant with respect to a given group of transformations. These representations are minimal and capture completely the properties of each level of description considered: Euclidean (in the context of calibration, and in the context of structure from motion, which we distinguish clearly), a ne, and projective, that we also relate to each other. In the last case, a new decomposition of the wellknown fundamental matrix is obtained. Dependencies, which appear when three or more views are available, are studied in the context of the canonic decomposition, and new composition formulas are established. The theory is illustrated by tutorial examples with real images.
Relative Orientation
 International Journal of Computer Vision
, 1990
"... Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the in ..."
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Cited by 130 (2 self)
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Abstract: Before corresponding points in images taken with two cameras can be used to recover distances to objects in a scene, one has to determine the position and orientation of one camera relative to the other. This is the classic photogrammetric problem of relative orientation, central to the interpretation of binocular stereo information. Iterative methods for determining relative orientation were developed long ago; without them we would not have most of the topographic maps we do today. Relative orientation is also of importance in the recovery of motion and shape from an image sequence when successive frames are widely separated in time. Workers in motion vision are rediscovering some of the methods of photogrammetry. Described here is a simple iterative scheme for recovering relative orientation that, unlike existing methods, does not require a good initial guess for the baseline and the rotation. The data required is a pair of bundles of corresponding rays from the two projection centers to points in the scene. It is well known that at least five pairs of rays are needed. Less appears to be known about the existence of multiple solutions and their interpretation. These issues are discussed here. The unambiguous determination of all of the parameters of relative orientation is not possible when the observed points lie on a critical surface. These surfaces and their degenerate forms are analysed as well.
SelfCalibration of a Moving Camera From Point Correspondences and Fundamental Matrices
, 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 orien ..."
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Cited by 99 (2 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 ...
Relative 3D Reconstruction Using Multiple Uncalibrated Images
, 1995
"... In this paper, we show how relative 3D reconstruction from point correspondences of multiple uncalibrated images can be achieved through reference points. The original contributions with respect to related works in the field are mainly a direct global method for relative 3D reconstruction, and a geo ..."
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Cited by 90 (14 self)
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In this paper, we show how relative 3D reconstruction from point correspondences of multiple uncalibrated images can be achieved through reference points. The original contributions with respect to related works in the field are mainly a direct global method for relative 3D reconstruction, and a geometrical method to select a correct set of reference points among all image points. Experimental results from both simulated and real image sequences are presented, and robustness of the method and reconstruction precision of the results are discussed. Key words: relative reconstruction, projective geometry, uncalibration, geometric interpretation 1 Introduction 1.1 Relative positioning From a single image, no depth can be computed without a priori information. Even more, no invariant can be computed from a general set of points as shown by Burns, Weiss and Riseman (1990). This problem becomes feasible using multiple images. The process is composed of two major steps. First, image feature...
Theory and Practice of Projective Rectification
, 1998
"... This paper gives a new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of "matched epipolar projections". These are projections in which the epipolar lines run parallel with the xaxis and consequently ..."
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Cited by 72 (0 self)
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This paper gives a new method for image rectification, the process of resampling pairs of stereo images taken from widely differing viewpoints in order to produce a pair of "matched epipolar projections". These are projections in which the epipolar lines run parallel with the xaxis and consequently, disparities between the images are in the x direction only. The method is based on an examination of the fundamental matrix of LonguetHiggins which describes the epipolar geometry of the image pair. The approach taken is consistent with that recently advocated by Faugeras ([1]) of avoiding camera calibration. The paper uses methods of projective geometry to determine a pair of 2D projective transformations to be applied to the two images in order to match the epipolar lines. The advantages include the simplicity of the 2D projective transformation which allows very fast resampling as well as subsequent simplification in the identification of matched points and scene reconstruction. 1 In...
Motion estimation via dynamic vision
 IN PROC. EUROPEAN CONF. ON COMPUTER VISION
, 1996
"... Estimating the threedimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although “visual motion estimation” ..."
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Cited by 71 (8 self)
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Estimating the threedimensional motion of an object from a sequence of projections is of paramount importance in a variety of applications in control and robotics, such as autonomous navigation, manipulation, servo, tracking, docking, planning, and surveillance. Although “visual motion estimation” is an old problem (the first formulations date back to the beginning of the century), only recently have tools from nonlinear systems estimation theory hinted at acceptable solutions. In this paper we formulate the visual motion estimation lproblem in terms of identification of nonlinear implicit systems with parameters on a topological manifold and propose a dynamic solution either in the local coordinates or in the embedding space of the parameter manifold. Such a formulation has structural advantages over previous recursive schemes, since the estimation of motion is decoupled from the estimation of the structure of
Euclidean Reconstruction from Constant Intrinsic Parameters
"... In this paper a new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters a ..."
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Cited by 69 (5 self)
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In this paper a new method for Euclidean reconstruction from sequences of images taken by uncalibrated cameras, with constant intrinsic parameters, is described. Our approach leads to a variant of the so called Kruppa equations. It is shown that it is possible to calculate the intrinsic parameters as well as the Euclidean reconstruction from at least three images. The novelty of our approach is that we build our calculation on a projective reconstruction, obtained without the assumption on constant intrinsic parameters. This assumption simplifies the analysis, because a projective reconstruction is already obtained and we need ‘only’ to find the correct Euclidean reconstruction among all possible projective reconstructions.
Projective Structure from Uncalibrated Images: Structure from Motion and Recognition
, 1994
"... We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call proj ..."
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Cited by 62 (14 self)
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We address the problem of reconstructing 3D space in a projective framework from two or more views, and the problem of artificially generating novel views of the scene from two given views (reprojection). We describe an invariance relation which provides a new description of structure, we call projective depth, which is captured by a single equation relating image point correspondences across two or more views and the homographies of two arbitrary virtual planes. The framework is based on knowledge of correspondence of features across views, is linear, extremely simple, and the computations of structure readily extends to overdetermination using multiple views. Experimental results demonstrate a high degree of accuracy in both tasks  reconstruction and reprojection. KeywordsVisual Recognition, 3D Reconstruction from 2D Views, Projective Geometry, Algebraic and Geometric Invariants. I. Introduction The geometric relation between objects (or scenes) in the world and their imag...