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Linear Multi View Reconstruction and Camera Recovery
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2001
"... This paper presents a linear algorithm for the simultaneous computation of 3D points and camera positions from multiple perspective views, based on having four points on a reference plane visible in all views. The reconstruction and camera recovery is achieved, in a single step, by finding the null ..."
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Cited by 68 (5 self)
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This paper presents a linear algorithm for the simultaneous computation of 3D points and camera positions from multiple perspective views, based on having four points on a reference plane visible in all views. The reconstruction and camera recovery is achieved, in a single step, by finding the nullspace of a matrix using singular value decomposition. Unlike factorization algorithms, the presented algorithm does not require all points to be visible in all views. By simultaneously reconstructing points and views the numerically stabilizing effect of having wide spread cameras with large mutual baselines is exploited. Experimental results are presented for both finite and infinite reference planes. An especially interesting application of this method is the reconstruction of architectural scenes with the reference plane taken as the plane at infinity which is visible via three orthogonal vanishing points. This is demonstrated by reconstructing the outside and inside (courtyard) of a building on the basis of 35 views in one single SVD.
Plane + Parallax, Tensors and Factorization
 In Proc. of ECCV
, 2000
"... Abstract. We study the special form that the general multiimage tensor formalism takes under the plane + parallax decomposition, including matching tensors and constraints, closure and depth recovery relations, and intertensor consistency constraints. Plane + parallax alignment greatly simplifies ..."
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Cited by 31 (1 self)
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Abstract. We study the special form that the general multiimage tensor formalism takes under the plane + parallax decomposition, including matching tensors and constraints, closure and depth recovery relations, and intertensor consistency constraints. Plane + parallax alignment greatly simplifies the algebra, and uncovers the underlying geometric content. We relate plane + parallax to the geometry of translating, calibrated cameras, and introduce a new parallaxfactorizing projective reconstruction method based on this. Initial plane + parallax alignment reduces the problem to a single rankone factorization of a matrix of rescaled parallaxes into a vector of projection centres and a vector of projective heights above the reference plane. The method extends to 3D lines represented by viapoints and 3D planes represented by homographies.
Ambiguous configurations for 3view projective reconstruction
 In European Conf. Computer Vision
, 2000
"... The critical configurations for projective reconstruction from three views are discussed. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and cameras uniquely, up to projective transformation. For two views, t ..."
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Cited by 15 (4 self)
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The critical configurations for projective reconstruction from three views are discussed. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and cameras uniquely, up to projective transformation. For two views, the classification of critical configurations is well knownthe configuration is critical if and only if the points and camera centres all lie on a ruled quadric. For three views the critical configurations have not been identified previously. In this paper it is shown that for any placement of three given cameras there always exists a critical set consisting of a fourthdegree curve – any number of points on the curve form a critical set for the three cameras. Dual to this result, for a set of seven points there exists a fourthdegree curve such that a configuration of any number of cameras placed on this curve is critical for the set of points. Other critical configurations exist in cases where the points all lie in a plane, or one of the cameras lies on a twisted cubic. 1
Ambiguous Configurations for the 1D Structure and Motion Problem
"... In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of po ..."
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Cited by 8 (3 self)
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In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D (calibrated or uncalibrated) perspective camera irrespective of the number of points and views. It is wellknown that the calibrated and uncalibrated case are linked through the circular points. This link enables us to solve for both cases simultaneously. Another important tool is the duality in exchanging points and cameras and corresponding Cremona transformation. These concepts are generalized to the 1D case and used for the investigation of ambiguous configurations. Several examples and illustrations are also provided to explain the results and to provide geometrical insight.
Critical curves and surfaces for Euclidean reconstruction
 In European Conf. Computer Vision
, 2002
"... Abstract. The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are s ..."
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Cited by 6 (4 self)
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Abstract. The problem of recovering scene structure and camera motion from images has a number of inherent ambiguities. In this paper, configurations of points and cameras are analyzed for which the image points alone are insufficient to recover the scene geometry uniquely. Such configurations are said to be critical. For two views, it is wellknown that a configuration is critical only if the two camera centres and all points lie on a ruled quadric. However, this is only a necessary condition. We give a complete characterization of the critical surfaces for two calibrated cameras and any number of points. Both algebraic and geometric characterizations of such surfaces are given. The existence of critical sets for nview projective reconstruction has recently been reported in the literature. We show that there are critical sets for nview Euclidean reconstruction as well. For example, it is shown that for any placement of three calibrated cameras, there always exists a critical set consisting of any number of points on a fourthdegree curve. 1
Reconstruction From SixPoint Sequences
"... An algorithm is given for computing projective structure from a set of six points seen in a sequence of many images. The method is based on the notion of duality between cameras and points first pointed out by Carlsson and Weinshall. The current implementation avoids the weakness inherent in previou ..."
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Cited by 3 (0 self)
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An algorithm is given for computing projective structure from a set of six points seen in a sequence of many images. The method is based on the notion of duality between cameras and points first pointed out by Carlsson and Weinshall. The current implementation avoids the weakness inherent in previous implementations of this method in which numerical accuracy is compromised by the distortion of image point error distributions under projective transformation. It is shown in this paper that one may compute the dual fundamental matrix by minimizing a cost function giving a firstorder approximation to geometric distance error in the original untransformed image measurements. This is done by a modification of a standard nearoptimal method for computing the fundamental matrix. Subsequently, the error measurements are adjusted optimally to conform with exact imaging geometry by application of the triangulation method of HartleySturm.
A critical configuration for reconstruction from rectilinear motion
 In Conf. Computer Vision and Pattern Recognition
, 2003
"... This paper investigates critical configurations for projective reconstruction from multiple images taken by a camera moving in a straight line. Projective reconstruction refers to a determination of the 3D geometrical configuration of a set of 3D points and cameras, given only correspondences betwee ..."
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Cited by 1 (1 self)
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This paper investigates critical configurations for projective reconstruction from multiple images taken by a camera moving in a straight line. Projective reconstruction refers to a determination of the 3D geometrical configuration of a set of 3D points and cameras, given only correspondences between points in the images. A configuration of points and cameras is critical if it can not be determined uniquely (up to a projective transform) from the image coordinates of the points. It is shown that a configuration consisting of any number of cameras lying on a straight line, and any number of points lying on a twisted cubic constitutes a critical configuration. An alternative configuration consisting of a set of points and cameras all lying on a rational quartic curve exists. 1
CRITICAL CONFIGURATIONS FOR 1D RETINA VISION
"... In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D perspective camera irrespective of the number of points and views. Several examp ..."
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In this paper we investigate, determine and classify the critical configurations for solving structure and motion problems for 1D retina vision. We give a complete categorization of all ambiguous configurations for a 1D perspective camera irrespective of the number of points and views. Several examples and illustrations are provided to explain the results and to provide geometrical insight. 1.
Highlevel scene structure using visibility and occlusion
"... We demonstrate a new method for extracting highlevel scene information from the type of data available from simultaneous localisation and mapping systems. We model the scene with a collection of primitives (such as bounded planes), and make explicit use of both visible and occluded points in order ..."
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We demonstrate a new method for extracting highlevel scene information from the type of data available from simultaneous localisation and mapping systems. We model the scene with a collection of primitives (such as bounded planes), and make explicit use of both visible and occluded points in order to refine the model. Since our formulation allows for different kinds of primitives and an arbitrary number of each, we use Bayesian model evidence to compare very different models on an even footing. Additionally, by making use of Bayesian techniques we can also avoid explicitly finding the optimal assignment of map landmarks to primitives. The results show that explicit reasoning about occlusion improves model accuracy and yields models which are suitable for aiding data association. 1
Critical Configurations for Nview Projective Reconstruction
, 2001
"... In this paper we give a complete characterization of critical configurations for projective reconstruction with any number of points and views. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and the cameras u ..."
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In this paper we give a complete characterization of critical configurations for projective reconstruction with any number of points and views. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and the cameras uniquely, up to a projective transformation. For two views, the critical configurations are wellknown. In this paper it is shown that a configuration of n 3 cameras and m points is critical if all points and cameras lie on the intersection of two distinct ruled quadrics. Contrary to the twoview case, which in general allows two ambiguous solutions, there is a family of ambiguous reconstructions for the nview case. Conversely, it is shown that (except for minimal cases) for any critical configuration, all the points and cameras lie on the intersection of two ruled quadrics.