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20
A unifying framework for structure and motion recovery from image sequences.
 In Proc. 5th Int. Conf. on Computei Vision,
, 1995
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Rigid Body Segmentation and Shape Description from Dense Optical Flow under Weak Perspective
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1997
"... We present an algorithm for identifying and tracking independently moving rigid objects from optical flow. Some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field. While discontinuities do indicate a change in scene depth, they do not in gene ..."
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Cited by 31 (0 self)
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We present an algorithm for identifying and tracking independently moving rigid objects from optical flow. Some previous attempts at segmentation via optical flow have focused on finding discontinuities in the flow field. While discontinuities do indicate a change in scene depth, they do not in general signal a boundary between two separate objects. The proposed method uses the fact that each distinct object has a unique epipolar constraint associated with its motion. Thus motion discontinuities based on selfocclusion are distinguished from those due to separate objects. The use of epipolar geometry allows for the determination of individual motion parameters for each object as well as the recovery of relative depth for each point on the object. The segmentation problem is formulated as a scene partitioning problem and a statisticbased algorithm which uses only nearest neighbor interactions and a finite number of iterations is developed. After the initial segmentation, each rigid obj...
A New Multistage Approach to Motion and Structure Estimation: From Essential Parameters to Euclidean Motion Via Fundamental Matrix
, 1996
"... The classical approach to motion and structure estimation problem from two perspective projections consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor, which is a linear estimation problem; (ii) refining the motion estimation ba ..."
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Cited by 27 (2 self)
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The classical approach to motion and structure estimation problem from two perspective projections consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor, which is a linear estimation problem; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Unfortunately, the results obtained using this approach are often not satisfactory, especially when the motion is small or when the observed points are close to a degenerate surface (e.g. plane). The problem is that the second stage is very sensitive to the initial guess, and that it is very difficult to obtain a precise initial estimate from the first stage. This is because we perform a projection of a set of quantities which are estimated in a space of 8 dimensions, much higher than that of the real space which is fivedimensional. We propose in this paper a novel approach by introducing...
Motion and structure from two perspective views: From essential parameters to euclidean motion via fundamental matrix
 Journal of the Optical Society of America A
, 1997
"... The standard approach consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Un ..."
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Cited by 24 (8 self)
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The standard approach consists of two stages: (i) using the 8point algorithm to estimate the 9 essential parameters defined up to a scale factor; (ii) refining the motion estimation based on some statistically optimal criteria, which is a nonlinear estimation problem on a fivedimensional space. Unfortunately, the results obtained are often not satisfactory. The problem is that the second stage is very sensitive to the initial guess, and that it is very difficult to obtain a precise initial estimate from the first stage. This is because we perform a projection of a set of quantities which are estimated in a space of 8 dimensions (by neglecting the constraints on the essential parameters), much higher than that of the real space which is fivedimensional. We propose in this paper a novel approach by introducing an intermediate stage which consists in estimating a 3 × 3 matrix defined up to a scale factor by imposing the rank2 constraint (the matrix has seven independent parameters, and is known as the fundamental matrix). The idea is to gradually project parameters estimated in a high dimensional space onto a slightly lower space, namely from 8 dimensions to 7 and finally to 5. The proposed approach has been tested with synthetic and real data, and a considerable improvement has been observed. Our conjecture from this work is that the imposition of the constraints arising from projective geometry should be used as an intermediate step in order to obtain reliable 3D Euclidean motion and structure estimation from multiple calibrated images. The software is available from the Internet.
Recursive 3D Visual Motion Estimation Using Subspace Constraints
"... The 3D motion of a camera within a static environment produces a sequence of timevarying images that can be used for reconstructing the relative motion between the scene and the viewer. The problem of reconstructing rigid motion from a sequence of perspective images may be characterized as the est ..."
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Cited by 24 (2 self)
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The 3D motion of a camera within a static environment produces a sequence of timevarying images that can be used for reconstructing the relative motion between the scene and the viewer. The problem of reconstructing rigid motion from a sequence of perspective images may be characterized as the estimation of the state of a nonlinear dynamical system, which is defined by the rigidity constraint and the perspective measurement map. The timederivative of the measured output of such a system, which is called the "2D motion field" and is approximated by the "optical flow", is bilinear in the motion parameters, and may be used to specify a subspace constraint on the direction of heading independent of rotation and depth, and a pseudomeasurement for the rotational velocity as a function of the estimated heading. The subspace constraint may be viewed as an implicit dynamical model with parameters on a differentiable manifold, and the visual motion estimation problem may be cast in a system...
3D Structure From Visual Motion: Modeling, Representation and Observability
 Automatica
, 1997
"... The problem of "Structure From Motion" concerns the reconstruction of the threedimensional structure of a scene from its projection onto a moving twodimensional surface. Such a problem is solved effectively by the human visual system, judging from the ease with which we perform delicate ..."
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Cited by 23 (7 self)
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The problem of "Structure From Motion" concerns the reconstruction of the threedimensional structure of a scene from its projection onto a moving twodimensional surface. Such a problem is solved effectively by the human visual system, judging from the ease with which we perform delicate control tasks involving vision as a sensor such as reaching for objects in the environment or driving a car. In this paper we study "Structure From Motion" from the point of view of dynamical systems: we first formalize the problem of threedimensional structure and motion reconstruction as the estimation of the state of certain nonlinear dynamical models. Then we study the feasibility of "Structure From Motion" by analyzing the observability of such models. The models which define the visual motion estimation problem for feature points in the Euclidean 3D space are not locally observable; however, the nonobservable manifold can be easily isolated by imposing metric constraints on the statespace. O...
Observability/Identifiability of Rigid Motion under Perspective Projection
 In Proc. of the 33rd IEEE Conf. on Decision and Control
, 1994
"... The "visual motion estimation" problem concerns the estimation of the motion of an object viewed under projection. This paper addresses the feasibility of such a problem. We will show that the model which defines the visual motion estimation problem for feature points in the Euclidean 3D s ..."
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Cited by 15 (12 self)
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The "visual motion estimation" problem concerns the estimation of the motion of an object viewed under projection. This paper addresses the feasibility of such a problem. We will show that the model which defines the visual motion estimation problem for feature points in the Euclidean 3D space lacks both linear and local (weak) observability. The locally observable manifold is covered with three levels of Lie differentiations. It is possible, indeed, to reduce the set of indistinguishable states by imposing metric constraints on the statespace. We analyze a model for visual motion estimation in terms of identification of an exterior differential system, whose parameters live on a topological manifold, called the essential manifold, which explicitly encodes the forementioned metric constraints. We show that rigid motion is globally observable/identifiable under perspective projection with zero level of Lie differentiation under some general position conditions. Such conditions hold wh...
Robust Tracking and Structure from Motion with Sample Based Uncertainty Representation
, 2002
"... is critical in autonomous mapping and robot navigation. Geometric reconstruction involves feature tracking, i.e., locating corresponding image features in consecutive images, and structure from motion (SFM), i.e., recovering the 3D structure of the environment from a set of correspondences between ..."
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Cited by 8 (0 self)
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is critical in autonomous mapping and robot navigation. Geometric reconstruction involves feature tracking, i.e., locating corresponding image features in consecutive images, and structure from motion (SFM), i.e., recovering the 3D structure of the environment from a set of correspondences between images. Although algorithms for feature tracking and structure from motion are wellestablished, their use in practical robot mobile applications is still difficult because of occluded features, nonsmooth motion between frames, and ambiguous patterns in images. In this paper, we show how a samplingbased representation can be used in place of the traditional Gaussian representation of uncertainty. We show how sampling can be used for both feature tracking and SFM and we show how they are combined in this framework. The approach is exercised in the context of a mobile robot navigating through an outdoor environment with an omnidirectional camera.
Tubaro: “A Multiview Trinocular System for Automatic 3D Object Modeling and Rendering
 XVIII International Congress for Photogrammetry and Remote Sensing
, 1996
"... For several applications of closerange photogrammetry, there is a growing interest in systems that are able to automatically perform a 3D reconstruction of objects from stereo correspondences on CCD camera views. For such applications, a full3D reconstruction of the object is often very desirable ..."
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Cited by 7 (7 self)
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For several applications of closerange photogrammetry, there is a growing interest in systems that are able to automatically perform a 3D reconstruction of objects from stereo correspondences on CCD camera views. For such applications, a full3D reconstruction of the object is often very desirable. In fact, most automatic systems for 3D reconstruction based on stereo matching can only reconstruct the front side of the imaged scene. In order to obtain a full3D reconstruction, it is necessary to observe the scene from several significant viewpoints. Furthermore, an exact determination of position and orientation of the cameras for all considered viewpoints (cameramotion) becomes crucial. In this paper we present a lowcost, highaccuracy, full3D reconstruction system based on a calibrated set of three standardresolution CCD cameras. No special positioning devices are needed as the cameramotion is retrieved for each position of the trinocular system from stereomatching of unconstrained fiducial marks.
Recursive estimation of camera motion from uncalibrated image sequences
 in Proc. ICIP94
, 1994
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