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In this paper, we will introduce a common framework for the definition and operations on the different multiple view tensors. The novelty of the proposed formulation is to not fix any parameters of the camera matrices, but instead letting a group act on them and look at the different orbits. In this setting the multiple view geometry can be viewed as a four-dimensional linear manifold in IR3 ...
This paper gives a practical and accurate algorithm for the computation of the quadrifocal tensor and extraction of camera matrices from it. Previous methods for using the quadrifocal tensor in projective scene reconstruction have not emphasized accuracy of the algorithm in conditions of noise. Methods given in this paper minimize algebraic error either through a non-iterative linear algorithm, or...
We introduce the concept of self-calibration of a 1D projective camera from point correspondences, and describe a method for uniquely determining the two internal parameters of a 1D camera based on the trifocal tensor of three 1D images. The method requires the estimation of the trifocal tensor which can be achieved linearly with no approximation unlike the trifocal tensor of 2D images, and solving...
This contribution describes an automatic 3D surface modeling system that extracts dense metric 3D surfaces from an uncalibrated video sequence. A static 3D scene is observed from multiple viewpoints by freely moving a video camera around the object. No restrictions on camera movement and internal camera parameters like zoom are imposed, as the camera pose and intrinsic parameters are calibrated from...
In this paper, we study the statistical theory of shape for ordered finite point configurations, or otherwise stated, the uncertainty of geometric invariants. Such studies have been made for affine invariants in e.g. [GHJ92], [Wer93], where in the former case a bound on errors are used instead of errors described by density functions, and in the latter case a first order approximation gives an ellipsis...
This paper describes the theory and a practical algorithm for the autocalibration of a moving projective camera, from m ≥ 5 views of a planar scene. The unknown camera calibration, motion and scene geometry are recovered up to scale, from constraints encoding the motion-invariance of the camera's internal parameters. This extends the domain of autocalibration from the classical non-planar case to...
This paper deals with the problem of characterizing and parametrizing the manifold of trifocal tensors that describe the geometry of three views like the fundamental matrix characterizes the geometry of two. The paper contains two new results. First a new, simpler, set of algebraic constraints that characterizes the set of trifocal tensors is presented. Second, we give a new parametrization of the...
We present a new function that operates on Fundamental matrices across a sequence of views. The operation, we call “threading”, connects two consecutive Fundamental matrices using the Trilinear tensor as the connecting thread. The threading operation guarantees that consecutive camera matrices are consistent with a unique 3D model, without ever recovering a 3D model. Applications include recovery...
This paper addresses the problem of computing three-dimensional structure and motion from an unknown rigid configuration of point and lines viewed by an affine projection model. An algebraic structure, analogous to the trilinear tensor for three perspective cameras, is defined for configurations of three centered affine cameras. This centered affine trifocal tensor contains 12 non-zero coefficients...
This article raises the problem of errors caused by the metrology of a calibration pattern to the accurate estimation of the intrinsic and extrinsic calibration parameters modeling the video system. In order to take into account these errors a new approach is proposed that enables us to compute in the same time the traditional calibration parameters and the 3D geometry of the calibration pattern using...
We discuss optimal rotation estimation from two sets of 3-D points in the presence of anisotropic and inhomogeneous noise. We first present a theoretical accuracy bound and then give a method that attains that bound, which can be viewed as describing the reliability of the solution. We also show that an efficient computational scheme can be obtained by using quaternions and applying renormalization...
We show that we can effectively fit arbitrarily complex animation models to noisy image data. Our approach is based on leastsquares adjustment using of a set of progressively finer control triangulations and takes advantage of three complementary sources of information: stereo data, silhouette edges and 2-D feature points. In this way, complete head models—including ears and hair—can be acquired...
Different applications in the field of vision-based navigation of autonomous mobile robots depend on the degree of knowledge of the environment. Indoor environment applications often use landmarks or maps for navigation. Others have only knowledge of known and expected objects. In such applications, parts of the scene are classified in these objects, e.g. road junctions, doors, walls, furniture, and...
This paper presents fundamental theory and design of central panoramic cameras. Panoramic cameras combine a convex hyperbolic or parabolic mirror with a perspective camera to obtain a large field of view. We show how to design a panoramic camera with a tractable geometry and we propose a simple calibration method. We derive the image formation function for such a camera. The main contribution of the...
Binocular stereo is the process of obtaining depth information from a pair of left and right views of a scene. We present a new approach to compute the disparity map by solving a global optimization problem that models occlusions, discontinuities, and epipolar-line interactions. In the model, geometric constraints require every disparity discontinuity along the epipolar line in one eye to always...
When a symmetric object in 3D is projected to an image, the symmetry properties are lost except for specific relative viewpoints. For sufficiently complex objects however, it is still possible to infer symmetry in 3D from a single image of an uncalibrated camera. In this paper we give a general computational procedure for computing 3D structure and finding image symmetry constraints from single view...
A projectively invariant representation for groups of planar disjoint contours is proposed as a simultaneous polar reparametrization of multiple curves. Its origin is an invariant point and for each ray orientation, the cross-ratio of the intersections with its closest curves is taken as a value associated to the radius. The sequence of cross-ratio values for all orientations represents a signature...
Robust techniques are developed for determining structure from motion in the uncalibrated case. The structure recovery is based on previous work [7] in which it was shown that a camera undergoing unknown motion and having an unknown, and possibly varying, focal length can be self-calibrated via closed-form expressions in the entries of two matrices derivable from an instantaneous optical flow field...
A factorization method is proposed for recovering camera motion and object shapes from point correspondences observed in multiple images with perspective projection. For any factorization-based approaches for perspective images, scaling parameters called projective depths must be estimated in order to obtain a measurement matrix that could be decomposed into motion and shape. One possible approach,...
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