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128
An evaluation of intrinsic dimensionality estimators
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1995
"... only holds if we consider the whole set &. If more information about the curves are given, e.g. if fiducial points are given, then it might be possible to construct invariants which are nonconstant and continuThus the euclidean nature of image distorsion and the projective nature of camera geo ..."
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Cited by 49 (1 self)
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geometry do not interact well. It is possible that one could construct projective invariants which are continuous with respect to some other metric, but would this metric be relevant? ous. ACKNOWLEDGEMENTS I would like to thank my supervisor Gunnar Sparr for inspiration and guidance. I would also like
Preface
"... th Int. Conf. on Computer Vision, Kerkyra, Greece, pages 285292, 1999. [MO7] M. Oskarsson and K. strm. Map merging in structure and motion applications. In Proc. Symposium on Image Analysis, Halmstad, Sweden, 2000. motion problem for 1d retinal vision. Journal of Mathematical Imaging and Vision, ..."
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, 12(2):121135, 2000. vi Acknowledgments First of all I would like to thank my two supervisors Kalle strm and Gunnar Sparr. Without them this thesis would not have been written and their careful reading of the thesis has most certainly improved its quality. It has been a joy to see ones ideas
Extension of Affine Shape
, 1999
"... In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3Dcurves up to projective transformations, from a number ..."
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Cited by 13 (1 self)
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In this paper, we extend the notion of affine shape, introduced by Sparr, from finite point sets to more general sets. It turns out to be possible to generalize most of the theory. The extension makes it possible to reconstruct, for example, 3Dcurves up to projective transformations, from a number
Stratification of 3D vision: Projective, affine, and metric representations
"... In this article we provide a conceptual framework in which to think of the relationships between the threedimensional structure of the physical space and the geometric properties of a set of cameras which provide pictures from which measurements can be made. We usually think of the physical space a ..."
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Cited by 51 (4 self)
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In this article we provide a conceptual framework in which to think of the relationships between the threedimensional structure of the physical space and the geometric properties of a set of cameras which provide pictures from which measurements can be made. We usually think of the physical space as being embedded in a threedimensional euclidean space where measurements of lengths and angles do make sense. It turns out that for artificial systems, such as robots, this is not a mandatory viewpoint and that it is sometimes sufficient to think of the physical space as being embedded in an affine or even projective space. The question then arises of how to relate these models to image measurements and to geometric properties of sets of cameras. We show that in the case of two cameras, a stereo rig, the projective structure of the world can be recovered as soon as the epipolar geometry of the stereo rig is known and that this geometry is summarized by a single 3 3 matrix, which we called the fundamental matrix [1, 2]. The affine structure can then be recovered if we add to this information a projective transformation between the two images which is induced by the plane at infinity. Finally, the euclidean structure (up to a similitude) can be recovered if we add to these two elements the knowledge of two conics (one for each camera) which are the images of the absolute conic, a circle of radius p;1 in the plane at in nity. In all three cases we showhowthe threedimensional information can be recovered directly from the images without explicitely reconstructing the scene structure. This defines a natural hierarchy of geometric structures, a set of three strata, that we overlay onthephysical world and which we show to be recoverable by simple procedures relying on two items, the physical space itself together with possibly, but not necessarily, some a priori information about it, and some voluntary motions of the set of cameras.
Recursive Structure and Motion from Image Sequences using Shape and Depth Spaces
 IN SCIA97
, 1997
"... In this paper a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace metho ..."
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Cited by 41 (5 self)
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In this paper a novel recursive method for estimating structure and motion from image sequences is presented. The novelty lies in the fact that the output of the algorithm is independent of the chosen coordinate systems in the images as well as the ordering of the points. It relies on subspace methods and is derived from both ordinary coordinate representations and camera matrices and from a so called depth and shape analysis. Furthermore, no initial phase is needed to start up the algorithm. It starts directly with the first two images and incorporates new images as soon as new corresponding points are obtained. The performance of the algorithm is shown on simulated data. Moreover, the two different approaches, one using camera matrices and the other using the concepts of affine shape and depth, are unified into a general theory of structure and motion from image sequences.
Geometry and Algebra of Multiple Projective Transformations
, 1995
"... In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformatio ..."
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Cited by 34 (8 self)
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In this thesis several dioeerent cases of reconstruction of 3D objects from a number of 2D images, obtained by projective transformations, are considered. Firstly, the case where the images are taken by uncalibrated cameras, making it possible to reconstruct the object up to projective transformations, is described. The minimal cases of two images of seven points and three images of six points are solved, giving threefold solutions in both cases. Then linear methods for the cases where more points or more images are available are given, using multilinear constraints, based on a canonical representation of the multiple view geometry. The case of a continuous stream of images is also treated, giving multilinear constraints on the image coordinates and their derivatives. Secondly, the algebraic properties of the multilinear functions and the ideals generated by them are investigated. The main result is that the ideal generated by the bilinearities for three views have a primary decomposit...
Motion Estimation in Image Sequences Using the Deformation of Apparent Contours
 In IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1998
"... In this paper it is shown how to use the generalised epipolar constraint on apparent contours or silhouettes. One such constraint is obtained for each frontier point in each image pair in a sequence of images, to estimate the camera motion. 1. Introduction ...n#got h#r... In [] it was shown how the ..."
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Cited by 25 (4 self)
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In this paper it is shown how to use the generalised epipolar constraint on apparent contours or silhouettes. One such constraint is obtained for each frontier point in each image pair in a sequence of images, to estimate the camera motion. 1. Introduction ...n#got h#r... In [] it was shown how the viewer motion can be calculated from the contraints on the camera motion and the frontier points. However, only a pair of images was considered at the same time. In this situation the problem is often illconditioned and therefore it is diOEcult to accurately estimate the motion parameters. We extend this idea to treat pairs of images simultaneously to obtain more stable results and to recover the full motion of the camera in an image sequence. In this paper, we limit the derivation to the case of an uncalibrated camera with possibly varying intrinsic parameters. It is then wellknown that the motion can only be recovered up to a projective transformation, cf []. The generalisation to other...
A Common Framework for Kinetic Depth, Reconstruction and Motion for Deformable Objects
 ECCV'94, Lecture notes in Computer Science, Vol
, 1994
"... . In this paper, problems related to depth, reconstruction and motion from a pair of projective images are studied under weak assumptions. Only relative information within each image is used, nothing about their interrelations or about camera calibration. Objects in the scene may be deformed between ..."
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Cited by 32 (2 self)
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. In this paper, problems related to depth, reconstruction and motion from a pair of projective images are studied under weak assumptions. Only relative information within each image is used, nothing about their interrelations or about camera calibration. Objects in the scene may be deformed between the imaging instants, provided that the deformations can be described locally by affine transformations. It is shown how the problems can be treated by a common method, based on a novel interpretation of a theorem in projective geometry of M. Chasles, and the notion of "affine shape". No epipolar geometry is used. The method also enables the computation of the "depth flow", i.e. a relative velocity in the direction of the ray of sight. Keywords: Depth, shape, reconstruction, motion, invariants. 1 Introduction Central problems in computer vision are concerned with reconstruction and recovery of motion from image pairs. A number of algorithms exist, in general based on iterative numerical t...
Depth Computations from Polyhedral Images
, 1992
"... A method is developed for the computation of depth maps, modulo scale, from one single image of a polyhedral scene. Only affine shape properties of the scene and image are used, hence no metrical information. Results from simple experiments show good performance, both what concerns exactness and rob ..."
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Cited by 29 (4 self)
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A method is developed for the computation of depth maps, modulo scale, from one single image of a polyhedral scene. Only affine shape properties of the scene and image are used, hence no metrical information. Results from simple experiments show good performance, both what concerns exactness and robustness. It is also shown how the underlying theory may be used to single out and characterise certain singular situations that may occur in machine interpretation of line drawings.
Simultaneous Reconstruction of Scene Structure and Camera Locations From Uncalibrated Image Sequences
 In 13th International Conference on Pattern Recognition
, 1996
"... The paper deals with the structuremotion problem for images of point configurations taken by uncalibrated cameras. Using a parametrisation by affine shape and kinetic depth, a complete and explicit characterisation of the imaging geometry is given, including the shape of the object configuration a ..."
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Cited by 28 (4 self)
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The paper deals with the structuremotion problem for images of point configurations taken by uncalibrated cameras. Using a parametrisation by affine shape and kinetic depth, a complete and explicit characterisation of the imaging geometry is given, including the shape of the object configuration and the positions of the cameras relative to the scene. No epipolar geometry is used. It is shown that not only the projective but also the affine structure of the scene can be recovered when knowing the relative placement of five of the camera centres (four if they are coplanar). Variational algorithms for reconstruction and motion are presented, thus avoiding numerically unstable solving of algebraic equations. Any number of points in any number of images can be treated simultaneously and uniformly, without preselection of reference points. The performances of the algorithms are illustrated on simulations and experiments. Keywords: Depth, shape, reconstruction, motion, invariants, proximit...
Results 1  10
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