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Algebraic Functions For Recognition
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1994
"... In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment  yielding a direct reprojection method that cuts through the computations of camera transformation, sce ..."
Abstract

Cited by 147 (29 self)
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In the general case, a trilinear relationship between three perspective views is shown to exist. The trilinearity result is shown to be of much practical use in visual recognition by alignment  yielding a direct reprojection method that cuts through the computations of camera transformation, scene structure and epipolar geometry. Moreover, the direct method is linear and sets a new lower theoretical bound on the minimal number of points that are required for a linear solution for the task of reprojection. The proof of the central result may be of further interest as it demonstrates certain regularities across homographies of the plane and introduces new view invariants. Experiments on simulated and real image data were conducted, including a comparative analysis with epipolar intersection and the linear combination methods, with results indicating a greater degree of robustness in practice and a higher level of performance in reprojection tasks. Keywords Visual Recognition, Al...
Example Based Image Analysis and Synthesis
, 1993
"... Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physicallybased, 3D models. We describe here novel techniques for the analysis and the synthesis of new greylevel (and color) images. With the first technique, ffl the mapping from ..."
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Cited by 101 (26 self)
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Image analysis and graphics synthesis can be achieved with learning techniques using directly image examples without physicallybased, 3D models. We describe here novel techniques for the analysis and the synthesis of new greylevel (and color) images. With the first technique, ffl the mapping from novel images to a vector of "pose" and "expression" parameters can be learned from a small set of example images using a function approximation technique that we call an analysis network; ffl the inverse mapping from input "pose" and "expression" parameters to output greylevel images can be synthesized from a small set of example images and used to produce new images under realtime control using a similar learning network, called in this case a synthesis network. This technique relies on (i) using a correspondence algorithm that matches corresponding pixels among pairs of greylevel images and effectively "vectorizes" them, and (ii) exploiting a class of multidimensional interpolation n...
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...
Relative Affine Structure: Canonical Model for 3D from 2D Geometry and Applications
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 1996
"... We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projec ..."
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Cited by 59 (9 self)
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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projective and affine  in a natural and simple way, and introduces new, extremely simple, algorithms for the tasks of reconstruction from multiple views, recognition by alignment, and certain image coding applications.
Relative Affine Structure: Theory and Application to 3D Reconstruction From Perspective Views
 In IEEE Conference on Computer Vision and Pattern Recognition
, 1994
"... We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, proje ..."
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Cited by 58 (12 self)
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We propose an affine framework for perspective views, captured by a single extremely simple equation based on a viewercentered invariant we call relative affine structure. Via a number of corollaries of our main results we show that our framework unifies previous work  including Euclidean, projective and affine  in a natural and simple way. Finally, the main results were applied to a real image sequence for purpose of 3D reconstruction from 2D views. 1 Introduction The introduction of affine and projective tools into the field of computer vision have brought increased activity in the fields of structure from motion and recognition by alignment in the recent few years. The emerging realization is that nonmetric information, although weaker than the information provided by depth maps and rigid camera geometries, is nonetheless useful in the sense that the framework may provide simpler algorithms, camera calibration is not required, more freedom in picturetaking is allowed  ...
On Geometric and Algebraic Aspects of 3D Affine and Projective Structures from Perspective 2D Views
 In Proceedings of the 2nd European Workshop on Invariants, Ponta Delagada, Azores
, 1993
"... Part I of this paper investigates the differences  conceptually and algorithmically  between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a ..."
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Cited by 23 (8 self)
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Part I of this paper investigates the differences  conceptually and algorithmically  between affine and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an affine invariant exists between any view and a fixed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment schemes for visual recognition, projective invariants are not really necessary. The projective extension is then derived, showing that it is necessary only for tasks for which a reference view is not available  such as happens when updating scene structure from a moving stereo rig. The geometric difference between the two proposed invariants are that the affine invariant measures the relative deviation from a single reference plane, whereas the projective invariant measures the relative deviation from two reference planes. The affine invariant can be computed from three correspondin...