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36
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 ..."
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Cited by 154 (30 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...
SBA: a software package for generic sparse bundle adjustment
 ACM Transactions on Mathematical Software
, 2009
"... Foundation for Research and Technologyâ€”Hellas ..."
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 64 (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.
Pattern Regularity as a Visual Key
 Image and Vision Computing
, 1998
"... Regular structures, flat and nonflat, are perceived as regular in a wide range of viewing angles and under varying illumination. In this papers, we exploit this simple observation and develop an invariant measure of pattern regularity. ..."
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Cited by 38 (15 self)
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Regular structures, flat and nonflat, are perceived as regular in a wide range of viewing angles and under varying illumination. In this papers, we exploit this simple observation and develop an invariant measure of pattern regularity.
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 24 (9 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...
Outlier Detection in Video Sequences under Affine Projection
 In Proc. CVPR
, 2001
"... A novel robust method for outlier detection in structure and motion recovery for afJine cameras is presented. It is an extension of the wellknown TomasiKanade factorization technique designed to handle outliers. It can also be seen as an importation of the LMedS technique or W S A C into the fact ..."
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Cited by 19 (1 self)
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A novel robust method for outlier detection in structure and motion recovery for afJine cameras is presented. It is an extension of the wellknown TomasiKanade factorization technique designed to handle outliers. It can also be seen as an importation of the LMedS technique or W S A C into the factorization framework. Based on the computation of distances between subspaces, it relates closely with the subspacebased factorization methods for the perspective case presented by Sparr and others and the subspacebased factorization for afine cameras with missing data by Jacobs. Key features of the method presented here are its ability to compare different subspaces and the complete automation of the detection and elimination of outliers. Its pe flormance and effectiveness are demonstrated by experiments involving simulated and real video sequences. 1.
Alignment Using An Uncalibrated Camera System
 IEEE Trans. on Robotics and Automation
, 1993
"... We propose two methods for visual control of a robotic system which do not require the formulation of an explicit calibration between image space and the world coordinate system. Calibration is known to be a difficult and error prone process. By extracting control information directly from the im ..."
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Cited by 16 (4 self)
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We propose two methods for visual control of a robotic system which do not require the formulation of an explicit calibration between image space and the world coordinate system. Calibration is known to be a difficult and error prone process. By extracting control information directly from the image, we free our techniques from the errors normally associated with a fixed calibration. The two algorithms we propose both utilize feedback from a simple geometric effect, rotational invariance, to control the positioning servo loop. We attach a camera system to a robot such that the camera system and the robot's gripper rotate simultaneously. We also constrain the camera to lie in a position where it can observe the gripper's rotational axis. As the camera system rotates about the gripper's rotational axis, the circular path traced out by a pointlike feature projects to an elliptical path in image space. We gather the projected feature points over part of a rotation (=2 radians) ...
Model Acquisition Using Stochastic Projective Geometry
, 1993
"... This thesis presents a methodology for scene reconstruction that is based on the principles of projective geometry, while dealing with uncertainty at a fundamental level. Uncertainty in geometric features is represented and manipulated using probability density functions on projective space, allowin ..."
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Cited by 14 (1 self)
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This thesis presents a methodology for scene reconstruction that is based on the principles of projective geometry, while dealing with uncertainty at a fundamental level. Uncertainty in geometric features is represented and manipulated using probability density functions on projective space, allowing geometric constructions to be carried out via statistical inference. The main contribution of this thesis is the development of stochastic projective geometry, a formalism for performing uncertain geometric reasoning during the scene reconstruction process. The homogeneous coordinates of points and lines in the projective plane are represented by antipodal pairs of points on the unit sphere, and geometric uncertainty in their location is represented...
Outlier correction in image sequences for the affine camera
 In Proc. ICCV
, 2003
"... It is widely known that, for the affine camera model, both shape and motion can be factorized directly from the socalled image measurement matrix constructed from image point coordinates. The ability to extract both shape and motion from this matrix by a single SVD operation makes this shapefromm ..."
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Cited by 12 (0 self)
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It is widely known that, for the affine camera model, both shape and motion can be factorized directly from the socalled image measurement matrix constructed from image point coordinates. The ability to extract both shape and motion from this matrix by a single SVD operation makes this shapefrommotion approach attractive; however, it can not deal with missing feature points and, in the presence of outliers, a direct SVD to the matrix would yield highly unreliable shape and motion components. In this paper, we present an outlier correction scheme that iteratively updates the elements of the image measurement matrix. The magnitude and sign of the update to each element is dependent upon the residual robustly estimated in each iteration. The result is that outliers are corrected and retained, giving improved reconstruction and smaller reprojection errors. Our iterative outlier correction scheme has been applied to both synthesized and real video sequences. The results obtained are remarkably good. 1.
The active camera as a projective pointing device
 Proc. 6th British Machine Vision Conference
, 1995
"... ..."