The Experts below are selected from a list of 38304 Experts worldwide ranked by ideXlab platform
Uwe D. Hanebeck - One of the best experts on this subject based on the ideXlab platform.
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fitting Conics to noisy data using stochastic linearization
Intelligent Robots and Systems, 2011Co-Authors: Marcus Baum, Uwe D. HanebeckAbstract:Fitting conic sections, e.g., ellipses or circles, to noisy data points is a fundamental sensor data processing problem, which frequently arises in robotics. In this paper, we introduce a new procedure for deriving a recursive Gaussian state estimator for fitting Conics to data corrupted by additive Gaussian noise. For this purpose, the original exact implicit measurement equation is reformulated with the help of suitable approximations as an explicit measurement equation corrupted by multiplicative noise. Based on stochastic linearization, an efficient Gaussian state estimator is derived for the explicit measurement equation. The performance of the new approach is evaluated by means of a typical ellipse fitting scenario.
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IROS - Fitting Conics to noisy data using stochastic linearization
2011 IEEE RSJ International Conference on Intelligent Robots and Systems, 2011Co-Authors: Marcus Baum, Uwe D. HanebeckAbstract:Fitting conic sections, e.g., ellipses or circles, to noisy data points is a fundamental sensor data processing problem, which frequently arises in robotics. In this paper, we introduce a new procedure for deriving a recursive Gaussian state estimator for fitting Conics to data corrupted by additive Gaussian noise. For this purpose, the original exact implicit measurement equation is reformulated with the help of suitable approximations as an explicit measurement equation corrupted by multiplicative noise. Based on stochastic linearization, an efficient Gaussian state estimator is derived for the explicit measurement equation. The performance of the new approach is evaluated by means of a typical ellipse fitting scenario.
Long Quan - One of the best experts on this subject based on the ideXlab platform.
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single axis geometry by fitting Conics
European Conference on Computer Vision, 2002Co-Authors: Long Quan, Guang Jiang, Hungtat Tsui, Andrew ZissermanAbstract:In this paper, we describe a new approach for recovering 3D geometry from an uncalibrated image sequence of a single axis (turntable) motion. Unlike previous methods, the computation of multiple views encoded by the fundamental matrix or trifocal tensor is not required. Instead, the new approach is based on fitting a conic locus to corresponding image points over multiple views. It is then shown that the geometry of single axis motion can be recovered given at least two such Conics. In the case of two Conics the reconstruction may have a two fold ambiguity, but this ambiguity is removed if three Conics are used.The approach enables the geometry of the single axis motion (the 3D rotation axis and Euclidean geometry in planes perpendicular to this axis) to be estimated using the minimal number of parameters. It is demonstrated that a Maximum Likelihood Estimation results in measurements that are as good as or superior to those obtained by previous methods, and with a far simpler algorithm. Examples are given on various real sequences, which show the accuracy and robustness of the new algorithm.
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Joint Invariants of a Triplet of Coplanar Conics: Stability and Discriminating Power for Object Recognition
Computer Vision and Image Understanding, 1998Co-Authors: Long Quan, Françoise VeillonAbstract:Joint invariants of a pair of coplanar Conics have played a central role in the initial work on the application of invariants to object recognition. In this paper, we are concerned with the invariants of a triplet of coplanar Conics. It will be shown that, in addition to the invariants associated to all pairs of three Conics, there exists one new invariant which is only associated to the triplet of Conics. This new invariant of the three Conics can therefore be used to discriminate triplets of Conics which might be pair-wise similar. All joint invariants of a triplet of coplanar Conics will first be derived based on the invariant algebra of a net of ternary quadratic forms. Then, experimentations for discriminating power, accuracy, and stability of joint invariants are conducted both for simulated and real images. Finally, it is also shown that the method developed for a triplet of coplanar Conics can be extended to any number of coplanar Conics.
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Invariant of a Pair of non-Coplanar Conics in Space: Definition, Geometric Interpretation and Computation
1995Co-Authors: Long QuanAbstract:The joint invariants of a pair of coplanar Conics has been widely used in recent vision literature. In this paper, the algebraic invariant of a pair of non-coplanar Conics in space is concerned. The algebraic invariant of a pair of non-coplanar Conics is first derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space Conics. Then, this algebraic invariant is geometrically interpreted in terms of cross-ratios. Finally, an analytical procedure for projective reconstruction of a space conic from two uncalibrated images is developed and the correspondence conditions of the Conics between two views are also explicited. Experimentations for the discriminality of the correspondence conditions and the accuracy and stability of the projective reconstruction and the computation of the invariant are conducted both for simulated and real images.
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Invariant of a Pair of non-Coplanar Conics in Space
1995Co-Authors: Long QuanAbstract:The joint invariants of a pair of coplanar Conics has been widely used in recent vision literature. In this paper, the algebraic invariant of a pair of non-coplanar Conics in space is concerned. The algebraic invariant of a pair of non-coplanar Conics is first derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space Conics. Then, this algebraic invariant is geometrically interpreted in terms of cross-ratios. Finally, an analytical procedure for projective reconstruction of a space conic from two uncalibrated images is developed and the correspondence conditions of the Conics between two views are also explicited.
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Algebraic and Geometric Invariant of a Pair of non-Coplanar Conics in Space
Journal of Mathematical Imaging and Vision, 1995Co-Authors: Long QuanAbstract:It is easy to construct the geometric invariant of a pair of non-coplanar Conics in space. It is the crossratio of the 4 intersection points of the two Conics with the common line of the two conic planes. In this paper, the algebraic invariant of a pair of non-coplanar Conics is derived from the invariant algebra of a pair of quaternary quadratic forms by using the dual representation of space Conics. Then, the relationship between the algebraic invariant and the geometric invariant is established.
Anders Heyden - One of the best experts on this subject based on the ideXlab platform.
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affine structure and motion from points lines and Conics
International Journal of Computer Vision, 1999Co-Authors: Fredrik Kahl, Anders HeydenAbstract:In this paper several new methods for estimating scene structure and camera motion from an image sequence taken by affine cameras are presented. All methods can incorporate both point, line and conic features in a unified manner. The correspondence between features in different images is assumed to be known. Three new tensor representations are introduced describing the viewing geometry for two and three cameras. The centred affine epipoles can be used to constrain the location of corresponding points and Conics in two images. The third order, or alternatively, the reduced third order centred affine tensors can be used to constrain the locations of corresponding points, lines and Conics in three images. The reduced third order tensors contain only 12 components compared to the 16 components obtained when reducing the trifocal tensor to affine cameras. A new factorization method is presented. The novelty lies in the ability to handle not only point features, but also line and conic features concurrently. Another complementary method based on the so-called closure constraints is also presented. The advantage of this method is the ability to handle missing data in a simple and uniform manner. Finally, experiments performed on both simulated and real data are given, including a comparison with other methods.
In So Kweon - One of the best experts on this subject based on the ideXlab platform.
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Euclidean Structure from Confocal Conics: Theory and Application to Camera Calibration
2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'06), 2006Co-Authors: Pierre Gurdjos, Junho Kim, In So KweonAbstract:Plane-based calibration is now a very popular procedure because of its flexibility. One key step consists in detecting a set of coplanar features, from which the Euclidean structure of the corresponding 3D plane has to be computed. We suggest to use confocal Conics as calibration targets, as they offer undeniable advantages over other ones (e.g., points or lines) in terms of detection and estimation, especially in the presence of partial occlusion. We introduce important projective and Euclidean properties of the linear family of Conics (i.e., the confocal conic range), spanned by two confocal Conics. In particular, we rely on the fact that the circular point-envelope - a rank-2 conic that encodes the 2D Euclidean structure - is a degenerate member of any confocal conic range. This allows us to give closed-form solutions in three cases: one conic with known foci, two confocal Conics with known product of ratios of semi axes, and two unknown confocal Conics. The performances of the proposed algorithms (consisting of a few lines of Matlab-like code) show up high accuracies for both intrinsic and extrinsic camera parameters. In addition to experiments with synthetic data, a video sequence is processed, showing off the interest of using confocal Conics as calibration targets, for augmented reality purposes.
Zijian Zhao - One of the best experts on this subject based on the ideXlab platform.
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Conics with a common axis of symmetry properties and applications to camera calibration
International Joint Conference on Artificial Intelligence, 2011Co-Authors: Zijian ZhaoAbstract:We focus on recovering the 2D Euclidean structure in one view from the projections of N parallel Conics in this paper. This work denotes that the conic dual to the absolute points is the general form of the conic dual to the circular points, but it does not encode the Euclidean structure. Therefore, we have to recover the circular point-envelope to find out some useful information about the Euclidean structure, which relies on the fact that the line at infinity and the symmetric axis can be recovered. We provide a solution to recover the two lines and deduce the constraints for recovering the conic dual to the circular points, then apply them on the camera calibration. Our work relaxes the problem conditions and gives a more general framework than the past. Experiments with simulated and real data are carried out to show the validity of the proposed algorithm. Especially, our method is applied in the endoscope operation to calibrate the camera for tracking the surgical tools, that is the main interest-point we pay attention to.
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IJCAI - Conics with a common axis of symmetry: properties and applications to camera calibration
2011Co-Authors: Zijian ZhaoAbstract:We focus on recovering the 2D Euclidean structure in one view from the projections of N parallel Conics in this paper. This work denotes that the conic dual to the absolute points is the general form of the conic dual to the circular points, but it does not encode the Euclidean structure. Therefore, we have to recover the circular point-envelope to find out some useful information about the Euclidean structure, which relies on the fact that the line at infinity and the symmetric axis can be recovered. We provide a solution to recover the two lines and deduce the constraints for recovering the conic dual to the circular points, then apply them on the camera calibration. Our work relaxes the problem conditions and gives a more general framework than the past. Experiments with simulated and real data are carried out to show the validity of the proposed algorithm. Especially, our method is applied in the endoscope operation to calibrate the camera for tracking the surgical tools, that is the main interest-point we pay attention to.