Conics are widely accepted as one of the most fundamental image features together with points and line segments. The problem of space reconstruction and correspondence of two conics from two views is addressed in this paper. It is shown that there are two independent polynomial conditions on the corresponding pair of conics across two views, given the relative orientation of the two views. These two correspondence conditions are derived algebraically and one of them is shown to be fundamental in establishing the correspondences of conics. A unified closed-form solution is also developed for both projective reconstruction of conics in space from two views for uncalibrated cameras and metric reconstruction from calibrated cameras. Experiments are conducted to demonstrate the discriminality of the correspondence conditions and the accuracy and stability of the reconstruction both for simulated and real images. Keywords--- conic, stereo correspondence, reconstruction. I. Introduction In...

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Computing the intersection curve of two quadrics is a fundamental problem in computer graphics and solid modeling. We present an algebraic method for classifying and parameterizing the intersection curve of two quadric surfaces. The method is based on the observation that the intersection curve of two quadrics is birationally related to a plane cubic curve. In the method this plane cubic curve is computed first and the intersection curve of the two quadrics is then found by transforming the cubic curve by a rational quadratic mapping. Topological classification and parameterization of the intersection curve are achieved by invoking results from algebraic geometry on plane cubic curves.

this paper -- we enumerate all 35 di#erent morphologies of QSIC, and characterize each of these morphologies using a signature sequence that can exactly be computed using rational arithmetic. The third problem, not handled here, leads to a lengthy case by case study which depends a lot on the application behind. Consider the intersection curve of two quadrics given by BX = 0, where X = (x, y, z, w) and A, B are 4 4 real symmetric matrices. The characteristic polynomial of (1) and f(#) = 0 is called the characteristic equation of B

For inner products defined by a symmetric indefinite matrix \Sigma p;q , we study canonical forms for real or complex \Sigma p;q -Hermitian matrices, \Sigma p;q -skew Hermitian matrices and \Sigma p;q -unitary matrices under equivalence transformations which keep the class invariant.

this paper we study matrix pencils

Abstract. Couples of proper, non-empty real projective conics can be classified modulo rigid isotopy and ambient isotopy. We characterize the classes by equations, inequations and inequalities in the coefficients of the quadratic forms defining the conics. The results are well–adapted to the study of the relative position of two conics defined by equations depending on parameters. MSC2000: 13A50 (invariant theory), 13J30 (real algebra).

Abstract. In this paper, we give predicates of bidegree at most (6, 6) in the input for characterizing the relative position of two projective conics. By relative position we mean the morphology of the intersection, the rigid isotopy class and which conic is inside the other when applicable. The predicates are derived by analyzing the algebraic invariant theory of pencils of conics and related constructions. 1. Introduction. Geometric

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In this paper we give a complete characterization of critical configurations for projective reconstruction with any number of points and views. A set of cameras and points is said to be critical if the projected image points are insufficient to determine the placement of the points and the cameras uniquely, up to a projective transformation. For two views, the critical configurations are well-known. In this paper it is shown that a configuration of n 3 cameras and m points is critical if all points and cameras lie on the intersection of two distinct ruled quadrics. Contrary to the two-view case, which in general allows two ambiguous solutions, there is a family of ambiguous reconstructions for the n-view case. Conversely, it is shown that (except for minimal cases) for any critical configuration, all the points and cameras lie on the intersection of two ruled quadrics.