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Autocalibration and the absolute quadric
 in Proc. IEEE Conf. Computer Vision, Pattern Recognition
, 1997
"... We describe a new method for camera autocalibration and scaled Euclidean structure and motion, from three or more views taken by a moving camera with fixed but unknown intrinsic parameters. The motion constancy of these is used to rectify an initial projective reconstruction. Euclidean scene structu ..."
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Cited by 248 (7 self)
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structure is formulated in terms of the absolute quadric — the singular dual 3D quadric ( rank 3 matrix) giving the Euclidean dotproduct between plane normals. This is equivalent to the traditional absolute conic but simpler to use. It encodes both affine and Euclidean structure, and projects very simply
Spinor Sheaves on Singular Quadrics
, 2009
"... We define sheaves on a singular quadric Q that generalize the spinor bundles on smooth quadrics, using matrix factorizations of the equation of Q. We study the first properties of these spinor sheaves, prove an analogue of Horrocks ’ criterion, and show that they are semistable, and indeed stable i ..."
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Cited by 4 (2 self)
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We define sheaves on a singular quadric Q that generalize the spinor bundles on smooth quadrics, using matrix factorizations of the equation of Q. We study the first properties of these spinor sheaves, prove an analogue of Horrocks ’ criterion, and show that they are semistable, and indeed stable
On the Semiaxes of Touching Quadrics
"... : In this paper the semiaxes of quadrics which touch each other are investigated. If two quadrics Q ; Q 0 are given, it turns out that we can rotate Q 0 such that it touches Q in two opposite points if and only if the squared semiaxes of Q ; Q 0 do not separate each other. This is equivale ..."
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Cited by 1 (1 self)
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. This is equivalent to the statement that for two symmetric matrices A;B there is an orthogonal matrix S with det(A \Gamma S T BS) = 0 if and only if the eigenvalues of A and B do not separate each other. Math. Subject Classification: 51M, 15A63 Keywords: quadric, semiaxes, symmetric matrix. Introduction
Ternary linear codes and quadrics
"... For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A tflat Π in Σ is called an (i, j)t flat if (i, j) = (Π ∩ F0, Π ∩ F1), where F0 = {P ∈ Σ  wG(P) ≡ 0 (mod 3)}, F1 = {P ∈ Σ  wG(P) ̸ ≡ 0 ..."
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Cited by 1 (1 self)
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For an [n, k, d]3 code C with gcd(d, 3) = 1, we define a map wG from Σ = PG(k − 1, 3) to the set of weights of codewords of C through a generator matrix G. A tflat Π in Σ is called an (i, j)t flat if (i, j) = (Π ∩ F0, Π ∩ F1), where F0 = {P ∈ Σ  wG(P) ≡ 0 (mod 3)}, F1 = {P ∈ Σ  wG(P) ̸
BLAS3 for the Quadrics Parallel Computer
"... . A scalable parallel algorithm for matrix multiplication on SISAMD computers is presented. Our method enables us to implement an efficient BLAS library on the Italian APE100/Quadrics SISAMD massively parallel computer on which hitherto scalable parallel BLAS3 were not available. The approach propo ..."
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Cited by 4 (2 self)
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. A scalable parallel algorithm for matrix multiplication on SISAMD computers is presented. Our method enables us to implement an efficient BLAS library on the Italian APE100/Quadrics SISAMD massively parallel computer on which hitherto scalable parallel BLAS3 were not available. The approach
Autocalibration via rankconstrained estimation of the absolute quadric
 In CVPR
, 2007
"... We present an autocalibration algorithm for upgrading a projective reconstruction to a metric reconstruction by estimating the absolute dual quadric. The algorithm enforces the rank degeneracy and the positive semidefiniteness of the dual quadric as part of the estimation procedure, rather than as a ..."
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Cited by 9 (2 self)
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We present an autocalibration algorithm for upgrading a projective reconstruction to a metric reconstruction by estimating the absolute dual quadric. The algorithm enforces the rank degeneracy and the positive semidefiniteness of the dual quadric as part of the estimation procedure, rather than
c © 2003 Universitat de Barcelona Curves on a smooth quadric
, 2002
"... We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines the cu ..."
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We associate to every curve on a smooth quadric a polynomial equation that defines it as a divisor; this polynomial is defined through a matrix. In this way we can study several properties of these curves; in particular we can give a geometrical meaning to the rank of the matrix which defines
DIASSTP0309 Fuzzy Complex Quadrics and Spheres
, 2008
"... A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom for descr ..."
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Cited by 6 (1 self)
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A matrix algebra is constructed which consists of the necessary degrees of freedom for a finite approximation to the algebra of functions on the family of orthogonal Grassmannians of real dimension 2N, known as complex quadrics. These matrix algebras contain the relevant degrees of freedom
A MATRIX POINCARE ́ FORMULA FOR HOLOMORPHIC AUTOMORPHISMS OF QUADRICS OF HIGHER CODIMENSION. REAL ASSOCIATIVE
"... Abstract. In this paper we describe the holomorphic automorphisms for two infinite series of quadrics: quadrics of codimension 2 in Cn+2 and a special class of quadrics of codimension n in C2n with large automorphism groups (Real Associative Quadrics). We give explicit formulas of the automorphisms ..."
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Abstract. In this paper we describe the holomorphic automorphisms for two infinite series of quadrics: quadrics of codimension 2 in Cn+2 and a special class of quadrics of codimension n in C2n with large automorphism groups (Real Associative Quadrics). We give explicit formulas
Walls in supersymmetric massive nonlinear sigma model on complex quadric surface
, 908
"... The Bogomol’nyiPrasadSommerfield (BPS) multiwall solutions are constructed in a massive Kähler nonlinear sigma model on the complex quadric surface, Q N = SO(N+2) SO(N)×SO(2) in 3dimensional spacetime. The theory has a nontrivial scalar potential generated by the ScherkSchwarz dimensional redu ..."
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The Bogomol’nyiPrasadSommerfield (BPS) multiwall solutions are constructed in a massive Kähler nonlinear sigma model on the complex quadric surface, Q N = SO(N+2) SO(N)×SO(2) in 3dimensional spacetime. The theory has a nontrivial scalar potential generated by the ScherkSchwarz dimensional
Results 1  10
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53