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The homogeneous coordinate ring of a toric variety
, 1992
"... This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X) of ..."
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Cited by 474 (7 self)
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This paper will introduce the homogeneous coordinate ring S of a toric variety X. The ring S is a polynomial ring with one variable for each onedimensional cone in the fan ∆ determining X, and S has a natural grading determined by the monoid of effective divisor classes in the Chow group An−1(X
Pyramidal implementation of the Lucas Kanade feature tracker
 Intel Corporation, Microprocessor Research Labs
, 2000
"... grayscale value of the two images are the location x = [x y] T, where x and y are the two pixel coordinates of a generic image point x. The image I will sometimes be referenced as the first image, and the image J as the second image. For practical issues, the images I and J are discret function (or ..."
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Cited by 308 (0 self)
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grayscale value of the two images are the location x = [x y] T, where x and y are the two pixel coordinates of a generic image point x. The image I will sometimes be referenced as the first image, and the image J as the second image. For practical issues, the images I and J are discret function (or
On the Convergence of Pattern Search Algorithms
"... . We introduce an abstract definition of pattern search methods for solving nonlinear unconstrained optimization problems. Our definition unifies an important collection of optimization methods that neither computenor explicitly approximate derivatives. We exploit our characterization of pattern sea ..."
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Cited by 243 (13 self)
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search methods to establish a global convergence theory that does not enforce a notion of sufficient decrease. Our analysis is possible because the iterates of a pattern search method lie on a scaled, translated integer lattice. This allows us to relax the classical requirements on the acceptance
DENSITY OF INTEGER POINTS ON AFFINE HOMOGENEOUS VARIETIES
 DUKE MATHEMATICAL JOURNAL
, 1993
"... Let F be an affine variety defined over Z by integral polynomials x,]: (1.1) V {x e C": f(x) O, j 1,..., v} A basic problem of diophantine analysis is to investigate the asymptotics as T of (1.2) N(T, V) = {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of Apoints of V. Henc ..."
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Cited by 105 (4 self)
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Let F be an affine variety defined over Z by integral polynomials x,]: (1.1) V {x e C": f(x) O, j 1,..., v} A basic problem of diophantine analysis is to investigate the asymptotics as T of (1.2) N(T, V) = {m V(Z): Ilmll T} where we denote by V(A), for any ring A, the set of Apoints of V. Hence I1 " is some Euclidean norm on R". The only general method available for such problems is the HardyLittlewood circle method, which however has certain limitations, requiring roughly that the codimension of V in the ambient space A", as well as the degree of the equations (1.1), be small relative to n. Furthermore, there are restrictions on the size of the singular sets of the related varieties: V u {x e C": f(x) &, j 1,..., v}, u () e c". We refer to [Bi] and [Sch] for a discussion of the restriction. Regardless of these restrictions, one hopes that for many more cases N(T, V) can be given in the form predicted by the HardyLittlewood method, that is, as a product of local densities: (,) N(T, V) lI l,(V)lUoo ( T, v), p <oo where the "singular series " II,< #(V) #,(V) is given by padic densities: lira k # v(z/pz) and/(T, V) is a real densitymthe "singular integral. " Following Schmidt [Sch], we say that V is a HardyLittlewood system if the above asymptotics (,) is valid. pk dim V
Realtime visual tracking of complex structures
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2002
"... This paper presents a novel framework for threedimensional modelbased tracking. Graphical rendering technology is combined with constrained active contour tracking to create a robust wireframe tracking system. It operates in real time at video frame rate (25 Hz) on standard hardware. It is based ..."
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Cited by 226 (7 self)
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components, or of multiple structures with constraints. The methodology used to achieve this exploits the simple geometric nature of the Lie group formalism which renders the constraints linear and homogeneous. The adjoint representation of the group is used to transform measurements into common coordinate
INTEGER
"... Note: before using this routine, please read the Users ’ Note for your implementation to check the interpretation of bold italicised terms and other implementationdependent details. 1 Purpose F11JAF computes an incomplete Cholesky factorization of a real sparse symmetric matrix, represented in symm ..."
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in symmetric coordinate storage format. This factorization may be used as a preconditioner in combination with F11GEF or F11JCF.
INTEGER
"... Note: Before using this routine, please read the Users ’ Note for your implementation to check for implementationdependent details. You are advised to enclose any calls to NAG Parallel Library routines between calls to Z01AAFP and Z01ABFP. 1 Descrip tion Z01CDFP (INDXG2P) identifies the row (or col ..."
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column) coordinate of a processor within the logical processor grid which processes a particular element of a matrix distributed in a cyclic 2d block fashion. The row (or column) index of the matrix element must be the index in the full matrix, not the submatrix as described in the F07 and F08 routines
Homogeneous Coordinates
 Visual Comput 10:176–187
, 1994
"... this paper we have offered a unified view of homogeneous coordinates within a Computer Graphics context. First, a brief historical review revealed that, as the understanding of perspective and projections increased, new coordinate systems were developed to represent the underlying spaces; one of the ..."
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Cited by 12 (0 self)
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this paper we have offered a unified view of homogeneous coordinates within a Computer Graphics context. First, a brief historical review revealed that, as the understanding of perspective and projections increased, new coordinate systems were developed to represent the underlying spaces; one
Exact Representation and Operations on Spherical Maps
, 1997
"... We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point. These ope ..."
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We develop exact algorithms for geometric operations on general circles and circular arcs on the sphere, using integer homogeneous coordinates. The algorithms include testing a point against a circle, computing the intersection of two circles, and ordering three arcs out of the same point
Results 1  10
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2,969