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17
SBA: a software package for generic sparse bundle adjustment
 ACM Transactions on Mathematical Software
, 2009
"... Foundation for Research and Technology—Hellas ..."
Mixedinteger quadrangulation
 ACM TRANS. GRAPH
, 2009
"... We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion un ..."
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Cited by 106 (12 self)
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We present a novel method for quadrangulating a given triangle mesh. After constructing an as smooth as possible symmetric cross field satisfying a sparse set of directional constraints (to capture the geometric structure of the surface), the mesh is cut open in order to enable a low distortion unfolding. Then a seamless globally smooth parametrization is computed whose isoparameter lines follow the cross field directions. In contrast to previous methods, sparsely distributed directional constraints are sufficient to automatically determine the appropriate number, type and position of singularities in the quadrangulation. Both steps of the algorithm (cross field and parametrization) can be formulated as a mixedinteger problem which we solve very efficiently by an adaptive greedy solver. We show several complex examples where high quality quad meshes are generated in a fully automatic manner.
Dynamic supernodes in sparse Cholesky update/downdate and triangular solves
 ACM Trans. Math. Software
, 2006
"... The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorizatio ..."
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Cited by 30 (10 self)
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The supernodal method for sparse Cholesky factorization represents the factor L as a set of supernodes, each consisting of a contiguous set of columns of L with identical nonzero pattern. A conventional supernode is stored as a dense submatrix. While this is suitable for sparse Cholesky factorization where the nonzero pattern of L does not change, it is not suitable for methods that modify a sparse Cholesky factorization after a lowrank change to A (an update/downdate, A = A±WW T). Supernodes merge and split apart during an update/downdate. Dynamic supernodes are introduced, which allow a sparse Cholesky update/downdate to obtain performance competitive with conventional supernodal methods. A dynamic supernodal solver is shown to exceed the performance of the conventional (BLASbased) supernodal method for solving triangular systems. These methods are incorporated into CHOLMOD, a sparse Cholesky factorization and update/downdate package, which forms the basis of x=A\b in MATLAB when A is sparse and symmetric positive definite. 1
Practical MixedInteger Optimization for Geometry Processing
"... Abstract. Solving mixedinteger problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NPhard. Unfortunately, realworld problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasibl ..."
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Cited by 8 (3 self)
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Abstract. Solving mixedinteger problems, i.e., optimization problems where some of the unknowns are continuous while others are discrete, is NPhard. Unfortunately, realworld problems like e.g., quadrangular remeshing usually have a large number of unknowns such that exact methods become unfeasible. In this article we present a greedy strategy to rapidly approximate the solution of large quadratic mixedinteger problems within a practically sufficient accuracy. The algorithm, which is freely available as an open source library implemented in C++, determines the values of the discrete variables by successively solving relaxed problems. Additionally the specification of arbitrary linear equality constraints which typically arise as side conditions of the optimization problem is possible. The performance of the base algorithm is strongly improved by two novel extensions which are (1) simultaneously estimating sets of discrete variables which do not interfere and (2) a fillin reducing reordering of the constraints. Exemplarily the solver is applied to the problem of quadrilateral surface remeshing, enabling a great flexibility by supporting different types of user guidance within a realtime modeling framework for input surfaces of moderate complexity. Keywords: MixedInteger Optimization, Constrained Optimization 1
User Guide for CHOLMOD: a sparse Cholesky factorization and modification package
, 2009
"... CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for ..."
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Cited by 7 (0 self)
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CHOLMOD 1 is a set of routines for factorizing sparse symmetric positive definite matrices of the form A or AA T, updating/downdating a sparse Cholesky factorization, solving linear systems, updating/downdating the solution to the triangular system Lx = b, and many other sparse matrix functions for both symmetric and unsymmetric matrices. Its supernodal Cholesky factorization relies on LAPACK and the Level3 BLAS, and obtains a substantial fraction of the peak performance of the BLAS. Both real and complex matrices are supported. It also includes a nonsupernodal LDL T factorization method that can factorize symmetric indefinite matrices if all of their leading submatrices are wellconditioned (D is diagonal). CHOLMOD is written in ANSI/ISO C, with both C and MATLAB interfaces. This code works on Microsoft Windows and many versions of Unix and Linux. CHOLMOD Copyright c○20052009 by Timothy A. Davis. Portions are also copyrighted by William W. Hager (the Modify Module), and the University of Florida (the Partition and Core Modules). All Rights Reserved. Some of CHOLMOD’s Modules are distributed under the GNU General Public License, and others under the GNU Lesser General Public License. Refer to each Module for details. CHOLMOD is also available under other licenses that permit its use in proprietary applications; contact the authors for details. See
AN ORDERING METHOD FOR THE DIRECT SOLUTION OF SADDLEPOINT MATRICES ∗
"... Abstract. An ordering method and accompanying factorization for the direct solution of saddlepoint matrices is presented. A simple constraint on ordering together with an assumption on the rank of parts of the matrix are sufficient to guarantee the existence of the LDL T factorization, stability con ..."
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Cited by 7 (0 self)
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Abstract. An ordering method and accompanying factorization for the direct solution of saddlepoint matrices is presented. A simple constraint on ordering together with an assumption on the rank of parts of the matrix are sufficient to guarantee the existence of the LDL T factorization, stability concerns aside. In fact, D may be taken to be a diagonal matrix with ±1 along the diagonal, and be fully determined prior to factorization, giving rise to a “signed Cholesky ” factorization. A modified minimumdegreelike algorithm which incorporates this constraint is demonstrated, along with a simple algorithm to modify an existing fillreducing ordering to respect the constraint. While a stability analysis is lacking, numerical experiments indicate that this is generally sufficient to avoid the need for numerical pivoting during factorization, with clear benefits for performance possible. For example, a highly efficient Cholesky factorization routine, based on separate symbolic and numerical phases and possibly exploiting supernodes, can be easily adapted to this more general class of matrices.
A computational study of the use of an optimizationbased method for simulating large multibody systems
 OPTIMIZATION METHODS AND SOFTWARE
, 2008
"... ..."
Manifoldvalued ThinPlate Splines with Applications in Computer Graphics
 Computer Graphics Forum
"... We present a generalization of thinplate splines for interpolation and approximation of manifoldvalued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings betwee ..."
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Cited by 5 (4 self)
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We present a generalization of thinplate splines for interpolation and approximation of manifoldvalued data, and demonstrate its usefulness in computer graphics with several applications from different fields. The cornerstone of our theoretical framework is an energy functional for mappings between two Riemannian manifolds which is independent of parametrization and respects the geometry of both manifolds. If the manifolds are Euclidean, the energy functional reduces to the classical thinplate spline energy. We show how the resulting optimization problems can be solved efficiently in many cases. Our example applications range from orientation interpolation and motion planning in animation over geometric modelling tasks to color interpolation.
Topologyadaptive Multiview Photometric Stereo
"... In this paper, we present a novel technique that enables capturing of detailed 3D models from flash photographs integrating shading and silhouette cues. Our main contribution is an optimization framework which not only captures subtle surface details but also handles changes in topology. To incorpor ..."
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Cited by 3 (0 self)
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In this paper, we present a novel technique that enables capturing of detailed 3D models from flash photographs integrating shading and silhouette cues. Our main contribution is an optimization framework which not only captures subtle surface details but also handles changes in topology. To incorporate normals estimated from shading, we employ a meshbased deformable model using deformation gradient. This method is capable of manipulating precise geometry and, in fact, it outperforms previous methods in terms of both accuracy and efficiency. To adapt the topology of the mesh, we convert the mesh into an implicit surface representation and then back to a mesh representation. This simple procedure removes selfintersecting regions of the mesh and solves the topology problem effectively. In addition to the algorithm, we introduce a handheld setup to achieve multiview photometric stereo. The key idea is to acquire flash photographs from a wide range of positions in order to obtain a sufficient lighting variation even with a standard flash unit attached to the camera. Experimental results showed that our method can capture detailed shapes of various objects and cope with topology changes well. 1.
Controlled field generation for quadremeshing
 IN ACM SYMP. ON SOLID AND PHYS. MODELING
, 2008
"... Quadrangular remeshing of triangulated surfaces has received an increasing attention in recent years. A particularly elegant approach is the extraction of quads from the streamlines of a harmonic field. While the construction of such fields is by now a standard technique in geometry processing, enfo ..."
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Cited by 2 (0 self)
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Quadrangular remeshing of triangulated surfaces has received an increasing attention in recent years. A particularly elegant approach is the extraction of quads from the streamlines of a harmonic field. While the construction of such fields is by now a standard technique in geometry processing, enforcing design constraints is still not fully investigated. This work presents a technique for handling directional constraints by directly controlling the gradient of the field. In this way, line constraints sketched by the user or automatically obtained as feature lines can be fulfilled efficiently. Furthermore, we show the potential of quasiharmonic fields as a flexible tool for controlling the behavior of the field over the surface. Treating the surface as an inhomogeneous domain we can endow specific surface regions with field attraction/repulsion properties.