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436
Bundle adjustment – a modern synthesis
 Vision Algorithms: Theory and Practice, LNCS
, 2000
"... This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics c ..."
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Cited by 386 (12 self)
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This paper is a survey of the theory and methods of photogrammetric bundle adjustment, aimed at potential implementors in the computer vision community. Bundle adjustment is the problem of refining a visual reconstruction to produce jointly optimal structure and viewing parameter estimates. Topics covered include: the choice of cost function and robustness; numerical optimization including sparse Newton methods, linearly convergent approximations, updating and recursive methods; gauge (datum) invariance; and quality control. The theory is developed for general robust cost functions rather than restricting attention to traditional nonlinear least squares.
Algebraic Decision Diagrams and their Applications
, 1993
"... In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and results i ..."
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Cited by 261 (17 self)
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In this paper we present theory and experiments on the Algebraic Decision Diagrams (ADD's). These diagrams extend BDD's by allowing values from an arbitrary finite domain to be associated with the terminal nodes. We present a treatment founded in boolean algebras and discuss algorithms and results in applications like matrix multiplication and shortest path algorithms. Furthermore, we outline possible applications of ADD's to logic synthesis, formal verification, and testing of digital systems.
A sparse approximate inverse preconditioner for nonsymmetric linear systems
 SIAM J. SCI. COMPUT
, 1998
"... This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner f ..."
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Cited by 155 (23 self)
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This paper is concerned with a new approach to preconditioning for large, sparse linear systems. A procedure for computing an incomplete factorization of the inverse of a nonsymmetric matrix is developed, and the resulting factorized sparse approximate inverse is used as an explicit preconditioner for conjugate gradient–type methods. Some theoretical properties of the preconditioner are discussed, and numerical experiments on test matrices from the Harwell–Boeing collection and from Tim Davis’s collection are presented. Our results indicate that the new preconditioner is cheaper to construct than other approximate inverse preconditioners. Furthermore, the new technique insures convergence rates of the preconditioned iteration which are comparable with those obtained with standard implicit preconditioners.
CUTE: Constrained and unconstrained testing environment
, 1993
"... The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we belie ..."
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Cited by 152 (3 self)
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The purpose of this paper is to discuss the scope and functionality of a versatile environment for testing small and largescale nonlinear optimization algorithms. Although many of these facilities were originally produced by the authors in conjunction with the software package LANCELOT, we believe that they will be useful in their own right and should be available to researchers for their development of optimization software. The tools are available by anonymous ftp from a number of sources and may, in many cases, be installed automatically. The scope of a major collection of test problems written in the standard input format (SIF) used by the LANCELOT software package is described. Recognising that most software was not written with the SIF in mind, we provide tools to assist in building an interface between this input format and other optimization packages. These tools already provide a link between the SIF and an number of existing packages, including MINOS and OSL. In ad...
Multiresolution markov models for signal and image processing
 Proceedings of the IEEE
, 2002
"... This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coheren ..."
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Cited by 122 (18 self)
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This paper reviews a significant component of the rich field of statistical multiresolution (MR) modeling and processing. These MR methods have found application and permeated the literature of a widely scattered set of disciplines, and one of our principal objectives is to present a single, coherent picture of this framework. A second goal is to describe how this topic fits into the even larger field of MR methods and concepts–in particular making ties to topics such as wavelets and multigrid methods. A third is to provide several alternate viewpoints for this body of work, as the methods and concepts we describe intersect with a number of other fields. The principle focus of our presentation is the class of MR Markov processes defined on pyramidally organized trees. The attractiveness of these models stems from both the very efficient algorithms they admit and their expressive power and broad applicability. We show how a variety of methods and models relate to this framework including models for selfsimilar and 1/f processes. We also illustrate how these methods have been used in practice. We discuss the construction of MR models on trees and show how questions that arise in this context make contact with wavelets, state space modeling of time series, system and parameter identification, and hidden
An UnsymmetricPattern Multifrontal Method for Sparse LU Factorization
 SIAM J. MATRIX ANAL. APPL
, 1994
"... Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops ..."
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Cited by 118 (29 self)
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Sparse matrix factorization algorithms for general problems are typically characterized by irregular memory access patterns that limit their performance on parallelvector supercomputers. For symmetric problems, methods such as the multifrontal method avoid indirect addressing in the innermost loops by using dense matrix kernels. However, no efficient LU factorization algorithm based primarily on dense matrix kernels exists for matrices whose pattern is very unsymmetric. We address this deficiency and present a new unsymmetricpattern multifrontal method based on dense matrix kernels. As in the classical multifrontal method, advantage is taken of repetitive structure in the matrix by factorizing more than one pivot in each frontal matrix thus enabling the use of Level 2 and Level 3 BLAS. The performance is compared with the classical multifrontal method and other unsymmetric solvers on a CRAY YMP.
Lineartime dynamics using lagrange multipliers
 In SIGGRAPH 96 Conference Proceedings, Computer Graphics Proceedings, Annual Conference Series
, 1996
"... Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics ..."
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Cited by 101 (0 self)
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Current lineartime simulation methods for articulated figures are based exclusively on reducedcoordinate formulations. This paper describes a general, noniterative lineartime simulation method based instead on Lagrange multipliers. Lagrange multiplier methods are important for computer graphics applications because they bypass the difficult (and often intractable) problem of parameterizing a system’s degrees of freedom. Given a loopfree set of n equality constraints acting between pairs of bodies, the method takes O(n) time to compute the system’s dynamics. The method does not rely on matrix bandwidth, so no assumptions about the constraints’ topology are needed. Bodies need not be rigid, constraints can be of various dimensions, and unlike reducedcoordinate approaches, nonholonomic (e.g. velocitydependent) constraints are allowed. An additional set of k onedimensional constraints which induce loops and/or handle inequalities can be accommodated with cost O(kn). This makes it practical to simulate complicated, closedloop articulated figures with jointlimits and contact at interactive rates. A complete description of a sample implementation is provided in pseudocode. 1
Iterative Solution of Linear Systems
 Acta Numerica
, 1992
"... this paper is as follows. In Section 2, we present some background material on general Krylov subspace methods, of which CGtype algorithms are a special case. We recall the outstanding properties of CG and discuss the issue of optimal extensions of CG to nonHermitian matrices. We also review GMRES ..."
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Cited by 100 (8 self)
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this paper is as follows. In Section 2, we present some background material on general Krylov subspace methods, of which CGtype algorithms are a special case. We recall the outstanding properties of CG and discuss the issue of optimal extensions of CG to nonHermitian matrices. We also review GMRES and related methods, as well as CGlike algorithms for the special case of Hermitian indefinite linear systems. Finally, we briefly discuss the basic idea of preconditioning. In Section 3, we turn to Lanczosbased iterative methods for general nonHermitian linear systems. First, we consider the nonsymmetric Lanczos process, with particular emphasis on the possible breakdowns and potential instabilities in the classical algorithm. Then we describe recent advances in understanding these problems and overcoming them by using lookahead techniques. Moreover, we describe the quasiminimal residual algorithm (QMR) proposed by Freund and Nachtigal (1990), which uses the lookahead Lanczos process to obtain quasioptimal approximate solutions. Next, a survey of transposefree Lanczosbased methods is given. We conclude this section with comments on other related work and some historical remarks. In Section 4, we elaborate on CGNR and CGNE and we point out situations where these approaches are optimal. The general class of Krylov subspace methods also contains parameterdependent algorithms that, unlike CGtype schemes, require explicit information on the spectrum of the coefficient matrix. In Section 5, we discuss recent insights in obtaining appropriate spectral information for parameterdependent Krylov subspace methods. After that, 4 R.W. Freund, G.H. Golub and N.M. Nachtigal
CACTUS  Clustering Categorical Data Using Summaries
, 1999
"... Clustering is an important data mining problem. Most of the earlier work on clustering focussed on numeric attributes which have a natural ordering on their attribute values. Recently, clustering data with categorical attributes, whose attribute values do not have a natural ordering, has received so ..."
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Cited by 94 (0 self)
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Clustering is an important data mining problem. Most of the earlier work on clustering focussed on numeric attributes which have a natural ordering on their attribute values. Recently, clustering data with categorical attributes, whose attribute values do not have a natural ordering, has received some attention. However, previous algorithms do not give a formal description of the clusters they discover and some of them assume that the user postprocesses the output of the algorithm to identify the final clusters. In this paper, we introduce a novel formalization of a cluster for categorical attributes by generalizing a definition of a cluster for numerical attributes. We then describe a very fast summarizationbased algorithm called CACTUS that discovers exactly such clusters in the data. CACTUS has two important characteristics. First, the algorithm requires only two scans of the dataset, and hence is very fast and scalable. Our experiments on a variety of datasets show that CACTUS outperforms previous work by a factor of 3 to 10. Second, CACTUS can find clusters in subsets of all attributes and can thus perform a subspace clustering of the data. This feature is important if clusters do not span all attributes, a likely scenario if the number of attributes is very large. In a thorough experimental evaluation, we study the performance of CACTUS on real and synthetic datasets. 1