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413
Statistical Cue Integration in DAG Deformable Models
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... Deformable models are a useful modeling paradigm in computer vision. A deformable model is a curve, a surface, or a volume, whose shape, position, and orientation are controlled through a set of parameters. They can represent manufactured objects, human faces and skeletons, and even bodies of flu ..."
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Cited by 21 (6 self)
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Deformable models are a useful modeling paradigm in computer vision. A deformable model is a curve, a surface, or a volume, whose shape, position, and orientation are controlled through a set of parameters. They can represent manufactured objects, human faces and skeletons, and even bodies of fluid.
A Constraint Satisfaction Approach to a Circuit Design Problem
, 1998
"... A classical circuitdesign problem from Ebers and Moll [6] features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne [23] in the box [0; 10] 9 . Their ..."
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Cited by 21 (1 self)
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A classical circuitdesign problem from Ebers and Moll [6] features a system of nine nonlinear equations in nine variables that is very challenging both for local and global methods. This system was solved globally using an interval method by Ratschek and Rokne [23] in the box [0; 10] 9 . Their algorithm had enormous costs (i.e., over 14 months using a network of 30 Sun Sparc1 workstations) but they state that "at this time, we know no other method which has been applied to this circuit design problem and which has led to the same guaranteed result of locating exactly one solution in this huge domain, completed with a reliable error estimate." The present paper gives a novel branchandprune algorithm that obtains a unique safe box for the above system within reasonable computation times. The algorithm combines traditional interval techniques with an adaptation of discrete constraintsatisfaction techniques to continuous problems. Of particular interest is the simplicity o...
Safe Bounds in Linear and MixedInteger Programming
 Math. Prog
"... Current mixedinteger linear programming solvers are based on linear programming routines that use floating point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. It is shown how, using directed rounding ..."
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Cited by 21 (2 self)
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Current mixedinteger linear programming solvers are based on linear programming routines that use floating point arithmetic. Occasionally, this leads to wrong solutions, even for problems where all coefficients and all solution components are small integers. It is shown how, using directed rounding and interval arithmetic, cheap pre and postprocessing of the linear programs arising in a branchandcut framework can guarantee that no solution is lost, at least for mixedinteger programs in which all variables can be bounded rigorously by bounds of reasonable size.
Decomposition of Arithmetic Expressions to Improve the Behavior of Interval Iteration for Nonlinear Systems
, 1991
"... Interval iteration can be used, in conjunction with other techniques, for rigorously bounding all solutions to a nonlinear system of equations within a given region, or for verifying approximate solutions. However, because of overestimation which occurs when the interval Jacobian matrix is accumul ..."
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Cited by 20 (9 self)
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Interval iteration can be used, in conjunction with other techniques, for rigorously bounding all solutions to a nonlinear system of equations within a given region, or for verifying approximate solutions. However, because of overestimation which occurs when the interval Jacobian matrix is accumulated and applied, straightforward linearization of the original nonlinear system sometimes leads to nonconvergent iteration. In this paper, we examine interval iterations based on an expanded system obtained from the intermediate quantities in the original system. In this system, there is no overestimation in entries of the interval Jacobi matrix, and nonlinearities can be taken into account to obtain sharp bounds. We present an example in detail, algorithms, and detailed experimental results obtained from applying our algorithms to the example.
Experimental Uncertainty Estimation and Statistics for Data Having Interval Uncertainty
, 2007
"... This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute variou ..."
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Cited by 20 (14 self)
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This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties.
Double bubbles minimize
 Ann. of Math
"... The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a sin ..."
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Cited by 19 (1 self)
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The classical isoperimetric inequality in R 3 states that the surface of smallest area enclosing a given volume is a sphere. We show that the least area surface enclosing two equal volumes is a double bubble, a surface made of two pieces of round spheres separated by a flat disk, meeting along a single circle at an angle of 120 ◦. 1.
The Extended Real Interval System
, 1998
"... Three extended real interval systems are defined and distinguished by their implementation complexity and result sharpness. The three systems are closed with respect to interval arithmetic and the enclosure of functions and relations, notwithstanding domain restrictions or the presence of singularit ..."
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Cited by 17 (1 self)
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Three extended real interval systems are defined and distinguished by their implementation complexity and result sharpness. The three systems are closed with respect to interval arithmetic and the enclosure of functions and relations, notwithstanding domain restrictions or the presence of singularities. 1 Overview Section 2 introduces the problem of defining closed interval systems. In Section 3, real and extended points and intervals are defined. In Section 4, the empty and entire intervals are used to close the extended interval system. Section ?? shows how incorrect conclusions have been reached about the result of certain interval arithmetic operatoroperand combinations. The author is grateful to Professor Arnold Neumaier for originally raising this issue. Section 9 describes how to legitimately use IEEE floatingpoint arithmetic to obtain the sharp results described in Section ??. Section 6 generalizes extended interval arithmetic to define interval enclosures of functions, with...
NumericSymbolic Algorithms for Evaluating OneDimensional Algebraic Sets
 APPEARED IN PROCEEDINGS OF ISSAC'95
, 1995
"... We present efficient algorithms based on a combination of numeric and symbolic techniques for evaluating onedimensional algebraic sets in a subset of the real domain. Given a description of a onedimensional algebraic set, we compute its projection using resultants. We represent the resulting plane ..."
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Cited by 17 (5 self)
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We present efficient algorithms based on a combination of numeric and symbolic techniques for evaluating onedimensional algebraic sets in a subset of the real domain. Given a description of a onedimensional algebraic set, we compute its projection using resultants. We represent the resulting plane curve as a singular set of a matrix polynomial as opposed to roots of a bivariate polynomial. Given the matrix formulation, we make use of algorithms from numerical linear algebra to compute start points on all the components, partition the domain such that each resulting region contains only one component and evaluate it accurately using marching methods. We also present techniques to handle singularities for wellconditioned inputs. The resulting algorithm is iterative and its complexity is output sensitive. It has been implemented in oatingpoint arithmetic and we highlight its performance in the context of computing intersection of highdegree algebraic surfaces.
Consistency Techniques in Ordinary Differential Equations
, 2000
"... This paper takes a fresh look at the application of interval analysis to ordinary differential equations and studies how consistency techniques can help address the accuracy problems typically exhibited by these methods, while trying to preserve their efficiency. It proposes to generalize interval t ..."
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Cited by 16 (1 self)
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This paper takes a fresh look at the application of interval analysis to ordinary differential equations and studies how consistency techniques can help address the accuracy problems typically exhibited by these methods, while trying to preserve their efficiency. It proposes to generalize interval techniques intoatwostep process: a forward process that computes an enclosure and a backward process that reduces this enclosure. Consistency techniques apply naturally to the backward (pruning) step but can also be applied to the forward phase. The paper describes the framework, studies the various steps in detail, proposes a number of novel techniques, and gives some preliminary experimental results to indicate the potential of this new research avenue.
A FormalNumerical Approach to Determine the Presence of Singularity within the . . .
"... Determining if there is a singularity within a given workspace of a parallel robot is an important step during the design process of this type of robot. As this singular configuration must be avoided the designer may be interested only in a straight yes/no answer. We consider ..."
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Cited by 16 (6 self)
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Determining if there is a singularity within a given workspace of a parallel robot is an important step during the design process of this type of robot. As this singular configuration must be avoided the designer may be interested only in a straight yes/no answer. We consider