Results 11  20
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624
Conformal Curvature Flows: From Phase Transitions to Active Vision
, 1995
"... In this paper, we analyze geometric active contour models from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel edgedetection paradigm in which the feature of interest may be consid ..."
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Cited by 117 (30 self)
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In this paper, we analyze geometric active contour models from a curve evolution point of view and propose some modifications based on gradient flows relative to certain new featurebased Riemannian metrics. This leads to a novel edgedetection paradigm in which the feature of interest may be considered to lie at the bottom of a potential well. Thus an edgeseeking curve is attracted very naturally and efficiently to the desired feature. Comparison with the AllenCahn model clarifies some of the choices made in these models, and suggests inhomogeneous models which may in return be useful in phase transitions. We also consider some 3D active surface models based on these ideas. The justification of this model rests on the careful study of the viscosity solutions of evolution equations derived from a levelset approach. Key words: Active vision, antiphase boundary, visual tracking, edge detection, segmentation, gradient flows, Riemannian metrics, viscosity solutions, geometric heat equ...
Choosing Good Distance Metrics and Local Planners for Probabilistic Roadmap Methods
 In Proc. IEEE Int. Conf. Robot. Autom. (ICRA
, 1998
"... Abstract This paper presents a comparative evaluation of different distance metrics and local planners within the context of probabilistic roadmap methods for motion planning. Both Cspace andWorkspace distance metrics and local planners are considered. The study concentrates on cluttered threedim ..."
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Cited by 84 (22 self)
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Abstract This paper presents a comparative evaluation of different distance metrics and local planners within the context of probabilistic roadmap methods for motion planning. Both Cspace andWorkspace distance metrics and local planners are considered. The study concentrates on cluttered threedimensionalWorkspaces typical, e.g., of mechanical designs. Our results include recommendations for selecting appropriate combinationsof distance metrics and local planners for use in motion planning methods, particularly probabilistic roadmap methods. Wefind that each local planner makes some connections than none of the others do indicating that better connectedroadmaps will beconstructed using multiple local planners. We propose a new local planning method we call rotateats that outperforms the commonstraightline in Cspace method in crowded environments. 1
A Search Algorithm for Motion Planning with Six Degrees of Freedom
 ARTIFICIAL INTELLIGENCE
, 1987
"... The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given highlevel specifications of tasks and geometric models of the robot and obstacles. The "Movers'" p ..."
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Cited by 75 (4 self)
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The motion planning problem is of central importance to the fields of robotics, spatial planning, and automated design. In robotics we are interested in the automatic synthesis of robot motions, given highlevel specifications of tasks and geometric models of the robot and obstacles. The "Movers'" problem is to find a continuous, collisionfree path for a moving object through an environment containing obstacles. We present an implemented algorithm for the classical formulation of the threedimensional Movers' problem: Given an arbitrary rigid polyhedral moving object P with three translational and three rotational degrees of freedom, find a continuous, collisionfree path taking P from some initial configuration to a desired goal configuration. This paper describes an implementation of a complete algorithm (at a given resolution)for the full six degree of freedom Movers' problem. The algorithm transforms the six degree of freedom planning problem into a point navigation problem in a sixdimensional configuration space (called Cspace). The Cspace obstacles, which characterize the physically unachievable configurations, are directly represented by sixdimensional manifolds whose boundaries are fivedimensional Csurfaces. By characterizing these surfaces and their intersections, collisionfree paths may be found by the
Seamless Texture Mapping of Subdivision Surfaces by Model Pelting and Texture Blending
"... Subdivision surfaces solve numerous problems related to the geometry of character and animation models. However, unlike on parametrised surfaces there is no natural choice of texture coordinates on subdivision surfaces. Existing algorithms for generating texture coordinates on nonparametrised surfa ..."
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Cited by 59 (0 self)
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Subdivision surfaces solve numerous problems related to the geometry of character and animation models. However, unlike on parametrised surfaces there is no natural choice of texture coordinates on subdivision surfaces. Existing algorithms for generating texture coordinates on nonparametrised surfaces often find solutions that are locally acceptable but globally are unsuitable for use by artists wishing to paint textures. In addition, for topological reasons there is not necessarily any choice of assignment of texture coordinates to control points that can satisfactorily be interpolated over the entire surface. We introduce a technique, pelting, for finding both optimal and intuitive texture mapping over almost all of an entire subdivision surface and then show how to combine multiple texture mappings together to produce a seamless result.
Smooth Interpolation of Orientations with Angular Velocity Constraints using Quaternions
, 1992
"... In this paper we present methods to smoothly interpolate orientations, given N rotational keyframes of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to q ..."
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Cited by 56 (2 self)
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In this paper we present methods to smoothly interpolate orientations, given N rotational keyframes of an object along a trajectory. The methods allow the user to impose constraints on the rotational path, such as the angular velocity at the endpoints of the trajectory. We convert the rotations to quaternions, and then spline in that nonEuclidean space. Analogous to the mathematical foundations of flatspace spline curves, we minimize the net "tangential acceleration" of the quaternion path. We replace the flatspace quantities with curvedspace quantities, and numerically solve the resulting equation with finite difference and optimization methods. 1 Introduction The problem of using spline curves to smoothly interpolate mathematical quantities in flat Euclidean spaces is a wellstudied problem in computer graphics [bartels et al 87], [kochanek&bartels 84]. Many quantities important to computer graphics, however, such as rotations, lie in nonEuclidean spaces. In 1985, a method to...
Shortest Paths For The ReedsShepp Car: A Worked Out Example Of The Use Of Geometric Techniques In Nonlinear Optimal Control.
, 1991
"... We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion coul ..."
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Cited by 51 (5 self)
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We illustrate the use of the techniques of modern geometric optimal control theory by studying the shortest paths for a model of a car that can move forwards and backwards. This problem was discussed in recent work by Reeds and Shepp who showed, by special methods, (a) that shortest path motion could always be achieved by means of trajectories of a special kind, namely, concatenations of at most five pieces, each of which is either a straight line or a circle, and (b) that these concatenations can be classified into 48 threeparameter families. We show how these results fit in a much more general framework, and can be discovered and proved by applying in a systematic way the techniques of Optimal Control Theory. It turns out that the "classical" optimal control tools developed in the 1960's, such as the Pontryagin Maximum Principle and theorems on the existence of optimal trajectories, are helpful to go part of the way and get some information on the shortest paths, but do not suffice ...
Complementarity Modeling of Hybrid Systems
, 1998
"... A complementarity framework is described for the modeling of certain classes of mixed continuous /discrete dynamical systems. The use of such a framework is wellknown for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to sys ..."
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Cited by 51 (11 self)
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A complementarity framework is described for the modeling of certain classes of mixed continuous /discrete dynamical systems. The use of such a framework is wellknown for mechanical systems with inequality constraints, but we give a more general formulation which applies for instance also to systems with relays in a feedback loop. The main theoretical results in the paper are concerned with uniqueness of smooth continuations; the solution of this problem requires the construction of a map from the continuous state to the discrete state. A crucial technical tool is the socalled linear complementarity problem (LCP); we introduce various generalizations of this problem. Specific results are obtained for Hamiltonian systems, passive systems, and linear systems.
Multiscale representations for manifoldvalued data
 SIAM J. MULTISCALE MODEL. SIMUL
, 2005
"... We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S 2, the special orthogonal group SO(3), the positive definite matrices SPD(n), and the Grassmann manifolds G(n, k). The representations are based on the deployment of Desl ..."
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Cited by 50 (3 self)
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We describe multiscale representations for data observed on equispaced grids and taking values in manifolds such as the sphere S 2, the special orthogonal group SO(3), the positive definite matrices SPD(n), and the Grassmann manifolds G(n, k). The representations are based on the deployment of Deslauriers–Dubuc and averageinterpolating pyramids “in the tangent plane” of such manifolds, using the Exp and Log maps of those manifolds. The representations provide “wavelet coefficients ” which can be thresholded, quantized, and scaled in much the same way as traditional wavelet coefficients. Tasks such as compression, noise removal, contrast enhancement, and stochastic simulation are facilitated by this representation. The approach applies to general manifolds but is particularly suited to the manifolds we consider, i.e., Riemannian symmetric spaces, such as S n−1, SO(n), G(n, k), where the Exp and Log maps are effectively computable. Applications to manifoldvalued data sources of a geometric nature (motion, orientation, diffusion) seem particularly immediate. A software toolbox, SymmLab, can reproduce the results discussed in this paper.
Asymptotic model selection for directed networks with hidden variables
, 1996
"... We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a ..."
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Cited by 49 (15 self)
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We extend the Bayesian Information Criterion (BIC), an asymptotic approximation for the marginal likelihood, to Bayesian networks with hidden variables. This approximation can be used to select models given large samples of data. The standard BIC as well as our extension punishes the complexity of a model according to the dimension of its parameters. We argue that the dimension of a Bayesian network with hidden variables is the rank of the Jacobian matrix of the transformation between the parameters of the network and the parameters of the observable variables. We compute the dimensions of several networks including the naive Bayes model with a hidden root node. 1