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10,443
Probabilistic Roadmaps for Path Planning in HighDimensional Configuration Spaces
 IEEE INTERNATIONAL CONFERENCE ON ROBOTICS AND AUTOMATION
, 1996
"... A new motion planning method for robots in static workspaces is presented. This method proceeds in two phases: a learning phase and a query phase. In the learning phase, a probabilistic roadmap is constructed and stored as a graph whose nodes correspond to collisionfree configurations and whose edg ..."
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Cited by 1277 (120 self)
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nodes. The method is general and easy to implement. It can be applied to virtually any type of holonomic robot. It requires selecting certain parameters (e.g., the duration of the learning phase) whose values depend on the scene, that is the robot and its workspace. But these values turn out
Threedimensional object recognition from single twodimensional images
 Artificial Intelligence
, 1987
"... A computer vision system has been implemented that can recognize threedimensional objects from unknown viewpoints in single grayscale images. Unlike most other approaches, the recognition is accomplished without any attempt to reconstruct depth information bottomup from the visual input. Instead, ..."
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Cited by 484 (7 self)
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, a probabilistic ranking method is used to reduce the size of the search space during model based matching. Finally, a process of spatial correspondence brings the projections of threedimensional models into direct correspondence with the image by solving for unknown viewpoint and model parameters
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5411 (68 self)
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long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme
The geometry of graphs and some of its algorithmic applications
 COMBINATORICA
, 1995
"... In this paper we explore some implications of viewing graphs as geometric objects. This approach offers a new perspective on a number of graphtheoretic and algorithmic problems. There are several ways to model graphs geometrically and our main concern here is with geometric representations that res ..."
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Cited by 524 (19 self)
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tensions. 0 For graphs embeddable in lowdimensional spaces with a small distortion, we can find lowdiameter decompositions (in the sense of [4] and [34]). The parameters of the decomposition depend only on the dimension and the distortion and not on the size of the graph. 0 In graphs embedded this way
Fast approximate nearest neighbors with automatic algorithm configuration
 In VISAPP International Conference on Computer Vision Theory and Applications
, 2009
"... nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional problems ..."
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Cited by 455 (2 self)
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nearestneighbors search, randomized kdtrees, hierarchical kmeans tree, clustering. For many computer vision problems, the most time consuming component consists of nearest neighbor matching in highdimensional spaces. There are no known exact algorithms for solving these highdimensional
A Growing Neural Gas Network Learns Topologies
 Advances in Neural Information Processing Systems 7
, 1995
"... An incremental network model is introduced which is able to learn the important topological relations in a given set of input vectors by means of a simple Hebblike learning rule. In contrast to previous approaches like the "neural gas" method of Martinetz and Schulten (1991, 1994), this m ..."
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Cited by 401 (5 self)
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data is available but no information on the desired output. What can the goal of learning be in this situation? One possible objective is dimensionality reduction: finding a lowdimensional subspace of the input vector space containing most or all of the input data. Linear subspaces with this property
GLUING AN INFINITE NUMBER OF INSTANTONS
, 2006
"... Abstract. This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual YangMills gauge theory to an “infinite energy ” situation. We show that we can glue an infinite number of instantons, and tha ..."
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Cited by 8 (5 self)
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, and that the resulting instantons have infinite energy in general. Moreover they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson’s “alternating method”. 1.
GLUING OF INFINITELY MANY INSTANTONS
, 2005
"... Abstract. This paper is one step toward infinite energy gauge theory and the geometry of infinite dimensional moduli spaces. We generalize a gluing construction in the usual YangMills gauge theory to an “infinite energy ” situation. We show that we can glue an infinite number of instantons, and tha ..."
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, and that the resulting instantons have infinite energy in general. Moreover they have an infinite dimensional parameter space. Our construction is a generalization of Donaldson’s “alternating method”. 1.
3D modelbased tracking of humans in action: a multiview approach
, 1996
"... We present a vision system for the 3D modelbased tracking of unconstrained human movement. Using image sequences acquired simultaneously from multiple views, we recover the 3D body pose at each time instant without the use of markers. The pose recovery problem is formulated as a search problem ..."
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Cited by 355 (9 self)
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to search through the high dimensional pose parameter space. A robust variant of chamfer matching is used a sa fast similarity measure between synthesized and real edge images. We present initial
Support Vector Machines for Classification and Regression
 UNIVERSITY OF SOUTHAMPTON, TECHNICAL REPORT
, 1998
"... The problem of empirical data modelling is germane to many engineering applications.
In empirical data modelling a process of induction is used to build up a model of the
system, from which it is hoped to deduce responses of the system that have yet to be observed.
Ultimately the quantity and qualit ..."
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Cited by 357 (5 self)
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and quality of the observations govern the performance
of this empirical model. By its observational nature data obtained is finite and sampled;
typically this sampling is nonuniform and due to the high dimensional nature of the
problem the data will form only a sparse distribution in the input space
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