Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 13 of 13
Full-Text Articles in Physical Sciences and Mathematics
Combinatorial Approach To Planar Non-Colliding Robot Arm Motion Planning, Ileana Streinu
Combinatorial Approach To Planar Non-Colliding Robot Arm Motion Planning, Ileana Streinu
Computer Science: Faculty Publications
We propose a combinatorial approach to plan non-colliding motions for a polygonal bar-and-joint framework. Our approach yields very efficient deterministic algorithms for a category of robot arm motion planning problems with many degrees of freedom, where the known general roadmap techniques would give exponential complexity. It is based on a novel class of one-degree-of-freedom mechanisms induced by pseudo triangulations of planar point sets, for which we provide several equivalent characterization and exhibit rich combinatorial and rigidity theoretic properties. The main application is an efficient algorithm for the Carpenter's Rule Problem: convexify a simple bar-and-joint planar polygonal linkage using only non …
Computational Geometry Column 40, Joseph O'Rourke
Computational Geometry Column 40, Joseph O'Rourke
Computer Science: Faculty Publications
It has recently been established by Below, De Loera, and Richter-Gebert that finding a minimum size (or even just a small) triangulation of a convex polyhedron is NP-complete. Their 3SAT-reduction proof is discussed.
On Reconfiguring Tree Linkages: Trees Can Lock, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides
On Reconfiguring Tree Linkages: Trees Can Lock, Therese Biedl, Erik D. Demaine, Martin L. Demaine, Sylvain Lazard, Anna Lubiw, Joseph O'Rourke, Steve Robbins, Ileana Streinu, Godfried Toussaint, Sue Whitesides
Computer Science: Faculty Publications
It has recently been shown that any simple (i.e. nonintersecting) polygonal chain in the plane can be reconfigured to lie on a straight line, and any simple polygon can be reconfigured to be convex. This result cannot be extended to tree linkages: we show that there are trees with two simple configurations that are not connected by a motion that preserves simplicity throughout the motion. Indeed, we prove that an N-link tree can have 2Ω(N) equivalence classes of configurations.
Pushpush And Push-1 Are Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke
Pushpush And Push-1 Are Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that two pushing-blocks puzzles are intractable in 2D. One of our constructions improves an earlier result that established intractability in 3D [OS99] for a puzzle inspired by the game PushPush. The second construction answers a question we raised in [DDO00] for a variant we call Push-1. Both puzzles consist of unit square blocks on an integer lattice; all blocks are movable. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover when a …
Computational Geometry Column 39, Joseph O'Rourke
Computational Geometry Column 39, Joseph O'Rourke
Computer Science: Faculty Publications
The resolution of a decades-old open problem is described: polygonal chains cannot lock in the plane.
Examples, Counterexamples, And Enumeration Results For Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke
Examples, Counterexamples, And Enumeration Results For Foldings And Unfoldings Between Polygons And Polytopes, Erik D. Demaine, Martin L. Demaine, Anna Lubiw, Joseph O'Rourke
Computer Science: Faculty Publications
We investigate how to make the surface of a convex polyhedron (a polytope) by folding up a polygon and gluing its perimeter shut, and the reverse process of cutting open a polytope and unfolding it to a polygon. We explore basic enumeration questions in both directions: Given a polygon, how many foldings are there? Given a polytope, how many unfoldings are there to simple polygons? Throughout we give special attention to convex polygons, and to regular polygons. We show that every convex polygon folds to an infinite number of distinct polytopes, but that their number of combinatorially distinct gluings is …
Computational Geometry Column 38, Joseph O'Rourke
Computational Geometry Column 38, Joseph O'Rourke
Computer Science: Faculty Publications
Recent results on curve reconstruction are described.
Computational Geometry Column 37, Erik D. Demaine, Joseph O'Rourke
Computational Geometry Column 37, Erik D. Demaine, Joseph O'Rourke
Computer Science: Faculty Publications
Open problems from the 15th Annual ACM Symposium on Computational Geometry.
Pushpush Is Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke
Pushpush Is Np-Hard In 2d, Erik D. Demaine, Martin L. Demaine, Joseph O'Rourke
Computer Science: Faculty Publications
We prove that a particular pushing-blocks puzzle is intractable in 2D, improving an earlier result that established intractability in 3D [OS99]. The puzzle, inspired by the game *PushPush*, consists of unit square blocks on an integer lattice. An agent may push blocks (but never pull them) in attempting to move between given start and goal positions. In the PushPush version, the agent can only push one block at a time, and moreover, each block, when pushed, slides the maximal extent of its free range. We prove this version is NP-hard in 2D by reduction from SAT.
Bayesian Reconstruction Of 3d Human Motion From Single-Camera Video, Nicholas Howe, Michael E. Leventon, William T. Freeman
Bayesian Reconstruction Of 3d Human Motion From Single-Camera Video, Nicholas Howe, Michael E. Leventon, William T. Freeman
Computer Science: Faculty Publications
The three-dimensional motion of humans is underdetermined when the observation is limited to a single camera, due to the inherent 3D ambiguity of 2D video. We present a system that reconstructs the 3D motion of human subjects from single-camera video, relying on prior knowledge about human motion, learned from training data, to resolve those ambiguities. After initialization in 2D, the tracking and 3D reconstruction is automatic; we show results for several video sequences. The results show the power of treating 3D body tracking as an inference problem.
Integrating Color, Texture, And Geometry For Image Retrieval, Nicholas Howe, Daniel P. Huttenlocher
Integrating Color, Texture, And Geometry For Image Retrieval, Nicholas Howe, Daniel P. Huttenlocher
Computer Science: Faculty Publications
This paper examines the problem of image retrieval from large, heterogeneous image databases. We present a technique that fulfills several needs identified by surveying recent research in the field. This technique fairly integrates a diverse and expandable set of image properties (for example, color, texture, and location) in a retrieval framework, and allows end-users substantial control over their use. We propose a novel set of evaluation methods in addition to applying established tests for image retrieval; our technique proves competitive with state-of-the-art methods in these tests and does better on certain tasks. Furthermore, it improves on many standard image retrieval …
Data As Ensembles Of Records: Representation And Comparison, Nicholas Howe
Data As Ensembles Of Records: Representation And Comparison, Nicholas Howe
Computer Science: Faculty Publications
Many collections of data do not come packaged in a form amenable to the ready application of machine learning techniques. Nevertheless, there has been only limited research on the problem of preparing raw data for learning, perhaps because widespread differences between domains make generalization difficult. This paper focuses on one common class of raw data, in which the entities of interest actually comprise collections of (smaller pieces of) homologous data. We present a technique for processing such collections into high-dimensional vectors, suitable for the application of many learning algorithms including clustering, nearestneighbors, and boosting. We demonstrate the abilities of the …
Using Artificial Queries To Evaluate Image Retrieval, Nicholas Howe
Using Artificial Queries To Evaluate Image Retrieval, Nicholas Howe
Computer Science: Faculty Publications
This paper addresses the evaluation and comparison of algorithms for generalized image retrieval. The forms of evaluation currently in vogue are not calibrated with each other and thus do not allow the comparison of results reported by different research groups. We address the problem by proposing a class of tests that are algorithmically defined and relatively independent of the image test set. The proposed tests can be tailored to investigate retrieval performance under specific sets of adverse conditions, allowing additional insight into the strengths and weaknesses of different retrieval mechanisms.