9779472
H-Walk: hierarchical distance computation for moving convex bodies
This paper presents the Hierarchical Walk, or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. For convex polygons, we prove that H-Walk improves on the classic Lin-Canny and DobkinKirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. Experimental results indicate that, unlike previous incremental distance computation algorithms, H-Walk adapts well to variable coherence in the motion.
15556637
Proximity problems on moving points
A kinetic data structure for the maintenance of a multidimensional range search tree is introduced. This structure is used as a building block to obtain kinetic data structures for two classical geometric proximity problems in arbitrary dlmensions: the first structure maintains the closest pair of a set of continuously moving points, and is provably efficient. The second structure maintains a spanning tree of the moving points whose cost remains within some prescribed factor of the minimum spanning tree.
9035359
Visibility Queries in Simple Polygons and Applications
In this paper we explore some novel aspects of visibility for stationary and moving points inside a simple polygon P. We provide a mechanism for expressing the visibility polygon from a point as the disjoint union of logarithmically many canonical pieces using a quadraticspace data structure. This allows us to report visibility polygons in time proportional to their size, but without the cubic space overhead of earlier methods. The same canonical decomposition can be used to determine visibility within a frustum, or to compute various attributes of the visibility polygon efficiently. By exploring the connection between visibility polygons and shortest path trees, we obtain a kinetic algorithm that can track the visibility polygon as the viewpoint moves along polygonal paths inside P, at a polylogarithmic cost per combinatorial change in the visibility. The combination of the static and kinetic algorithms leads to a space query-time tradeoff for the visibility from a point problem and an output-sensitive algorithm for the weak visibility from a segment problem.
11907465
Deformable Free-Space Tilings for Kinetic Collision Detection†
We present kinetic data structures for detecting collisions between a set of polygons that are moving continuously. Unlike classical collision detection methods that rely on bounding volume hierarchies, our method is based on deformable tilings of the free space surrounding the polygons. The basic shape of our tiles is that of a pseudo-triangle, a shape sufficiently flexible to allow extensive deformation, yet structured enough to make detection of self-collisions easy. We show different schemes for maintaining pseudo-triangulations as a kinetic data structure, and we analyze their performance. Specifically, we first describe an algorithm for maintaining a pseudo-triangulation of a point set, and show that the pseudo-triangulation changes only quadratically many times if points move along algebraic arcs of constant degree. In addition, by refining the pseudo-triangulation, we show triangulations of points that only change about O(n 7 / 3 ) times for linear motion. We then describe an algorithm for maintaining a pseudo-triangulation of a set of convex polygons. Finally, we extend our algorithm to the general case of maintaining a pseudo-triangulation of a set of moving or deforming simple polygons.
100573
A hierarchical method for real-time distance computation among moving convex bodies
Abstract This paper presents the Hierarchical Walk , or H-Walk algorithm, which maintains the distance between two moving convex bodies by exploiting both motion coherence and hierarchical representations. For convex polygons, we prove that H-Walk improves on the classic Lin–Canny and Dobkin–Kirkpatrick algorithms. We have implemented H-Walk for moving convex polyhedra in three dimensions. Experimental results indicate that, unlike previous incremental distance computation algorithms, H-Walk adapts well to variable coherence in the motion and provides consistent performance.
591702
Compact Voronoi Diagrams for Moving Convex Polygons
We describe a kinetic data structure for maintaining a compact Voronoi-like diagram of convex polygons moving around in the plane. We use a compact diagram for the polygons, dual to the Voronoi, first presented in [MKS96]. A key feature of this diagram is that its size is only a function of the number of polygons and not of their complexity. We demonstrate a local certifying property of that diagram, akin to that of Delaunay triangulations of points. We then obtain a method for maintaining this diagram that is output-sensitive and costs O(log n) per update. Furthermore, we show that for a set of k polygons with a total of n vertices moving along bounded degree algebraic motions, this dual diagram, and thus their compact Voronoi diagram, changes combinatorially Ω(n2) and O(kn2β(k)β(n)) times, where β(ċ) is an extremely slowly growing function. This compact Voronoi diagram can be used for collision detection or retraction motion planning among the moving polygons.
6040398
C-DIST: efficient distance computation for rigid and articulated models in configuration space
The problem of distance computation arises in many applications including motion planning, CAD/CAM, dynamic simulation and virtual environments. Most prior work in this area has been restricted to separation or penetration distance computation between two objects. In this paper, we address the problem of computing a measure of distance between two configurations of a rigid or articulated model. The underlying distance metric is defined as the length of the longest displacement vector over the corresponding vertices of the model between two configurations. Our algorithm is based on Chasles theorem in Screw theory, and we show that the maximum distance can be realized only by a vertex of the convex hull of a rigid object. We use this formulation to compute the distance, and present two acceleration techniques to speed up the computation: incremental walking on the dual space of the convex hull and culling vertices on the convex hull using a bounding volume hierarchy (BVH). Our algorithm can be easily extended to articulated models by maximizing the distance over its each link and we also present culling techniques to accelerate the computation. We highlight the performance of our algorithm on many complex models and describe its application to proximity queries and motion planning.
8272677
Parameter estimation for MRF stereo
This paper presents a novel approach for estimating parameters for MRF-based stereo algorithms. This approach is based on a new formulation of stereo as a maximum a posterior (MAP) problem, in which both a disparity map and MRF parameters are estimated from the stereo pair itself. We present an iterative algorithm for the MAP estimation that alternates between estimating the parameters while fixing the disparity map and estimating the disparity map while fixing the parameters. The estimated parameters include robust truncation thresholds, for both data and neighborhood terms, as well as a regularization weight. The regularization weight can be either a constant for the whole image, or spatially-varying, depending on local intensity gradients. In the latter case, the weights for intensity gradients are also estimated. Experiments indicate that our approach, as a wrapper for existing stereo algorithms, moves a baseline belief propagation stereo algorithm up six slots in the middlebury rankings.
18118919
EnjoyPhoto: a vertical image search engine for enjoying high-quality photos
In this paper, we propose building a vertical image search engine called EnjoyPhoto that leverages rich metadata from various photo forum web sites to meet users' requirements for enjoying high-quality photos, which is virtually impossible in traditional image search engines. To solve the ranking problem when aggregating multiple photo forums, we propose a novel rank fusion algorithm that uses duplicate photos to normalize rating scores. To further improve user experiences in enjoying photos, we design an in-place image browsing interface, and compare it with several other interfaces in a user study. With rich metadata and rating information, more attractive user interfaces are enabled, including slideshow authoring and photo recommendations. We conducted experiments and user studies on a 2.5-million image database to evaluate the proposed rank fusion algorithm, investigate the rationale behind building a vertical image search engine, and study user interfaces and preferences for the purpose of enjoying high-quality photos. The experimental results demonstrate the effectiveness of the proposed ranking algorithm. The results also show that the 2.5-million high-quality image database in EnjoyPhoto performs comparably with Google's 1- billion image database for queries related to location, nature, and daily life categories. Finally, our results show that the in-place browsing interface-called Force-Transfer view-is much more convenient for users than traditional interfaces.
33433492
Disjoint NP-Pairs
We study the question of whether the class DisjNP of disjoint pairs (A, B) of NP-sets contains a complete pair. The question relates to the question of whether optimal proof systems exist, and we relate it to the previously studied question of whether there exists a disjoint pair of NP-sets that is NP-hard. We show under reasonable hypotheses that nonsymmetric disjoint NP-pairs exist, which provides additional evidence for the existence of P-inseparable disjoint NP-pairs. 
We construct an oracle relative to which the class of disjoint NP-pairs does not have a complete pair; an oracle relative to which optimal proof systems exist, and hence complete pairs exist, but no pair is NP-hard; and an oracle relative to which complete pairs exist, but optimal proof systems do not exist.
14591402
An analysis of convergence delay in path vector routing protocols
Path vector routing protocols such as the Border Gateway Protocol (BGP) are known to suffer from slow convergence following a change in the network topology or policy. Although a number of convergence enhancements have been proposed recently, there has been no general analytical framework to assess and compare the various proposed algorithms. In this paper we present such a general framework to analyze the upper bounds of path vector protocols' convergence delay under shortest path routing policy and single link failure. Our framework takes into account important factors such as network connectivity, failure location, and routing message processing delay. It can be used to analyze both standard BGP and all the proposed convergence improvement algorithms in the case of shortest path routing policy and single link failure. It enables us to obtain previously unavailable analytical results, including the delay bounds of path fail-over for standard BGP and its convergence enhancements. Our analysis shows that BGP fail-over delay bounds are mainly determined by two factors: (1) the distance between the failure location and the destination, and (2) the length of the longest alternate path to reach the destination after the failure. These two factors are captured formally by our analysis and can explain why existing convergence enhancements often provide only limited improvements in fail-over events. Moreover, explicitly modeling message processing delay reveals insights into the impacts of connectivity richness (i.e., node degree and total number of links in the network), and also the effectiveness of different enhancements. These new results enable one to better understand and compare the behavior of various path vector protocols under different topology structures, network sizes, and message delays.