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.
174192
Fault tolerant networks with small degree
In this paper, we study the design of fault tolerant networks for arrays and meshes by adding redundant nodes and edges. For a target graph <italic>G</italic> (linear array or mesh in this paper), a graph <italic>G</italic>′ is called a &kgr;-fault-tolerant graph of <italic>G</italic> if when we remove any &kgr; nodes from <italic>G</italic>′, it still contains a subgraph isomorphic to <italic>G</italic>. The major quality measures for a fault-tolerant graph are the number of spare nodes it uses and the maximum degree it has. The degree is particularly important in practice as it poses constraints on the scalability of the system. In this paper, we aim at designing fault-tolerant graphs with both small degree and small number of spare nodes. The graphs we obtain have degree <italic>O</italic>(1) for arrays and <italic>O</italic>(log<supscrpt>3</supscrpt> &kgr;) for meshes. The number of spare nodes used are <italic>O</italic>(&kgr; log<supscrpt>2</supscrpt> &kgr;) and <italic>O</italic>(&kgr;<supscrpt>2</supscrpt>/log &kgr;), respectively. Compared to the previous results, the number of spare nodes used in our construction has one fewer linear factor in &kgr;.
5430292
A practical evaluation of kinetic data structures
In many applications of computational geometry to modeling objects and processes in the physical world, the participating objects are in a state of continuous change. Motion is the most ubiquitous kind of continuous transformation but others, such as shape deformation, are also possible. In a recent paper, Baech, Guibas, and Hershberger [BGH97] proposed the framework of kinetic data structures (KDSS) as a way to maintain, in a completely on-line fashion, desirable information about the state of a geometric system in continuous motion or change. They gave examples of kinetic data structures for the maximum of a set of (changing) numbers, and for the convex hull and closest pair of a set of (moving) points in the plane. The KDS frameworkallowseach object to change its motion at will according to interactions with other moving objects, the environment, etc. We implemented the KDSSdescribed in [BGH97],es well as came alternative methods serving the same purpose, as a way to validate the kinetic data structures framework in practice. In this note, we report some preliminary results on the maintenance of the convex hull, describe the experimental setup, compare three alternative methods, discuss the value of the measures of quality for KDSS proposed by [BGH97],and highlight some important numerical issues.
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.
5478794
Euclidean proximity and power diagrams
Power diagrams [Aur87] are a useful generalization of Voronoi diagrams in which the sites defining the diagram are not points but balls. They derive their name from the fact that the distance used in their definition is not the standard Euclidean distance, but instead the classical notion of the power of a point with respect to a ball [Cox61]. The advantage of the power distance is that the ‘bisector surfaces’, the surfaces equidistant from two given balls, are hyper-planes, and thus the Euclidean structure of these diagrams is polyhedral and they are easier to compute and manipulate than standard Voronoi diagrams. Several algorithms and applications for the power diagrams are already known, including those referenced in [IIM85, Aur88]. Most recently power diagrams have played a key role in work related to alpha shapes and ‘skins’ [Ede93, EM94, Ede95], as collections of balls are a natural model for molecular structures. The Voronoi diagram of point sites in any dimension has many useful proximity properties. Let us say that two sites are neighbors in the Voronoi diagram if their Voronoi cells share a common facet. It is well known that, for a set of points S, the closest pair of points in S are neighbors in the Voronoi diagram of S — equivalently, the closest pair of points must define an edge of the dual Delaunay diagram. Even more is true: the nearest neighbor to any point p ∈ S is a neighbor to p in the Voronoi diagram (equivalently, is connected to this neighbor by a Delaunay edge). Surprisingly, it seems that analogous proximity properties have not been studied for the power diagram. In this note, we consider the the power diagram of a set of disjoint balls. We show that the closest pair of
3114897
Multi-graph enabled active learning for multimodal web image retrieval
In this paper, we propose a multimodal Web image retrieval technique based on multi-graph enabled active learning. The main goal is to leverage the heterogeneous data on the Web to improve retrieval precision. Three graphs are constructed on images' content features, textual annotations and hyperlinks respectively, namely Content-Graph, Text-Graph and Link-Graph, which provide complimentary information on the images. By analyzing the three graphs, a training dataset is automatically created and transductive learning is enabled. The transductive learner is a multi-graph based classifier, which simultaneously solves the learning problem and the problem of combining heterogeneous data. This proposed approach, overall, tackles the problem of unsupervised active learning on Web graph. Although the proposed approach is discussed in the context of WWW image retrieval, it can be applied to other domains. The experimental results show the effectiveness of our approach.
140083992
Boosting image classification with LDA-based feature combination for digital photograph management
Image classification is of great importance for digital photograph management. In this paper we propose a general statistical learning method based on boosting algorithm to perform image classification for photograph annotation and management. The proposed method employs both features extracted from image content (i.e., color moment and edge direction histogram) and features from the EXIF metadata recorded by digital cameras. To fully utilize potential feature correlations and improve the classification accuracy, feature combination is needed. We incorporate linear discriminant analysis (LDA) algorithm to implement linear combinations between selected features and generate new combined features. The combined features are used along with the original features in boosting algorithm for improving classification performance. To make the proposed learning algorithm more efficient, we present two heuristics for selective feature combinations, which can significantly reduce training computation without losing performance. The proposed image classification method has several advantages: small model size, computational efficiency and improved classification performance based on LDA feature combination.
14199573
Zapato: Automatic Theorem Proving for Predicate Abstraction Refinement
Counterexample-driven abstraction refinement is an automatic process that produces abstract models of finite and infinite-state systems. When this process is applied to software, an automatic theorem prover for quantifier-free first-order logic helps to determine the feasibility of program paths and to refine the abstraction. In this paper we report on a fast, lightweight, and automatic theorem prover called Zapato which we have built specifically to solve the queries produced during the abstraction refinement process.
53235192
Spacetime faces: high resolution capture for modeling and animation
We present an end-to-end system that goes from video sequences to high resolution, editable, dynamically controllable face models. The capture system employs synchronized video cameras and structured light projectors to record videos of a moving face from multiple viewpoints. A novel spacetime stereo algorithm is introduced to compute depth maps accurately and overcome over-fitting deficiencies in prior work. A new template fitting and tracking procedure fills in missing data and yields point correspondence across the entire sequence without using markers. We demonstrate a data-driven, interactive method for inverse kinematics that draws on the large set of fitted templates and allows for posing new expressions by dragging surface points directly. Finally, we describe new tools that model the dynamics in the input sequence to enable new animations, created via key-framing or texture-synthesis techniques.
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.