Efficient traversal of well-behaved hierarchical trees of extents for ray-tracing complex scenes

Traversal of hierarchial trees of extents (HTE) requires computation of intersections between rays and bounding volumes whose faces are parallel to the cartesian axes. By redefining the HTE so that nonoverlapping bounding volumes are generated, a well-behaved data structure is obtained in which geometrical coherence is applied to speed up its traversal. We distinguish two types of bounding volumes: internal boxes contain the ray's origin whileexternal bounding volumes do not contain the ray's origin. To traverse the HTE, we look first to polygons in the internal bounding volumes and deal with external boxes only when no ray-polygon intersection is found in internal nodes. As external nodes in the HTE define pruned subtrees of external bounding volumes, geometrical characteristics of the boxes are exploited for HTE traversal. A coding scheme allows a 6-bit code to determine which faces of a bounding volume need to be tested for intersection. Also, our well-behaved HTE allows for reuse of intersection points at lower levels of the tree.     

Bounding Volume Hierarchies of Slab Cut Balls

We introduce a bounding volume hierarchy based on the Slab Cut Ball. This novel type of enclosing shape provides an attractive balance between tightness of fit, cost of overlap testing, and memory requirement. The hierarchy construction algorithm includes a new method for the construction of tight bounding volumes in worst case O(n) time, which means our tree data structure is constructed in O(n log n) time using traditional top‐down building methods. A fast overlap test method between two slab cut balls is also proposed, requiring as few as 28–99 arithmetic operations, including the transformation cost. Practical collision detection experiments confirm that our tree data structure is amenable for high performance collision queries. In all the tested benchmarks, our bounding volume hierarchy consistently gives performance improvements over the sphere tree, and it is also faster than the OBB tree in five out of six scenes. In particular, our method is asymptotically faster than the sphere tree, and it also outperforms the OBB tree, in close proximity situations.     

Tight and efficient surface bounds in meshless animation

This paper presents a fast approach for computing tight surface bounds in meshless animation, and its application to collision detection. Given a high-resolution surface animated by a comparatively small number of simulation nodes, we are able to compute tight bounding volumes with a cost linear in the number of simulation nodes. Our approach extends concepts about bounds of convex sets to the meshless deformation setting, and we introduce an efficient algorithm for finding extrema of these convex sets. The extrema can be used for efficiently updating bounding volumes such as AABBs or k-DOPs, as we show in our results. The choice of particular bounding volume may depend on the complexity of the contact configurations, but in all cases we can compute surface bound orders of magnitude faster and/or tighter than with previous methods.     

Velocity-Aligned Discrete Oriented Polytopes for dynamic collision detection

We propose an acceleration scheme for many-body dynamic collision detection at interactive rates. We use the Velocity-Aligned Discrete Oriented Politope (VADOP), a tight bounding volume representation that offers fast update rates and which is particularly suitable for applications with many fast-moving objects. The axes selection that determines the shape of our bounding volumes is based on spherical coverings. We demonstrate that we can robustly detect collisions that are missed by pseudo-dynamic collision detection schemes, with even greater performance due to substantial collision pruning by our bounding volumes.     

Graphics processing unit‐accelerated bounding for branch‐and‐bound applied to a permutation problem using data access optimization

Branch‐and‐bound (B&B) algorithms are attractive methods for solving to optimality combinatorial optimization problems using an implicit enumeration of a dynamically built tree‐based search space. Nevertheless, they are time‐consuming when dealing with large problem instances. Therefore, pruning tree nodes (subproblems) is traditionally used as a powerful mechanism to reduce the size of the explored search space. Pruning requires to perform the bounding operation, which consists of applying a lower bound function to the subproblems generated during the exploration process. Preliminary experiments performed on the Flow‐Shop scheduling problem (FSP) have shown that the bounding operation consumes over 98% of the execution time of the B&B algorithm. In this paper, we investigate the use of graphics processing unit (GPU) computing as a major complementary way to speed up the search. We revisit the design and implementation of the parallel bounding model on GPU accelerators. The proposed approach enables data access optimization. Extensive experiments have been carried out on well‐known FSP benchmarks using an Nvidia Tesla C2050 GPU card. Compared to a CPU‐based single core execution using an Intel Core i7‐970 processor without GPU, speedups higher than 100 times faster are achieved for large problem instances. At an equivalent peak performance, GPU‐accelerated B&B is twice faster than its multi‐core counterpart. Copyright © 2013 John Wiley & Sons, Ltd.     

Accurate Object Recognition with Shape Masks

In this paper we propose an object recognition approach that is based on shape masks—generalizations of segmentation masks. As shape masks carry information about the extent (outline) of objects, they provide a convenient tool to exploit the geometry of objects. We apply our ideas to two common object class recognition tasks—classification and localization. For classification, we extend the orderless bag-of-features image representation. In the proposed setup shape masks can be seen as weak geometrical constraints over bag-of-features. Those constraints can be used to reduce background clutter and help recognition. For localization, we propose a new recognition scheme based on high-dimensional hypothesis clustering. Shape masks allow to go beyond bounding boxes and determine the outline (approximate segmentation) of the object during localization. Furthermore, the method easily learns and detects possible object viewpoints and articulations, which are often well characterized by the object outline. Our experiments reveal that shape masks can improve recognition accuracy of state-of-the-art methods while returning richer recognition answers at the same time. We evaluate the proposed approach on the challenging natural-scene Graz-02 object classes dataset.     

Direct visualization of volume data

A combination of segmentation tools and fast volume renderers that provides an interactive exploration environment for volume visualization is discussed. The tools and renderers include mechanisms that distribute volume data across multiple processors, as well as image compositing techniques and solutions to representation problems in the selection and display of subregions within bounding volumes. A volume visualization technique using the interactive control of images rendered directly from volume data coupled with a user-controlled semantic classification tool is described. The variations of parallel volume rendering being explored on the Pixel-Planes 5 system and the region-of-interest selection methods and the interactive tools used by the system are presented. The flexibility and power of combining volume rendering with region-of-interest selection techniques are demonstrated using examples of medical imaging applications     

Automatic Hybrid Hierarchy Creation: a Cost-model Based Approach

While using hierarchical search structures has been proved as one of the most efficient acceleration techniques when rendering complex scenes, automatic creation of appropriate hierarchies is not solved yet. Well‐known algorithms for automatic creation of bounding volume hierarchies are not enough. Higher performance is achieved by introducing spatial uniform subdivision, although algorithms proposed up to now are not truly automatic, as they need some parameters to be adjusted. In this paper we present a full‐automatic hierarchy creation scheme that structures the scene in a hybrid way, combining bounding volumes and voxel grids in the same tree, selecting the search structure that best fits to each scene region. It uses no parameters at all. This efficient proposal relies on a new cost model that estimates the goodness of a hybrid hierarchy if used for rendering the scene. ACM CSS: I.3.7 Computer Graphics—Three‐Dimensional Graphics and Realism     

Enhancing Bounding Volumes using Support Plane Mappings for Collision Detection

In this paper we present a new method for improving the performance of the widely used Bounding Volume Hierarchies for collision detection. The major contribution of our work is a culling algorithm that serves as a generalization of the Separating Axis Theorem for non parallel axes, based on the well‐known concept of support planes. We also provide a rigorous definition of support plane mappings and implementation details regarding the application of the proposed method to commonly used bounding volumes. The paper describes the theoretical foundation and an overall evaluation of the proposed algorithm. It demonstrates its high culling efficiency and in its application, significant improvement of timing performance with different types of bounding volumes and support plane mappings for rigid body simulations.     

ACCELERATING RAY TRACING THROUGH POLYGON PROJECTION

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Adaptable image segmentation via simple pixel classification

We propose an approach to image segmentation that views it as one of pixel classification using simple features defined over the local neighborhood. We use a support vector machine for pixel classification, making the approach automatically adaptable to a large number of image segmentation applications. Since our approach utilizes only local information for classification, both training and application of the image segmentor can be done on a distributed computing platform. This makes our approach scalable to larger images than the ones tested. This article describes the methodology in detail and tests it efficacy against 5 other comparable segmentation methods on 2 well‐known image segmentation databases. Hence, we present the results together with the analysis that support the following conclusions: (i) the approach is as effective, and often better than its studied competitors; (ii) the approach suffers from very little overfitting and hence generalizes well to unseen images; (iii) the trained image segmentation program can be run on a distributed computing environment, resulting in linear scalability characteristics. The overall message of this paper is that using a strong classifier with simple pixel‐centered features gives as good or better segmentation results than some sophisticated competitors and does so in a computationally scalable fashion.     

A comparison of some methods for bounding connected and disconnected solution sets of interval linear systems

Summary Finding bounding sets to solutions to systems of algebraic equations with uncertainties in the coefficients, as well as rapidly but rigorously locating all solutions to nonlinear systems or global optimization problems, involves bounding the solution sets to systems of equations with wide interval coefficients. In many cases, singular systems are admitted within the intervals of uncertainty of the coefficients, leading to unbounded solution sets with more than one disconnected component. This, combined with the fact that computing exact bounds on the solution set is NP-hard, limits the range of techniques available for bounding the solution sets for such systems. However, the componentwise nature and other properties make the interval Gauss–Seidel method suited to computing meaningful bounds in a predictable amount of computing time. For this reason, we focus on the interval Gauss–Seidel method. In particular, we study and compare various preconditioning techniques we have developed over the years but not fully investigated, comparing the results. Based on a study of the preconditioners in detail on some simple, specially–designed small systems, we propose two heuristic algorithms, then study the behavior of the preconditioners on some larger, randomly generated systems, as well as a small selection of systems from the Matrix Market collection.      

“Meshsweeper”: dynamic point-to-polygonal mesh distanceand applications

We introduce a new algorithm for computing the distance from a point to an arbitrary polygonal mesh. Our algorithm uses a multiresolution hierarchy of bounding volumes generated by geometric simplification. Our algorithm is dynamic, exploiting coherence between subsequent queries using a priority process and achieving constant time queries in some cases. It can be applied to meshes that transform rigidly or deform nonrigidly. We illustrate our algorithm with a simulation of particle dynamics and collisions with a deformable mesh, the computation of distance maps and offset surfaces, the computation of an approximation to the expensive Hausdorff distance between two shapes, and the detection of self-intersections. We also report comparison results between our algorithm and an alternative algorithm using an octree, upon which our method permits an order-of-magnitude speed-up     

Reliable Collision Detection for Time-Dependent Parametric Surfaces

We improve on an algorithm by Von Herzen, Barr, and Zatz (HBZ) to detect geometric collisions between pairs of time-dependent parametric surfaces. The HBZ algorithm uses upper bounds on the parametric derivatives to guarantee detection of collisions and near misses, thus avoiding the defects of algorithms which sample the surfaces, possibly missing sharp spikes. Unfortunately, the user of the HBZ algorithm must supply not only routines computing the surface functions, but also routines bounding every component in the Jacobian of these surface functions over an arbitrary parametric range. Although they give helpful analyses for several types of surfaces, HBZ admit the need to provide Jacobian bounding routines as a disadvantage.We propose using interval arithmetic to bound functional values over a parametric input range, thus eliminating the need for the Jacobian entirely. Our interval version of the collision detection algorithm assumes neither bounded differentiability nor satisfaction of the Lipschitz criterion. Therefore, our code can detect geometric collisions for the much larger class of surface functions for which bounds on the function values can be computed using interval arithmetic. We contrast our code to that of HBZ and give timing comparisons.     

On Solutions of Linear Ordinary Difference Equations in their Coefficient Field

We extend the notion of monomial extensions of differential fields, i.e. simple transcendental extensions in which the polynomials are closed under differentiation, to difference fields. The structure of such extensions provides an algebraic framework for solving generalized linear difference equations with coefficients in such fields. We then describe algorithms for finding the denominator of any solution of those equations in an important subclass of monomial extensions that includes transcendental indefinite sums and products. This reduces the general problem of finding the solutions of such equations in their coefficient fields to bounding their degrees. In the base case, this yields in particular a new algorithm for computing the rational solutions of q -difference equations with polynomial coefficients.     

Visualizing the Uncertainty of Graph‐based 2D Segmentation with Min‐path Stability

This paper presents a novel approach to visualize the uncertainty in graph‐based segmentations of scalar data. Segmentation of 2D scalar data has wide application in a variety of scientific and medical domains. Typically, a segmentation is presented as a single unambiguous boundary although the solution is often uncertain due to noise or blur in the underlying data as well as imprecision in user input. Our approach provides insight into this uncertainty by computing the “min‐path stability”, a scalar measure analyzing the stability of the segmentation given a set of input constraints. Our approach is efficient, easy to compute, and can be generally applied to either graph cuts or live‐wire (even partial) segmentations. In addition to its general applicability, our new approach to graph cuts uncertainty visualization improves on the time complexity of the current state‐of‐the‐art with an additional fast approximate solution. We also introduce a novel query enabled by our approach which provides users with alternate segmentations by efficiently extracting local minima of the segmentation optimization. Finally, we evaluate our approach and demonstrate its utility on data from scientific and medical applications.     

Spacetime ray tracing for animation

Techniques for the efficient ray tracing of animated scenes are presented. They are based on two central concepts: spacetime ray tracing, and a hybrid adaptive space subdivision/boundary volume technique for generating efficient, nonoverlapping hierarchies of bounding volumes. In spacetime ray tracing, static objects are rendered in 4-D space-time using 4-D analogs to 3-D techniques. The bounding volume hierarchy combines elements of adaptive space subdivision and bounding volume techniques. The quality of hierarchy and its nonoverlapping character make it an improvement over previous algorithms, because both attributes reduce the number of ray/object intersections that must be computed. These savings are amplified in animation because of the much higher cost of computing ray/object intersections for motion-blurred animation. It is shown that it is possible to ray trace large animations more quickly with space-time ray tracing using this hierarchy than with straightforward frame-by-frame rendering     

刚体在软体对象环境中的碰撞检测的研究

刚体在软体对象环境中的碰撞检测在虚拟现实的研究领域具有很大的普遍性 ,但以往的研究较少 .文中给出了一种基于固定方向凸包 (FDH)包围盒树的碰撞检测方法 ,并着重论述了利用线性规划的思想以解决刚体自由运动后包围盒树的更新以及通过一种自底向上的方法解决软体对象变形后包围盒树的更新 .实验表明 ,该方法不仅能较好地解决刚体间的碰撞检测 ,而且能有效地解决刚体与软体间的碰撞检测     

An empirical measure of the performance of a document image segmentation algorithm

Document image segmentation is the first step in document image analysis and understanding. One major problem centres on the performance analysis of the evolving segmentation algorithms. The use of a standard document database maintained at the Universities/Research Laboratories helps to solve the problem of getting authentic data sources and other information, but some methodologies have to be used for performance analysis of the segmentation. We describe a new document model in terms of a bounding box representation of its constituent parts and suggest an empirical measure of performance of a segmentation algorithm based on this new graph-like model of the document. Besides the global error measures, the proposed method also produces segment-wise details of common segmentation problems such as horizontal and vertical split and merge as well as invalid and mismatched regions. Received July 14, 2000 / Revised June 12, 2001[-1mm]     

Towards seamless mobility on pervasive hardware

Preserving one’s uniquely customized computing environment as one moves to different locations is an enduring challenge in mobile computing. We examine why this capability is valued so highly, and what makes it so difficult to achieve for personal computing applications. We describe a new mechanism called Internet Suspend/Resume (ISR) that overcomes many of the limitations of previous approaches to realizing this capability. ISR enables a hands-free approach to mobile computing that appears well suited to future pervasive computing environments in which commodity hardware may be widely deployed for transient use. We show that ISR can be implemented by layering virtual machine technology on distributed file system technology. We also report on measurements from a prototype that confirm that ISR is already usable today for some common usage scenarios.