Perfect sampling for closed queueing networks

In this paper we investigate coupling from the past (CFTP) algorithms for closed queueing networks. The stationary distribution has a product form only in a very limited number of particular cases when queue capacity is finite, and numerical algorithms are intractable due to the cardinality of the state space. Moreover, closed networks do not exhibit any monotonic property enabling efficient CFTP. We derive a bounding chain for the CFTP algorithm for closed queueing networks. This bounding chain is based on a compact representation of sets of states that enables exact sampling from the stationary distribution without considering all initial conditions in the CFTP. The coupling time of the bounding chain is almost surely finite, and numerical experiments show that it is close to the coupling time of the exact chain.     

Geometry Presorting for Implicit Object Space Partitioning

We present a new data structure for object space partitioning that can be represented completely implicitly. The bounds of each node in the tree structure are recreated at run‐time from the scene objects contained therein. By applying a presorting procedure to the geometry, only a known fraction of the geometry is needed to locate the bounding planes of any node. We evaluate the impact of the implicit bounding plane representation and compare our algorithm to a classic bounding volume hierarchy. Though the representation is completely implicit, we still achieve interactive frame rates on commodity hardware.     

Efficient Image‐Based Proximity Queries with Object‐Space Precision

We present an efficient algorithm for object‐space proximity queries between multiple deformable triangular meshes. Our approach uses the rasterization capabilities of the GPU to produce an image‐space representation of the vertices. Using this image‐space representation, inter‐object vertex‐triangle distances and closest points lying under a user‐defined threshold are computed in parallel by conservative rasterization of bounding primitives and sorted using atomic operations. We additionally introduce a similar technique to detect penetrating vertices. We show how mechanisms of modern GPUs such as mipmapping, Early‐Z and Early‐Stencil culling can optimize the performance of our method. Our algorithm is able to compute dense proximity information for complex scenes made of more than a hundred thousand triangles in real time, outperforming a CPU implementation based on bounding volume hierarchies by more than an order of magnitude.     

一种高效的基于相似性查找时间序列的位符号化表示方法*

到目前为止能够计算字符化时间序列的距离度量的方法很少,为此,提出了一种新的字符化的时间序列表示方法BSAP。该方法既能进行维度约简又允许在符号化后的时间序列表示法上定义距离度量。实验分别在合成数据和实际数据上进行,实验表明该方法具有更高的运算效率且需要较少的空间。     

联合多层注意力网络矩阵分解的推荐算法

许多推荐算法如基于矩阵分解因无法充分挖掘用户对项目的偏好信息而无法取得令人满意的推荐效果.为了解决上述问题,该文设计了两个模块,首先,利用多层感知机技术学习输入的信息以获得较好的特征表示,在原始输入时通过点积操作得到关系信息,并将其命名为深度矩阵分解(DeepMF);其次,在多层感知机中加入多层注意力网络,这样能够得到...     

Signed algebraic level sets on NURBS surfaces and implicit Boolean compositions for isogeometric CAD–CAE integration

Boundary-representation (B-rep) geometrical models, often mathematically represented using Non-Uniform Rational B-Spline (NURBS) surfaces, are the starting point for complex downstream product life-cycle evaluations including Computer-Aided Engineering (CAE). Boolean operations during B-rep model generation require surface intersection computations to describe the composed entity. However, for parametric NURBS surfaces, intersection operations are non-trivial and typically carried out numerically. The numerical intersection computations introduce challenges relating to the accuracy of the resulting representation, efficiency with which the computation is carried out, and robustness of the result to small variations in geometry. Often, for downstream CAE evaluations, an implicit, procedural knowledge of the Boolean operations between the composed objects that can resolve point containment queries (exact to the original NURBS bounding surfaces) maybe sufficient during quadrature. However, common point containment queries on B-rep models are numerical, iterative and relatively expensive. Thus, the first goal of the present paper is to describe a purely algebraic, and therefore non-iterative, approach to carrying out point containment queries on complex B-rep models built using low-degree NURBS surfaces. For CAE operations, the boundary representation of B-rep solids is, in general, not convenient and as a result, the B-rep model is converted to a meshed volumetric approximation. The major challenges to such a conversion include capturing the geometric features accurately when constructing the secondary (meshed) representation, apart from the efficiency of carrying out such a mesh generation step repeatedly as the geometric shape evolves. Thus, an ideal analysis procedure would operate directly on B-rep CAD models, without needing a secondary mesh, and would procedurally unify the geometric operations during CAD as well as CAE stages. Therefore, the second and broader goal of the present paper is to demonstrate CAD–CAE integration using signed algebraic level set operations directly on B-rep models by embedding or immersing the bounding surfaces within a discretized domain while preserving the geometric accuracy of the surfaces exact to the original NURBS representation during analysis.     

Safe human–robot interaction based on dynamic sphere-swept line bounding volumes

This paper presents a geometric representation for human operators and robotic manipulators, which cooperate in the development of flexible tasks. The main goal of this representation is the implementation of real-time proximity queries, which are used by safety strategies for avoiding dangerous collisions between humans and robotic manipulators. This representation is composed of a set of bounding volumes based on swept-sphere line primitives, which encapsulate their links more precisely than previous sphere-based models. The radius of each bounding volume does not only represent the size of the encapsulated link, but it also includes an estimation of its motion. The radii of these dynamic bounding volumes are obtained from an algorithm which computes the linear velocity of each link. This algorithm has been implemented for the development of a safety strategy in a real human–robot interaction task.     

Lossless compression of 3-D point data in QSplat representation

We propose a lossless compression algorithm for three-dimensional point data in graphics applications. In typical point representation, each point is treated as a sphere and its geometrical and normal data are stored in the hierarchical structure of bounding spheres. The proposed algorithm sorts child spheres according to their positions to achieve a higher coding gain for geometrical data. Also, the proposed algorithm compactly encodes normal data by exploiting high correlation between parent and child normals. Simulation results show that the proposed algorithm saves up to 60% of storage space.     

Image database design based on 9D-SPA representation for spatial relations

Spatial relationships between objects are important features for designing a content-based image retrieval system. We propose a new scheme, called 9D-SPA representation, for encoding the spatial relations in an image. With this representation, important functions of intelligent image database systems such as visualization, browsing, spatial reasoning, iconic indexing, and similarity retrieval can be easily achieved. The capability of discriminating images based on 9D-SPA representation is much more powerful than any spatial representation method based on minimum bounding rectangles or centroids of objects. The similarity measures using 9D-SPA representation provide a wide range of fuzzy matching capability in similarity retrieval to meet different user's requirements. Experimental results showed that our system is very effective in terms of recall and precision. In addition, the 9D-SPA representation can be incorporated into a two-level index structure to help reduce the search space of each query processing. The experimental results also demonstrated that, on average, only 0.1254 percent /spl sim/ 1.6829 percent of symbolic pictures (depending on various degrees of similarity) were accessed per query in an image database containing 50,000 symbolic pictures.     

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.     

Solving nonlinear polynomial systems in the barycentric Bernstein basis

We present a method for solving arbitrary systems of N nonlinear polynomials in n variables over an n-dimensional simplicial domain based on polynomial representation in the barycentric Bernstein basis and subdivision. The roots are approximated to arbitrary precision by iteratively constructing a series of smaller bounding simplices. We use geometric subdivision to isolate multiple roots within a simplex. An algorithm implementing this method in rounded interval arithmetic is described and analyzed. We find that when the total order of polynomials is close to the maximum order of each variable, an iteration of this solver algorithm is asymptotically more efficient than the corresponding step in a similar algorithm which relies on polynomial representation in the tensor product Bernstein basis. We also discuss various implementation issues and identify topics for further study.     

Reductions in the search space for deriving a fractal set of an arbitrary shape

At present, the problem of finding a quick and efficient way of representing an arbitrary shape as a set of contraction mappings (an iterated function system) is unresolved. Such a representation is particularly useful in shape representation since the primitives used to construct the shape will automatically have the correct morphology. Several attempts have been made to solve this problem and some of these are discussed. The main difficulty with these approaches is the large size and great complexity of the search space. This paper examines several constraints, all of a low computational complexity, which can be placed on each of the mappings which make up a possible solution. These constraints reduce the search space of four of the six coefficients of a mapping by between 20% and 85%, and of the other two by between 75% and 95% (the size of the reduction depends only on the size of the bounding box of the shape). Since these constraints apply to each mapping of an IFS, their cumulative effect on the search space is substantial. It is anticipated that these reductions in the search space can be used to aid a variety of search algorithms.     

三维空间中3DR44方向关系表示模型

现有方向关系模型无法表示参照对象的最小包围盒的内部空间方向.针对该不足,提出3DR44方向关系表示模型,给出动态邻接关系以及双向映射关系,利用交集对的有序序列处理特定目标对象与参照对象间的复杂方向关系,并将该模型转化为二维空间中的方向关系模型进行处理.应用结果表明,该模型可增强空间数据库表示三维空间对象方向关系的能力.     

Representing images using nonorthogonal Haar-like bases

Efficient and compact representation of images is a fundamental problem in computer vision. In this paper, we propose methods that use Haar-like binary box functions to represent a single image or a set of images. A desirable property of these box functions is that their inner product operation with an image can be computed very efficiently. We propose two closely related novel subspace methods to model images: the non-orthogonal binary subspace (NBS) method and binary principal component analysis (B-PCA) algorithm. NBS is spanned directly by binary box functions and can be used for image representation, fast template matching and many other vision applications. B-PCA is a structure subspace that inherits the merits of both NBS (fast computation) and PCA (modeling data structure information). B-PCA base vectors are obtained by a novel PCA guided NBS method. We also show that BPCA base vectors are nearly orthogonal to each other. As a result, in the non-orthogonal vector decomposition process, the computationally intensive pseudo-inverse projection operator can be approximated by the direct dot product without causing significant distance distortion. Experiments on real image datasets show promising performance in image matching, reconstruction and recognition tasks with significant speed improvement.     

Binary Ostensibly-Implicit Trees for Fast Collision Detection

We present a simple, efficient and low-memory technique, targeting fast construction of bounding volume hierarchies (BVH) for broad-phase collision detection. To achieve this, we devise a novel representation of BVH trees in memory. We develop a mapping of the implicit index representation to compact memory locations, based on simple bit-shifts, to then construct and evaluate bounding volume test trees (BVTT) during collision detection with real-time performance. We model the topology of the BVH tree implicitly as binary encodings which allows us to determine the nodes missing from a complete binary tree using the binary representation of the number of missing nodes. The simplicity of our technique allows for fast hierarchy construction achieving over 6× speedup over the state-of-the-art. Making use of these characteristics, we show that not only it is feasible to rebuild the BVH at every frame, but that using our technique, it is actually faster than refitting and more memory efficient.     

RACBVHs: Random-Accessible Compressed Bounding Volume Hierarchies

We present a novel compressed bounding volume hierarchy (BVH) representation, random-accessible compressed bounding volume hierarchies (RACBVHs), for various applications requiring random access on BVHs of massive models. Our RACBVH representation is compact and transparently supports random access on the compressed BVHs without decompressing the whole BVH. To support random access on our compressed BVHs, we decompose a BVH into a set of clusters. Each cluster contains consecutive bounding volume (BV) nodes in the original layout of the BVH. Also, each cluster is compressed separately from other clusters and serves as an access point to the RACBVH representation. We provide the general BVH access API to transparently access our RACBVH representation. At runtime, our decompression framework is guaranteed to provide correct BV nodes without decompressing the whole BVH. Also, our method is extended to support parallel random access that can utilize the multicore CPU architecture. Our method can achieve up to a 12:1 compression ratio, and more importantly, can decompress 4.2 M BV nodes ({=}135 {rm MB}) per second by using a single CPU-core. To highlight the benefits of our approach, we apply our method to two different applications: ray tracing and collision detection. We can improve the runtime performance by more than a factor of 4 as compared to using the uncompressed original data. This improvement is a result of the fast decompression performance and reduced data access time by selectively fetching and decompressing small regions of the compressed BVHs requested by applications.     

SIMILARITY‐BASED RETRIEVAL WITH STRUCTURE‐SENSITIVE SPARSE BINARY DISTRIBUTED REPRESENTATIONS

We present an approach to similarity‐based retrieval from knowledge bases that takes into account both the structure and semantics of knowledge base fragments. Those fragments, or analogues, are represented as sparse binary vectors that allow a computationally efficient estimation of structural and semantic similarity by the vector dot product. We present the representation scheme and experimental results for the knowledge base that was previously used for testing of leading analogical retrieval models MAC/FAC and ARCS. The experiments show that the proposed single‐stage approach provides results compatible with or better than the results of two‐stage models MAC/FAC and ARCS in terms of recall and precision. We argue that the proposed representation scheme is useful for large‐scale knowledge bases and free‐structured database applications.