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• Introduction of Riemannian global illumination. • A path tracer algorithm to approximate the solution of the Riemannian global illumination. • A map of the algorithm to the GPU, using the RTX platform. • We apply the Non-Euclidean path tracer to render "Photorealistic" inside views of the 3D flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of the Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. This paper presents a novel path tracer algorithm for immersive visualization of Riemannian manifolds. To do this, we introduce Riemannian illumination, a generalization of classical Computer Graphics illumination models. In this context, global light transport is expressed by extending the rendering equation to Riemannian manifolds. Using Monte Carlo integration to solve this equation results in the novel path tracer for Non-Euclidean spaces. We discuss its basic principles, as well as the general CPU algorithm. Additionally, we discuss in detail how to implement a GPU version, using the RTX pipeline. Finally, we apply the algorithm to render "photorealistic" inside views of the flat torus, Poincaré sphere, and the hyperbolic mirrored dodecahedron. These are examples of Euclidean, spherical, and hyperbolic spaces: the Thurston classical geometries. [ABSTRACT FROM AUTHOR]

NURBS method is the standard mathematical method for describing the shapes of curves/surfaces/volumes, and it is extensively used in computer-aided design, computer-aided manufacturing, and computer graphics. The injectivity of NURBS volumes means that they do not have self-intersections. Since the injectivity of parameterizations depend on the signs of their Jacobian functions, and the Jacobian of a NURBS volume is determined by the determinant of its tangent vectors in three directions, we first propose a method to compute the bounding vectors of the tangent cones of NURBS volume in this paper. Then the sufficient condition for the injectivity of NURBS volume is proposed. A checking algorithm is also presented. Some examples are given to verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

A crossover refers to the intersection of two satellite ground tracks. Crossovers are required for performing crossover differences adjustment to remove the orbit error and for establishing the time series of elevation in surfaces, which is why crossovers are important for satellite altimetry measurements of ice sheet or ice shelf elevation changes. How to extract more crossovers precisely is the objective of this paper. On the basis of the traditional method of solving crossovers and computer graphics, this paper proposes an improved algorithm called improved rapid rejection and straddle test (IRST) for computing the position of the crossover point. This algorithm efficiently and accurately searches for two points in ascending pass and two points in descending pass that can form a crossover, and then computes crossovers' geolocation. By using CryoSat-2 satellite altimeter data, we conducted our study on the Antarctic Ross ice shelf and Filchner–Ronne ice shelf using the fixed iteration (FI) algorithm, rapid rejection and straddle test (RST) algorithm, and the IRST algorithm. Results show that IRST is superior to the two other algorithms in terms of the number of crossovers, geolocation accuracy and computational efficiency. These advantages are more noticeable in the border areas between the ice shelf and the mountain with large terrain slope, which solves the problem that crossovers are less in these areas with poor-quality data coverage. • The improved algorithm computes more crossover points efficiently. • Crossover points computed by the improved algorithm with high geolocation accuracy. • More crossover points cover on the steep areas using the improved algorithm. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a new method to control scene sampling in complex ray-based rendering environments. It proposes to constrain image sampling density with a combination of object features, which are known to be well perceived by the human visual system, and image space saliency, which captures effects that are not based on the object''s geometry. The presented method uses Non-Photorealistic Rendering techniques for the object space feature evaluation and combines the image space saliency calculations with image warping to infer quality hints from previously generated frames. In order to map different feature types to sampling densities, we also present an evaluation of the object space and image space features'' impact on the resulting image quality. In addition, we present an efficient, adaptively aligned fractal pattern that is used to reconstruct the image from sparse sampling data. Furthermore, this paper presents an algorithm which uses our method in order to guarantee a desired minimal frame rate. Our scheduling algorithm maximizes the utilization of each given time slice by rendering features in the order of visual importance values until a time constraint is reached. We demonstrate how our method can be used to boost or stabilize the rendering time in complex ray-based image generation consisting of geometric as well as volumetric data. [Copyright &y& Elsevier]

Abstract: In this paper we derive formulas for computing graphical derivatives of the (possibly multivalued) solution mapping for convex parametric quadratic programs. Parametric programming has recently received much attention in the control community, however most algorithms are based on the restrictive assumption that the so called critical regions of the solution form a polyhedral subdivision, i.e. the intersection of two critical regions is either empty or a face of both regions. Based on the theoretical results of this paper, we relax this assumption and show how we can efficiently compute all adjacent full dimensional critical regions along a facet of an already discovered critical region. Coupling the proposed approach with the graph traversal paradigm, we obtain very efficient algorithms for the solution of parametric convex quadratic programs. [ABSTRACT FROM AUTHOR]

Abstract: Interpolating scalar refinable functions with compact support are of interest in several applications such as sampling theory, signal processing, computer graphics, and numerical algorithms. In this paper, we shall generalize the notion of interpolating scalar refinable functions to compactly supported interpolating -refinable function vectors with any multiplicity and dilation factor . More precisely, we are interested in a -refinable function vector such that is an column vector of compactly supported continuous functions with the following interpolation property where and for . Now for any function , the function can be interpolated and approximated by Since is interpolating, for all , that is, agrees with on . Moreover, for or , such interpolating refinable function vectors can have the additional orthogonality property: for all and , while it is well-known that there does not exist a compactly supported scalar 2-refinable function with both the interpolation and orthogonality properties simultaneously. In this paper, we shall characterize both interpolating -refinable function vectors and orthogonal interpolating -refinable function vectors in terms of their masks. We shall study their approximation properties and present a family of interpolatory masks, for compactly supported interpolating -refinable function vectors, of type with increasing orders of sum rules. To illustrate the results in this paper, we also present several examples of compactly supported (orthogonal) interpolating refinable function vectors and biorthogonal multiwavelets derived from such interpolating refinable function vectors. [Copyright &y& Elsevier]

Abstract: The block-based medial axis transform (BB_MAT, for short) of a 3D (2D) binary image, denoted 3D_BB_MAT (2D_BB_MAT), is defined as the problem to find a minimal set of upright 1-cubes (1-squares) whose union corresponds exactly to the 1-voxels (1-pixels) in the binary image. Many parallel algorithms have been proposed for computing the 2D_BB_MAT, almost all proposed approaches are unable to extend to a solution of the 3D_BB_MAT problem. In this paper, we first propose a novel time algorithm for solving the 3D_BB_MAT (2D_BB_MAT) problem of a binary image of size () on a linear array with a reconfigurable pipelined bus system (LARPBS, for short) by peeling the 3D (2D) corner shell of each 1-voxel (1-pixel) of the image and revealing some properties of the 3D_BB_MAT (2D_BB_MAT). The 3D (2D) chessboard distance transform problem, denoted 3D_CDT (2D_CDT), is the problem for each 0-voxel (0-pixel) of a 3D (2D) binary image to find its nearest 1-voxel (1-pixel) in the binary image based on chessboard distance metric. In this paper, we also solve the 3D_CDT (2D_CDT) based on the computed 3D_BB_MAT (2D_BB_MAT). All the proposed algorithms are very innovative although they look like “straightforward”. To the best of our knowledge, the proposed 2D_BB_MAT (2D_CDT) algorithm is the first algorithm that can extend to a solution of the 3D_BB_MAT (3D_CDT) problem in parallel, and the 3D_BB_MAT (3D_CDT) algorithm is the first parallel algorithm proposed for solving the 3D_BB_MAT (3D_CDT) problem. [Copyright &y& Elsevier]

• In the paper we propose a novel approach for solving puzzles whose pieces are of general shape, which need not necessarily match precisely due to erosion, and which have degraded unevenly over time. • We define the notion of valid transformations and propose a method of sampling them. This method may find uses in other domains. • We define a novel dissimilarity score that takes into account the special characteristics of the domain. • We introduce the notion of confidence in the dissimilarity scores, which depends not only on the value of the dissimilarity, but also on those of the competing matches. Confidence may be used not only in re-assembly, but also in other applications that are based on dissimilarity. This paper focuses on the re-assembly of an archaeological artifact, given images of its fragments. This problem can be considered as a special challenging case of puzzle solving. The restricted case of re-assembly of a natural image from square pieces has been investigated extensively and was shown to be a difficult problem in its own right. Likewise, the case of matching "clean" 2D polygons/splines based solely on their geometric properties has been studied. But what if these ideal conditions do not hold? This is the problem addressed in the paper. Three unique characteristics of archaeological fragments make puzzle solving extremely difficult: (1) The fragments are of general shape; (2) They are abraded, especially at the boundaries (where the strongest cues for matching should exist); and (3) The domain of valid transformations between the pieces is continuous. The key contribution of this paper is a fully-automatic and general algorithm that addresses puzzle solving in this intriguing domain. We show that our approach manages to correctly reassemble dozens of broken artifacts and frescoes. [ABSTRACT FROM AUTHOR]

This paper presents a novel gradient-based image completion algorithm for removing significant objects from natural images or photographs. Our method reconstructs the region of removal in two phases. Firstly, the gradient maps in the removed area are completed through a patch-based filling algorithm. After that, the image is reconstructed from the gradient maps by solving a Poisson equation. A new patch-matching criterion is developed in our approach to govern the completion of gradient maps. Both the gradient and the color information are incorporated in this new criterion, so a better image completion result is obtained. Several examples and comparisons are given at the end of the paper to demonstrate the performance of our gradient-based image completion approach. [Copyright &y& Elsevier]

Abstract: A new method for 5-axis CNC tool positioning is presented in this paper that improves upon a previous tool positioning strategy named the rolling ball method (RBM), which was developed by the present authors [Gray P, Bedi F, Ismail S. Rolling ball method for 5-axis surface machining. Comput Aided Des 2003;35(4):347–57]. The special property of the RBM is that it computes tool positions by considering the area beneath the tool that the tool will be positioned to cut instead of using surface curvatures computed at a single point on the surface. This enables the RBM to generate gouge-free tool positions without secondary iterative gouge-check and correction algorithms. However, the RBM generates conservative tilt angles in order to guarantee gouge-free tool positions. The new arc-intersect method (AIM) presented in this paper improves upon the RBM by directly positioning the tool to contact the surface and thereby eliminates the conservative nature of the RBM to give optimal tool positions. Like the RBM, the AIM is an area-based method that generates gouge-free tool positions without the use of iterative gouge-check and correction algorithms. The implementation described in this paper uses triangulated surfaces and the computer''s graphics hardware to assist in the tool position calculations. However, the method can be applied to any surface representation since it only uses surface coordinates and surface normals for computation. A section of a stamping die was machined to demonstrate the AIM and to show the improvement over the RBM and for comparison with 3-axis ballnose machining. The results showed that the AIM was 1.33 times faster than the RBM and that the AIM, with single direction parallel tool passes, was 1.62 times faster than a zig-zag pattern 3-axis ballnose tool path for the same feed rate, cusp height and tool diameter. The workpieces were measured with a CMM and the data were compared to the CAD model to show no gouging occurred and to check the cusp heights. [Copyright &y& Elsevier]

Abstract: This paper presents several parallel algorithms for the construction of the Delaunay triangulation in E 2 and E 3—one of the fundamental problems in computer graphics. The proposed algorithms are designed for parallel systems with shared memory and several processors. Such a hardware configuration (especially the case with two-processors) became widely spread in the last few years in the computer graphics area. Some of the proposed algorithms are easy to be implemented but not very efficient, while some of them prove opposite characteristics. Some of them are usable in E 2 only, other work in E 3 as well. The algorithms themselves were already published in computer graphics where the computer graphics criteria were highlighted. This paper concentrates on parallel and systematic point of view and gives detailed information about the parallelization of a computational geometry application to parallel and distributed computation oriented community. [Copyright &y& Elsevier]

Texture characterisation for freeform non-Euclidean surfaces is becoming increasingly important due to the widespread of the use of such surfaces in different applications, e.g. the additive manufacturing. Four main steps are required to analyse and characterise those surfaces which include new surface representation, surface filtration and decomposition, texture representation methods and finally the calculation of the surface parameters. Recently, the representation, as well as the filtration and decomposition, of freeform surfaces have been investigated and some algorithms have been proposed. This paper, however, shed the light on how to represent the texture of freeform non-Euclidean surfaces before calculating the parameters. A novel model for freeform surface parameterisation is introduced; this new model proposes the use of a projection algorithm before the actual calculation of the parameters. Different projection algorithms have been adopted from the mesh projection techniques found in the field of computer graphics. The results of applying those algorithms to represent the texture of both simulated and bio-engineering surfaces are shown, also a comparison between those algorithms has been carried out. Furthermore, examples of calculating some of the surface parameters for freeform surfaces are given. [ABSTRACT FROM AUTHOR]

Video segmentation is an important preprocessing step for many computer vision and graphics tasks. Its main goal is to group the voxels in the video volume with similar appearance and motion into spatio-temporally consistent supervoxels. In this paper, we formulate video segmentation as an L 0 gradient minimization problem, so that the spatio-temporal coherence can be effectively enforced through a gradient sparsity pursuit way. In our method, the appearance and motion descriptor space is first built for over-segmented image patches of each video frame. Then the L 0 gradient minimization is performed in the descriptor space, for both spatial and temporal dimensions. To solve the non-convex L 0 norm minimization problem, we extend the fused coordinate descent algorithm from 2D image grids to 3D video volume. We conduct quantitative evaluation of our method in a public video segmentation benchmark LIBSVX. The experimental results demonstrate our superior performance to state-of-the-arts in segmentation accuracy and undersegmentation error, and comparable performance in boundary recall and explained variation. [ABSTRACT FROM AUTHOR]

In this paper we survey all known (including own recent results) properties of the longest-edge n -section algorithms. These algorithms (in classical and recently designed conforming form) are nowadays used in many applications, including finite element simulations, computer graphics, etc. as a reliable tool for controllable mesh generation. In addition, we present a list of open problems arising in and around this topic. [ABSTRACT FROM AUTHOR]

The design of reinforced concrete sections of arbitrary shape, namely with variable geometry, holes as well as with arbitrary distribution of reinforcing steel bars, is a very common task in civil engineering, reinforced concrete structures. The design of these sections requires the integration of non-linear stress fields on complex shapes, because of the non-linear behavior of concrete in compression. In this paper, a novel algorithm is proposed to compute the ultimate strength of reinforced concrete sections under biaxial bending. The algorithm includes section subdivision into trapezoidal elements using the techniques of polygon clipping algorithm proposed by Weiler–Atherton. Exact numerical integration for normal strength concrete ( f ck ⩽ 50 MPa) is achieved, for each trapezoid, using the change of variables theorem followed by Gauss–Legendre integration. The proposed technique is hereafter referred to as WAGL (Weiler–Atherton, Gauss–Legendre). The verification of the proposed algorithm is performed by comparing analytical results between the WAGL technique and methods proposed by other authors (five examples). Additionally, the results obtained are also compared with experimental results available in the literature. The application of the WAGL technique is illustrated with two RC cross-section design examples. [ABSTRACT FROM AUTHOR]

Sketch-based human motion retrieval is a hot topic in computer animation in recent years. In this paper, we present a novel sketch-based human motion retrieval method via selected 2-dimensional (2D) Geometric Posture Descriptor (2GPD). Specially, we firstly propose a rich 2D pose feature call 2D Geometric Posture Descriptor (2GPD), which is effective in encoding the 2D posture similarity by exploiting the geometric relationships among different human body parts. Since the original 2GPD is of high dimension and redundant, a semi-supervised feature selection algorithm derived from Laplacian Score is then adopted to select the most discriminative feature component of 2GPD as feature representation, and we call it as selected 2GPD. Finally, a posture-by-posture motion retrieval algorithm is used to retrieve a motion sequence by sketching several key postures. Experimental results on CMU human motion database demonstrate the effectiveness of our proposed approach. [ABSTRACT FROM AUTHOR]

Current strategies for real-time rendering of trimmed spline surfaces re-approximate the data, pre-process extensively or introduce visual artifacts. This paper presents a new approach to rendering trimmed spline surfaces that guarantees visual accuracy efficiently, even under interactive adjustment of trim curves and spline surfaces. The technique achieves robustness and speed by discretizing at a near-minimal correct resolution based on a tight, low-cost estimate of adaptive domain griding. The algorithm is highly parallel, with each trim curve writing itself into a slim lookup table. Each surface fragment then makes its trim decision robustly by comparing its parameters against the sorted table entries. Adding the table-and-test to the rendering pass of a modern graphics pipeline achieves anti-aliased sub-pixel accuracy at high render-speed, while using little additional memory and fragment shader effort, even during interactive trim manipulation. [ABSTRACT FROM AUTHOR]

Abstract: Pattern-based spatial modeling relies on training images as basic modeling component for generating geostatistical realizations. The methodology recognizes that working with the unit of a pattern aids its reproduction, particularly for large systems. In this paper improvements are made, in terms of both the computation time and conditioning, of a pattern-based simulation method that relies on the cross-correlation-based simulation (CCSIM), introduced by Tahmasebi et al. (2012). The extension lies on the use of a multi-scale (MS) representation of the training image along a pattern projection strategy that is markedly different from the traditional multi-grid methods employed in the current methodologies, and proposes acceleration of the method by carrying out most of the computations in the Fourier space. In the proposed multi-scale representation, we transform the high-resolution training image into a pyramid of consecutively up-gridded views of the same image. The pyramid allows for rapid search of the patterns that can be superimposed over a shared overlap area with previously simulated patterns. A second advantage of the multi-scale view lies in data conditioning by means of a new hard data-relocation algorithm and the use of a co-template for looking for conditioning points ahead of the raster path employed in CCSIM. Using synthetic and real-field multi-million cell examples with sparse, as well as dense datasets, we investigate quantitatively how the improved algorithm performs with respect to CCSIM, as well as the traditional MP simulation algorithms. [Copyright &y& Elsevier]

Abstract: Finite topological spaces and the notion of dimension play an important role in digital spaces, computer graphics, image synthesis and image analysis (see, Herman, 1998 [9]; Khalimsky et al., 1990 [10]; Rosenfeld, 1979 [15]). In Georgiou and Megaritis (2011) [7] we gave an algorithm for computing the covering dimension of a finite space X using the notion of the incidence matrix of X. This algorithm has exponential order. In this paper we give a new algorithm of polynomial order for computing the covering dimension of a finite space. [Copyright &y& Elsevier]

Abstract: This paper details an algorithm to simultaneously perform registration of computed tomography (CT) and cone-beam computed (CBCT) images, and image enhancement of CBCT. The algorithm employs a viscous fluid model which naturally incorporates two components: a similarity measure for registration and an intensity correction term for image enhancement. Incorporating an intensity correction term improves the registration results. Furthermore, applying the image enhancement term to CBCT imagery leads to an intensity corrected CBCT with better image quality. To achieve minimal processing time, the algorithm is implemented on a graphic processing unit (GPU) platform. The advantage of the simultaneous optimization strategy is quantitatively validated and discussed using a synthetic example. The effectiveness of the proposed algorithm is then illustrated using six patient datasets, three head-and-neck datasets and three prostate datasets. [Copyright &y& Elsevier]

Abstract: Parallel implementations of Ray Tracing have been enabling real time performance, as the algorithm is embarrassingly parallel. However, in order to achieve both interactivity and real time performance, the algorithm should run at a high frame rates, i.e. at least 60 frames per second. Thus, a custom parallel design in hardware is likely to achieve high rendering performance. In this paper, we improve the GridRT architecture presented in previous work. GridRT is capable of dealing with the main desirable features of Ray Tracing, such as shadows and reflection effects, imposing low area cost and a promising rendering performance. As to this work, an application-specific instruction has been added and the underlaying computation embedded into the processor’s microprogram in order to calculate the ray–triangle intersection computations. These computations are performed in pipeline, whenever possible, yielding to a considerable reduction in terms of cycles per intersection test. The presented architecture is based on the uniform grid acceleration structure. It allows for a massive twofold parallelism: parallel ray–triangle intersection tests as well as parallel processing of many rays. A hardware implementation of the improved architecture is presented, together with the corresponding performance results and resources requirements. The rendering time is reduced by 80% using a grid configuration of eight processing elements and each intersection computation time is reduced by 50% with respect to the original GridRT implementation. [Copyright &y& Elsevier]

Abstract: Realistic rain simulation is a challenging problem due to the variety of different phenomena to consider. In this paper we propose a new rain rendering algorithm that extends present state of the art in the field, achieving real-time rendering of rain streaks and splashes with complex illumination effects, along with fog, halos and light glows as hints of the participating media. Our algorithm creates particles in the scene using an artist-defined storm distribution (e.g., provided as a 2D cloud distribution). Unlike previous algorithms, no restrictions are imposed on the rain area dimension or shape. Our technique adaptively samples the storm area to simulate rain particles only in the relevant regions and only around the observer. Particle simulation is executed entirely in the graphics hardware, by placing the particles at their updated coordinates at each time-step, also checking for collisions with the scene. To render the rain streaks, we use precomputed images and combine them to achieve complex illumination effects. Several optimizations are introduced to render realistic rain with virtually millions of falling rain droplets. [Copyright &y& Elsevier]

Abstract: Point cloud matching is a central problem in Object Modeling with applications in Computer Vision and Computer Graphics. Although the problem is well studied in the case when an initial estimate of the relative pose is known (fine matching), the problem becomes much more difficult when this a priori knowledge is not available (coarse matching). In this paper we introduce a novel technique to speed up coarse matching algorithms for point clouds. This new technique, called Hierarchical Normal Space Sampling (HNSS), extends Normal Space Sampling by grouping points hierarchically according to the distribution of their normal vectors. This hierarchy guides the search for corresponding points while staying free of user intervention. This permits to navigate through the huge search space taking advantage of geometric information and to stop when a sufficiently good initial pose is found. This initial pose can then be used as the starting point for any fine matching algorithm. Hierarchical Normal Space Sampling is adaptable to different searching strategies and shape descriptors. To illustrate HNSS, we present experiments using both synthetic and real data that show the computational complexity of the problem, the computation time reduction obtained by HNSS and the application potentials in combination with ICP. [Copyright &y& Elsevier]

Abstract: In many applications, the first step into the topological analysis of a discrete point set P sampled from a manifold is the construction of a simplicial complex with vertices on P. In this paper, we present an algorithm for the efficient computation of the Čech complex of P for a given value of the radius of the covering balls. Experiments show that the proposed algorithm can generally handle input sets of several thousand points, while for the topologically most interesting small values of can handle inputs with tens of thousands of points. We also present an algorithm for the construction of all possible Čech complices on P. [Copyright &y& Elsevier]

Abstract: Full matrix capture allows for the complete ultrasonic time domain signals for each transmit and receive element of a linear array probe to be retrieved. While it is more common to use full matrix capture to post-process data to allow for electronic steering, focusing and imaging after the initial inspection processes, due to the data-acquisition and performance limitations of the focusing algorithms real-time inspection systems are not yet common place. This paper investigates several algorithm optimisation techniques utilising standard in-expensive PC architecture with parallelisation undertaken by the graphic processing unit. This approach is further combined with several other software engineering optimisation techniques including threaded data-capture, the use of look-up tables and half-matrix implementation to produce a real-world inspection scenario for benchmark and performance analysis. Experimental results are presented indicating that high frame rates inclusive of data-acquisition and image render are achievable with 32 active transmit and receive elements. This approach is shown to offer significant performance advantages with low implementation and development costs. [Copyright &y& Elsevier]

Abstract: Silhouettes of polyhedra are an important primitive in application areas such as machine vision and computer graphics. In this paper, we study how to select view points of convex polyhedra such that the silhouette satisfies certain properties. Specifically, we give algorithms to find all projections of a convex polyhedron such that a given set of edges, faces and/or vertices appear on the silhouette. We present an algorithm to solve this problem in time for k edges. For orthogonal projections, we give an improved algorithm that is fully adaptive in the number l of connected components formed by the edges, and has a time complexity of . We then generalize this algorithm to edges and/or faces appearing on the silhouette. [Copyright &y& Elsevier]

Abstract: This paper presents an irregular stock cutting system (NEST) developed on AutoCAD software platform. A detail description to its mechanism is included. This development is based on two known techniques: the bitmap representation to transform all shapes drawn by AutoCAD into pixel matrices before nesting, and the bottom-left-fill algorithm for nesting. The system NEST is developed for further research works on practical stock cutting problems. It provides two important parameters: one is the precision level which decides how the bitmap representation can precisely describe a shape and therefore affects the time taken by nesting procedure; the other is the unit rotation angle which make a shape self-rotates in steps with small angle and to be finally placed on sheet material with its best self-rotation angle. NEST can tightly position every shape on a sheet material and performs satisfyingly from practical view point. The nesting result is demonstrated by the original drawings of all shapes and the sheet material instead of their graphics transformed from pixel matrices. Several tests are carried out to show its performance. [Copyright &y& Elsevier]

Abstract: Parallelism is becoming the leading paradigm in today’s computer architectures. In order to take full advantage of this development, new algorithms have to be specifically designed for parallel execution while many old ones have to be upgraded accordingly. One field in which parallel computing has been firmly established for many years is computer graphics. Calculating and displaying three-dimensional computer generated imagery in real time requires complex numerical operations to be performed at high speed on a large number of objects. Since most of these objects can be processed independently, parallel computing is applicable in this field. Modern graphics processing units (GPUs) have become capable of performing millions of matrix and vector operations per second on multiple objects simultaneously. As a side project, a software tool is currently being developed at the Institute of Aerospace Systems that provides an animated, three-dimensional visualization of both actual and simulated space debris objects. Due to the nature of these objects it is possible to process them individually and independently from each other. Therefore, an analytical orbit propagation algorithm has been implemented to run on a GPU. By taking advantage of all its processing power a huge performance increase, compared to its CPU-based counterpart, could be achieved. For several years efforts have been made to harness this computing power for applications other than computer graphics. Software tools for the simulation of space debris are among those that could profit from embracing parallelism. With recently emerged software development tools such as OpenCL it is possible to transfer the new algorithms used in the visualization outside the field of computer graphics and implement them, for example, into the space debris simulation environment. This way they can make use of parallel hardware such as GPUs and Multi-Core-CPUs for faster computation. In this paper the visualization software will be introduced, including a comparison between the serial and the parallel method of orbit propagation. Ways of how to use the benefits of the latter method for space debris simulation will be discussed. An introduction to OpenCL will be given as well as an exemplary algorithm from the field of space debris simulation. [Copyright &y& Elsevier]

Abstract: The polygon mesh is an important primitive used in representing 3D models. Its specification consists of topological and geometrical quantities; where the former describes the connection nodes, edges and faces, and the latter describes attributes such as node positions, face colors, etc. Our interest here lies with the encoding of the topology. Specifically, this paper presents a linear-time information-theoretically optimal compression algorithm for encoding a planar 2-manifold polygon mesh to a bit string X. [Copyright &y& Elsevier]

Abstract: Transmission and visualization of large geographical maps have become a challenging research issue in GIS applications. This paper presents an efficient and robust way to simplify large geographical maps using frame buffers and Voronoi diagrams. The topological relationships are kept during the simplification by removing the Voronoi diagram’s self-overlapped regions. With the simplified vector maps, we establish different levels of detail (LOD) models of these maps. Then we introduce a client/server architecture which integrates our out-of-core algorithm, progressive transmission and rendering scheme based on computer graphics hardware. The architecture allows the viewers to view different regions interactively at different LODs on the network. Experimental results show that our proposed scheme provides an effective way for powerful transmission and manipulation of large maps. [ABSTRACT FROM AUTHOR]

Abstract: Copyright violation and illegal manipulation of digital data have been acute challenges for many sectors since the very same set of enabling techniques for generating and processing digital data started to emerge. Although traditional protective methods, such as encryption and digital signatures, have been in use for decades, their inability to provide protection after decryption and locating tampering has prompted the development of digital watermarking. In this paper, a semi-fragile watermarking algorithm for authenticating 2D CAD engineering graphics based on log-polar coordinate mapping is proposed. Firstly, the vertices are divided into groups, and for each group, the vertices for carrying a watermark are mapped to the log-polar coordinate system. Then the watermark is embedded in the mantissa of the real-valued log-polar coordinates via bit substitution. Theoretical analysis and experimental results show that the proposed algorithm is not only robust against incidental global operations such as rotation, translation and scaling, but can also detect and locate malicious attacks such as entity modification and entity addition/deletion. [ABSTRACT FROM AUTHOR]

Abstract: The proximity and topology among particles are often the most important factor for understanding the spatial structure of particles. Reasoning the morphological structure of molecules and reconstructing a surface from a point set are examples where proximity among particles is important. Traditionally, the Voronoi diagram of points, the power diagram, the Delaunay triangulation, and the regular triangulation, etc. have been used for understanding proximity among particles. In this paper, we present the theory of the -shape and the -complex and the corresponding algorithms for reasoning proximity among a set of spherical particles, both using the quasi-triangulation which is the dual of the Voronoi diagram of spheres. Given the Voronoi diagram of spheres, we first transform the Voronoi diagram to the quasi-triangulation. Then, we compute some intervals called -intervals for the singular, regular, and interior states of each simplex in the quasi-triangulation. From the sorted set of simplexes, the -shape and the -complex corresponding to a particular value of can be found efficiently. Given the Voronoi diagram of spheres, the quasi-triangulation can be obtained in time in the worst case, where represents the number of simplexes in the quasi-triangulation. Then, the -intervals for all simplexes in the quasi-triangulation can also be computed in time in the worst case. After sorting the simplexes using the low bound values of the -intervals of each simplex in time, the -shape and the -complex can be computed in O time in the worst case by a binary search followed by a sequential search in the neighborhood, where represents the number of simplexes in the -shape or the -complex. The presented theory of the -shape and the -complex will be equally useful for diverse areas such as structural biology, computer graphics, geometric modelling, computational geometry, CAD, physics, and chemistry, where the core hurdle lies in determining the proximity among spherical particles. [Copyright &y& Elsevier]

Abstract: This paper adds to the abundant visual tracking literature with two main contributions. First, we illustrate the interest of using Graphic Processing Units (GPU) to support efficient implementations of computer vision algorithms, and secondly, we introduce the use of point-based 3D models as a shape prior for real-time 3D tracking with a monocular camera. The joint use of point-based 3D models together with GPU allows to adapt and simplify an existing tracking algorithm originally designed for triangular meshes. Point-based models are of particular interest in this context, because they are the direct output of most laser scanners. We show that state-of-the-art techniques developed for point-based rendering can be used to compute in real-time intermediate values required for visual tracking. In particular, apparent motion predictors at each pixel are computed in parallel, and novel views of the tracked object are generated online to help wide-baseline matching. Both computations derive from the same general surface splatting technique which we implement, along with other low-level vision tasks, on the GPU, leading to a real-time tracking algorithm. [Copyright &y& Elsevier]

Abstract: The aim of this paper is to prove numerically, via computer graphic simulations, that the synthesis algorithmprovided by Danca et al. can be utilized to synthesize any attractor of a dynamical system modeling a two-predator, one prey Lotka–Volterra like system. The algorithm switches in a periodic deterministic or a random way the control parameter inside a set of a chosen values. The obtained attractor is the same with the attractor obtained for parameter value taken as averaged value of the switched control values. This simple and effective algorithm relies on a convex property induced in the set of the attractors corresponding to the chosen switching parameters. The algorithm was tested successfully on systems depending linearly on the control parameter like Lorenz, Chen, Rossler, networks and other systems. [Copyright &y& Elsevier]

Abstract: A dedicated media processor is used in many mobile consumer devices to accelerate video, image, graphics, and display processing. Increased demand for higher pixel resolution, higher quality image and video processing, more graphics performance necessitates dramatically increased signal processing capabilities. To provide the increased performance at acceptable cost and power requires redesign of the traditional architecture. By wisely partitioning algorithms across programmable and fixed-function blocks, the performance goals can be met while still maintaining flexibility for new feature requirements and new standards. For a better than acceptable user experience and playback time, all IPs (display, graphics, video, and imaging) have to be optimized as an “end to end” system. In this paper, an overview of the future trends of multimedia IP processor architectures is provided that describes the implications on system architecture, power, and performance. [Copyright &y& Elsevier]

Abstract: In this paper we introduce new algorithm implementations of a new parametric image processing framework that will accurately process images and speed up computation for addition, subtraction, and multiplication. Its potential applications include computer graphics, digital signal processing and other multimedia applications. This Parameterized Digital Electronic Arithmetic (PDEA) model replaces linear operations with non-linear ones. The implementation of a parameterized model is presented. We also present the design of arithmetic circuits including parallel counters, adders and multipliers based in two high performance threshold logic gate implementations that we have developed. We will also explore new microprocessor architectures to take advantage of arithmetic. The experiments executed have shown that the algorithm provides faster and better enhancements from those described in the literature. The FPGA chips used is Spartan 3E from Xilinix. The critical length in the circuit implemented on the FPGA had the minimum period for the proposed subsystem is 10.209ns (maximum frequency 97.957MHz). Maximum power consumed is 2.4mW using 32nm process and we used parallelism and reuse of the Hardware components to accomplish and speed up the process. [Copyright &y& Elsevier]

Abstract: The problem of identifying the topology implied by wireframe drawings of polyhedral objects requires the identification of face loops, loops of edges which correspond to a face in the object the drawing portrays. In this paper, we survey the advantages and limitations of known approaches, and present and discuss test results which illustrate the successes and failures of a currently popular approach based on Dijkstra’s Algorithm. We conclude that the root cause of many failure cases is that the underlying algorithm assumes that the cost of traversing an edge is fixed. We propose a new polynomial-order algorithm for finding faces in wireframes. This algorithm could be adapted to any graph-theoretical least-cost circuit problem where the cost of traversing an edge is not fixed but context-dependent. [Copyright &y& Elsevier]

Abstract: Drainage networks determination from digital elevation models (DEM) has been a widely studied problem in the last three decades. During this time, satellite technology has been improving and optimizing digitalized images, and computers have been increasing their capabilities to manage such a huge quantity of information. The rapid growth of CPU power and memory size has concentrated the discussion of DEM algorithms on the accuracy of their results more than their running times. However, obtaining improved running times remains crucial when DEM dimensions and their resolutions increase. Parallel computation provides an opportunity to reduce run times. Recently developed graphics processing units (GPUs) are computationally fast not only in Computer Graphics but in General Purpose Computation, the so-called GPGPU. In this paper we explore the parallel characteristics of these GPUs for drainage network determination, using the C-oriented language of CUDA developed by NVIDIA. The results are simple algorithms that run on low-cost technology with a high performance response, obtaining CPU improvements of up to . [Copyright &y& Elsevier]

Abstract: This paper presents a new algorithm to extract a color graph from a real image so that it can be efficiently represented in a compact way. The proposal presents two main novelties. First, a new PCA-based color feature vector has been defined. This vector is resistant against illumination changes, noise and microtextures. Second, the image is segmented by means of a fast, hierarchical split and merge algorithm based on a pyramid structure that implicitly provides a color graph. In order to test the suitability of the proposed representation technique, simple localization experiments have been conducted in different real environments. [Copyright &y& Elsevier]

Abstract: This paper reviews the research status of pulse-coupled neural networks (PCNN) in the past decade. Considering there are too many publications about the PCNN, we summarize main approaches and point out interesting parts of the PCNN researches rather than contemplate to go into details of particular algorithms or describe results of comparative experiments. First, the current status of the PCNN and some modified models are briefly introduced. Second, we review the PCNN applications in the field of image processing (e.g. image segmentation, image enhancement, image fusion, object and edge detection, pattern recognition, etc.), then applications in other fields also are mentioned. Subsequently, some existing problems are summarized, while we give some suggestions for the solutions to some puzzles. Finally, the trend of the PCNN is pointed out. [Copyright &y& Elsevier]

Abstract: Polycube map is a global cross-surface parameterization technique, where the polycube shape can roughly approximate the geometry of modeled objects while retaining the same topology. The large variation of shape geometry and its complex topological type in real-world applications make it difficult to effectively construct a high-quality polycube that can serve as a good global parametric domain for a given object. In practice, existing polycube map construction algorithms typically require a large amount of user interaction for either pre-constructing the polycubes with great care or interactively specifying the geometric constraints to arrive at the user-satisfied maps. Hence, it is tedious and labor intensive to construct polycube maps for surfaces of complicated geometry and topology. This paper aims to develop an effective method to construct polycube maps for surfaces with complicated topology and geometry. Using our method, users can simply specify how close the target polycube mimics a given shape in a quantitative way. Our algorithm can both construct a similar polycube of high geometric fidelity and compute a high-quality polycube map in an automatic fashion. In addition, our method is theoretically guaranteed to output a one-to-one map. To demonstrate the efficacy of our method, we apply the automatically-constructed polycube maps in a number of computer graphics applications, such as seamless texture tiling, T-spline construction, and quadrilateral mesh generation. [Copyright &y& Elsevier]

Abstract: This paper presents an algorithm for approximating arbitrary polygonal meshes with subdivision surfaces, with the objective of preserving the relevant features of the object while searching the coarsest possible control mesh. The main idea is to firstly extract the feature lines of the object, and secondly construct the subdivision surface over this network. Control points are created by approximating these lines while the connectivity is built with respect to the anisotropy of the object. Our algorithm reinforces the similarity between the subdivision surface and the original shape by affecting an integer sharpness degree to each control edge in order to accurately reproduce the different curvature radii of corresponding fillets and blends. [Copyright &y& Elsevier]

Abstract: In this paper, we propose a novel method that represents the highly complex point sets by clustering and reconstructing the points to normal-mapped B-spline surfaces (NBSs). The main idea is to construct elaborate normal maps on simple surfaces for the realistic rendering of complex point-set models. Based on this observation, we developed the coarse, NBSs to approximate the original point datasets with fine surface details. In our algorithm, a genetic clustering algorithm is proposed to automatically segment the point samples into several clusters according to their statistical properties, and a network of B-spline patches with normal maps are constructed according to the clustering results. In respect to signal processing, our algorithm decouples the original data into two collections: coarse geometry information and fine surface details. The multi-level B-spline surfaces are employed to describe the coarse geometry information, and the normal maps are constructed to capture the fine surface details. Our experimental results show that this representation facilitates the modeling and rendering of complex point sets without losing the visual qualities. [Copyright &y& Elsevier]

Abstract: This paper presents a new interpretation of a digital circle in terms of the distribution of square numbers in discrete intervals. The number-theoretic analysis that leads to many important properties of a digital circle succinctly captures the original perspectives of digital calculus and digital geometry for its visualization and characterization. To demonstrate the capability and efficacy of the proposed method, two simple algorithms for the construction of digital circles, based on simple number-theoretic concepts, have been reported. Both the algorithms require only a few primitive operations and are completely devoid of any floating-point computation. To speed up the computation, especially for circular arcs of high radii, a hybridized version of these two algorithms has been given. Experimental results have been furnished to elucidate the analytical power and algorithmic efficiency of the proposed approach. It has been also shown, how and why, for sufficiently high radius, the number-theoretic technique can expedite a circle construction algorithm. [Copyright &y& Elsevier]

Abstract: The traditional closest point criterion has been widely used for 3D free form shape matching, object recognition, internet search, computer graphics and medical imaging. However, the rationale of this criterion has not yet been well understood and exploited. In this paper, we apply vector operations and the triangle inequality to carefully analyse this criterion and reveal that this criterion can guarantee that the found point matches satisfy the orientation, rigidity and matching error constraints and thus, are of high relative quality. Such properties not only shed light on and deepen our understanding of this criterion about its generality and practicality and improve our awareness about whether the established point matches are consistent with each other, but also provide us with a possibility to develop novel algorithms for the reliability evaluation of existing point matches and an efficient establishment of more accurate point matches. The experimental results based on real images show that the possible point matches established through extracting and matching spin images often violate these constraints and these constraints can often be successfully applied to reject (probably part of) the unlikely point matches for more accurate free form shape matching results. [Copyright &y& Elsevier]

Abstract: The winged- and half-edge data structures are commonly used representations for polyhedron models. Due to the complexity, students in an introductory course to computer graphics usually have difficulty in handling these data structures and developing applications. This paper describes the authors’ effort in the development of a visualization and animation tool for teaching and learning these data structures. This tool also includes a simple pseudo-code-like language for algorithm design. Instructors may employ this tool for presentation and demonstration purposes. Students may use the simple language to develop and experiment with new algorithms before their actual implementation. The visualization and animation system may be used to explore and understand the relationship among mesh elements and algorithm execution. [Copyright &y& Elsevier]

Abstract: The development of an automated bio-micromanipulation system provides high manipulation rates with optimal reproducibility and makes quantitative bio-micromanipulation possible. Visual-servo control is necessary for realizing automated bio-micromanipulation and increasing accuracy of micromanipulator. We have developed a dual-hand bio-micromanipulation system with micro-visual-servo control to realize automated cell manipulation targeting on the biotechnology application. This paper overviews this development, including the discussion of (1) the framework and a prototype of the automated bio-micromanipulation system, (2) the design and control of the micromanipulators, (3) the micro-visual-servo architecture, modeling of image Jacobian and recognition algorithms of micro-objects, and (4) the experiment to validate various concepts proposed. A compliant mechanism with three degrees of freedom driven by PZT actuators is designed and implemented to realize the fine motion of the micro-injection with nanometer resolution. The design and control issues about the micromanipulators are discussed in detail. Different image processing algorithms are designed for the recognition of the cell and the end-effectors of the micromanipulators in the micro-visual-servo control system. The experimental results of micro-circle trajectory tracking and automatic transgenic operations demonstrate the effectiveness of the micro-visual-servo solution for the automated bio-micromanipulation system. [Copyright &y& Elsevier]

The Pythagorean tree is a fractal figure with a branching structure based upon the Pythagorean theorem. This paper describes the use of a greedy algorithm to encourage a homogenous spread of detail for asymmetrical trees and avoid localized regions of high detail. A model of prioritized branch growth based on this idea is used to optimize tree shape, allowing more visually interesting trees to be grown using significantly fewer segments. A comparison of the fractal dimension of the resulting shapes supports the general success of this approach. [Copyright &y& Elsevier]

The paper presents a new algorithm for point-in-polygon queries. By decomposing a polygon into a set of convex polygons and then constructing a BSP tree, the algorithm performs an inclusion query against the polygon in two steps. In the first step, it finds the convex polygon that is most likely to contain the query point through the BSP tree, and then in the second step, it tests whether the query point is in the convex polygon by employing advanced techniques for point-in-convex-polygon queries. The new algorithm is immune of singularity and has a performance of conducting a query by time demand in O(log n), and storage requirement in O(n). The time complexity of the preprocessing is O(n log n) for convex decomposition and BSP tree construction. The new algorithm has its performance in various aspects comparable to the state-of-art algorithms based on trapezoidation. Furthermore, as the number of convex polygons is always much fewer than the number of trapezoids in partitioning a polygon, and a high-quality search tree can always be constructed to manage the convex polygons, the new algorithm can run much faster than the trapezoidation-based algorithms, up to over double folds in maximum. [Copyright &y& Elsevier]