Efficient and Adaptive Rendering of 2-D Continuous Scatterplots

We extend the rendering technique for continuous scatterplots to allow for a broad class of interpolation methods within the spatial grid instead of only linear interpolation. To do this, we propose an approach that projects the image of a cell from the spatial domain to the scatterplot domain. We approximate this image using either the convex hull or an axis-aligned rectangle that forms a tight fit of the projected points. In both cases, the approach relies on subdivision in the spatial domain to control the approximation error introduced in the scatterplot domain. Acceleration of this algorithm in homogeneous regions of the spatial domain is achieved using an octree hierarchy. The algorithm is scalable and adaptive since it allows us to balance computation time and scatterplot quality. We evaluate and discuss the results with respect to accuracy and computational speed. Our methods are applied to examples of 2-D transfer function design.     

Illuminated 3D Scatterplots

In contrast to 2D scatterplots, the existing 3D variants have the advantage of showing one additional data dimension, but suffer from inadequate spatial and shape perception and therefore are not well suited to display structures of the underlying data. We improve shape perception by applying a new illumination technique to the pointcloud representation of 3D scatterplots. Points are classified as locally linear, planar, and volumetric structures—according to the eigenvalues of the inverse distance-weighted covariance matrix at each data element. Based on this classification, different lighting models are applied: codimension-2 illumination, surface illumination, and emissive volumetric illumination. Our technique lends itself to efficient GPU point rendering and can be combined with existing methods like semi-transparent rendering, halos, and depth or attribute based color coding. The user can interactively navigate in the dataset and manipulate the classification and other visualization parameters. We demonstrate our visualization technique by showing examples of multi-dimensional data and of generic pointcloud data.     

The generalized unified computation of multidimensional discrete orthogonal transforms

By introducing a form of reorder for multidimensional data, we propose a unified fast algo-rithm that jointly employs one-dimensional W transform and multidimensional discrete polynomial trans-form to compute eleven types of multidimensional discrete orthogonal transforms, which contain three types of m-dimensional discrete cosine transforms ( m-D DCTs) ,four types of m-dimensional discrete W transforms ( m-D DWTs) ( m-dimensional Hartley transform as a special case), and four types of generalized discrete Fourier transforms ( m-D GDFTs). For real input, the number of multiplications for all eleven types of the m-D discrete orthogonal transforms needed by the proposed algorithm are only 1/m times that of the commonly used corresponding row-column methods, and for complex input, it is further reduced to 1/(2m) times. The number of additions required is also reduced considerably. Furthermore, the proposed algorithm has a simple computational structure and is also easy to be im-plemented on computer, and th     

Interactive scientific visualization of fluid flow

Examples of scientific visualization techniques used for the interactive exploration of very large data sets from supercomputer simulations of fluid flow are presented. Interactive rendering of images from simulations of grids of 2 million or more computational zones are required to drive high-end graphics workstations to their limits with 2-D data. The author presents one such image and discusses interactive steering of 2-D flow simulations, a phenomenon now possible with grids of half a million computational zones. He uses a simulation of compressible turbulence on a grid of 134 million computational zones to set the scale for discussing interactive 3-D visualization techniques. A concept for a gigapixel-per-second video wall, or gigawall, which could be built with present technology to meet the demands of interactive visualization of the data sets that will be produced by the next generation of supercomputers, is discussed     

Fast, memory-efficient cell location in unstructured grids for visualization

Applying certain visualization techniques to datasets described on unstructured grids requires the interpolation of variables of interest at arbitrary locations within the dataset's domain of definition. Typical solutions to the problem of finding the grid element enclosing a given interpolation point make use of a variety of spatial subdivision schemes. However, existing solutions are memory- intensive, do not scale well to large grids, or do not work reliably on grids describing complex geometries. In this paper, we propose a data structure and associated construction algorithm for fast cell location in unstructured grids, and apply it to the interpolation problem. Based on the concept of bounding interval hierarchies, the proposed approach is memory-efficient, fast and numerically robust. We examine the performance characteristics of the proposed approach and compare it to existing approaches using a number of benchmark problems related to vector field visualization. Furthermore, we demonstrate that our approach can successfully accommodate large datasets, and discuss application to visualization on both CPUs and GPUs.     

Practical internal stability of n-D discrete systems

This paper deals with the problem of asymptotic stability for n-D discrete systems in the practical sense that the system input and output signals are unbounded in, at most, one dimension. A definition of practical internal stability is introduced, and necessary and sufficient conditions are derived. The obtained results show that practical internal stability is less restrictive and more relevant for practical applications than the conventional two-dimensional (2-D) internal stability     

Diffusion tensor visualization with glyph packing

A common goal of multivariate visualization is to enable data inspection at discrete points, while also illustrating larger-scale continuous structures. In diffusion tensor visualization, glyphs are typically used to meet the first goal, and methods such as texture synthesis or fiber tractography can address the second. We adapt particle systems originally developed for surface modeling and anisotropic mesh generation to enhance the utility of glyph-based tensor visualizations. By carefully distributing glyphs throughout the field (either on a slice, or in the volume) into a dense packing, using potential energy profiles shaped by the local tensor value, we remove undue visual emphasis of the regular sampling grid of the data, and the underlying continuous features become more apparent. The method is demonstrated on a DT-MRI scan of a patient with a brain tumor.     

Overset grid technology development at NASA Ames Research Center

The idea of overset grids arose from the need to model complex multi-component systems where an optimum body-fitted grid is used for each component. One of the main motivations behind the overset grid development work at NASA originated from the requirement to perform simulations involving multiple bodies in relative motion. This article traces the development of overset grid technologies at NASA Ames Research Center, including: data format and visualization software; and algorithms and software tools for surface grid generation, volume grid generation, domain connectivity, forces and moments calculation, and flow solution computation. Examples of the use of overset grids for NASA aerospace applications are given, and current and future work to improve overset grid technologies are summarized.     

General model of n-D system with variable coefficients and its reduction to 1-D system with variable structure

A general model of an n-D linear discrete system with variable coefficients and its solution are presented. A method for reduction of this model to an equivalent 1-D system with a variable structure is given.     

A 2-D wavelet decomposition-based bag-of-visual-words model for land-use scene classification

Previous works about spatial information incorporation into a traditional bag-of-visual-words (BOVW) model mainly consider the spatial arrangement of an image, ignoring the rich textural information in land-use remote-sensing images. Hence, this article presents a 2-D wavelet decomposition (WD)-based BOVW model for land-use scene classification, since the 2-D wavelet decomposition method does well not only in textural feature extraction, but also in the multi-resolution representation of an image, which is favourable for the use of both spatial arrangement and textural information in land-use images. The proposed method exploits the textural structures of an image with colour information transformed into greyscale. Moreover, it works first by decomposing the greyscale image into different sub-images using 2-D discrete wavelet transform (DWT) and then by extracting local features of the greyscale image and all the decomposed images with dense regions in which a given image is evenly sampled by a regular grid with a specified grid space. After that, the method generates the corresponding visual vocabularies and computes histograms of visual word occurrences of local features found in each former image. Specifically, the soft-assignment or multi-assignment (MA) technique is employed, accounting for the impact of clustering on visual vocabulary creation that two similar image patches may be clustered into different clusters when increasing the size of visual vocabulary. The proposed method is evaluated on a ground truth image dataset of 21 land-use classes manually extracted from high-resolution remote-sensing images. Experimental results demonstrate that the proposed method significantly outperforms previous methods, such as the traditional BOVW model, the spatial pyramid representation-based BOVW method, the multi-resolution representation-based BOVW method, and so on, and even exceeds the best result obtained from the creator of the land-use dataset. Therefore, the proposed approach is very suitable for land-use scene classification tasks.     

Interactive Visualization of Flood and Heavy Rain Simulations

In this paper, we present a real‐time technique to visualize large‐scale adaptive height fields with C ‐continuous surface reconstruction. Grid‐based shallow water simulation is an indispensable tool for interactive flood management applications. Height fields defined on adaptive grids are often the only viable option to store and process the massive simulation data. Their visualization requires the reconstruction of a continuous surface from the spatially discrete simulation data. For regular grids, fast linear and cubic interpolation are commonly used for surface reconstruction. For adaptive grids, however, there exists no higher‐order interpolation technique fast enough for interactive applications. Our proposed technique bridges the gap between fast linear and expensive higher‐order interpolation for adaptive surface reconstruction. During reconstruction, no matter if regular or adaptive, discretization and interpolation artifacts can occur, which domain experts consider misleading and unaesthetic. We take into account boundary conditions to eliminate these artifacts, which include water climbing uphill, diving towards walls, and leaking through thin objects. We apply realistic water shading with visual cues for depth perception and add waves and foam synthesized from the simulation data to emphasize flow directions. The versatility and performance of our technique are demonstrated in various real‐world scenarios. A survey conducted with domain experts of different backgrounds and concerned citizens proves the usefulness and effectiveness of our technique.     

二元超声速进气道数值仿真建模过程自动化

研究高速巡航导弹动力装置优化问题,针对进气道结构严重影响速度的提高,为减少人工建模的工作量,以提高数值仿真分析工作效率和满足二元超声速进气道设计方案的快速评比和选型的需要,提出建立流场计算域通用的结构化分区几何模型,统一基于所构造的基准进气道模型,一次性人工划分进气道结构化计算网格,根据边界几何控制,运用网格映射和比例变换方法,编程自动化实现由基准进气道计算网格映射生成实际结构不同的系列化二元进气道计算网格。用建立的模型进行仿真。结果证明,减少了建模工作量和提高了工作效率。     

Visual Analysis of Trajectories in Multi‐Dimensional State Spaces

Multi‐dimensional data originate from many different sources and are relevant for many applications. One specific sub‐type of such data is continuous trajectory data in multi‐dimensional state spaces of complex systems. We adapt the concept of spatially continuous scatterplots and spatially continuous parallel coordinate plots to such trajectory data, leading to continuous‐time scatterplots and continuous‐time parallel coordinates. Together with a temporal heat map representation, we design coordinated views for visual analysis and interactive exploration. We demonstrate the usefulness of our visualization approach for three case studies that cover examples of complex dynamic systems: cyber‐physical systems consisting of heterogeneous sensors and actuators networks (the collection of time‐dependent sensor network data of an exemplary smart home environment), the dynamics of robot arm movement and motion characteristics of humanoids.     

基于Zipf分布的网格密度峰值聚类算法

网格密度峰值聚类在兼顾密度峰值聚类算法可识别任意形状类簇的基础上,通过数据集的网格化简化整体计算量,成为当前备受关注的聚类方法.针对大规模数据,如何进一步区分稠密与稀疏网格,减少网格密度峰值聚类中参与计算的非空网格代表点的数量是解决“网格灾难”的关键.结合以网格密度为变量的概率密度分布呈现出类Zipf分布的特点,提出一种基于Zipf分布的网格密度峰值聚类算法.首先计算所有非空网格的密度并映射为Zipf分布,根据对应的Zipf分布筛选出稠密中心网格和稀疏边缘网格;然后仅对稠密中心网格进行密度峰值聚类,在自适应确定潜在聚类中心的同时减少欧氏距离的计算量,降低算法复杂度;最后通过对稀疏边缘网格的处理,进一步优化类簇边界并提高聚类精度.人工数据集和UCI数据集下的实验结果表明,所提出算法对大规模、类簇交叉数据的聚类具有明显优势,能够在保证聚类精度的同时降低时间复杂度.     

Fuzzy region connection calculus in finite discrete space domains

Many practical applications involving spatial aspects work with finite discrete space domains, e.g. map grids, railways track layouts and road networks. Such space domains are computationally tractable and often include specialised forms of spatial reasoning. Moreover, in such applications, the spatial information naturally includes various forms of approximation, uncertainty or inexactness. Fuzzy representations are then appropriate. In this paper, we reformulate the region connection calculus (RCC) framework for finite, discrete space domains in simple set-theoretical terms. We generalise RCC framework and develop several fuzzy spatial concepts like fuzzy regions, fuzzy directions, fuzzy named distances. We propose a fuzzification of standard spatial relations in RCC. For this purpose, we enhance the fuzzy set theory to include fuzzy definitions for membership, subset and set equality crisp binary relations between sets (fuzzy or crisp). We illustrate the approach using a discrete finite two-dimensional map grid as the space domain.     

Normalization of discrete planar objects

The case is made for normalization of discrete planar objects prior to comparison with test objects and an expression for normalization is derived using a Euclidean distance function based on the underlying continuous boundaries of the objects and their prototypes. The results are given in both the spatial and the frequency domain; an analysis of errors due to the quantization introduced by using a discrete grid is also given.     

Adaptive projection operators in multiresolution scientificvisualization

Recently multiresolution visualization methods have become an indispensable ingredient of real time interactive postprocessing. The enormous databases, typically coming along with some hierarchical structure, are locally resolved on different levels of detail to achieve a significant savings of CPU and rendering time. The method of adaptive projection and the corresponding operators on data functions, respectively are introduced. They are defined and discussed as mathematically rigorous foundations for multiresolution data analysis. Keeping in mind data from efficient numerical multigrid methods, this approach applies to hierarchical nested grids consisting of elements which are any tensor product of simplices, generated recursively by an arbitrary, finite set of refinement rules from some coarse grid. The corresponding visualization algorithms, e.g., color shading on slices or isosurface rendering, are confined to an appropriate depth first traversal of the grid hierarchy. A continuous projection of the data onto an adaptive, extracted subgrid is thereby calculated recursively. The presented concept covers different methods of local error measurement, time dependent data which have to be interpolated from a sequence of key frames, and a tool for local data focusing. Furthermore, it allows for a continuous level of detail     

Adaptive projection operators in multiresolution scientificvisualization

Recently, multiresolution visualization methods have become an indispensable ingredient of real-time interactive postprocessing. The enormous databases, typically coming along with some hierarchical structure, are locally resolved on different levels of detail to achieve a significant savings of CPU and rendering time. In this paper, the method of adaptive projection and the corresponding operators on data functions, respectively, are introduced. They are defined and discussed as mathematically rigorous foundations for multiresolution data analysis. Keeping in mind data from efficient numerical multigrid methods, this approach applies to hierarchical nested grids consisting of elements which are any tensor product of simplices, generated recursively by an arbitrary, finite set of refinement rules from some coarse grid. The corresponding visualization algorithms, e.g. color shading on slices or isosurface rendering, are confined to an appropriate depth-first traversal of the grid hierarchy. A continuous projection of the data onto an adaptive, extracted subgrid is thereby calculated recursively. The presented concept covers different methods of local error measurement, time-dependent data which have to be interpolated from a sequence of key frames, and a tool for local data focusing. Furthermore, it allows for a continuous level of detail     

DLSLA 3-D SAR imaging algorithm for off-grid targets based on pseudo-polar formatting and atomic norm minimization基于伪极坐标变换和原子范数最小化的网格偏离目标DLSLA 3-D SAR成像方法

This paper concerns the imaging problem for downward looking sparse linear array three-dimensional synthetic aperture radar (DLSLA 3-D SAR) under the circumstance of sparse and non-uniform cross-track dimensional virtual phase centers configuration. Since the 3-D imaging scene behaves typical sparsity in a certain domain, sparse recovery approaches hold the potential to achieve a better reconstruction performance. However, most of the existing compressive sensing (CS) algorithms assume the scatterers located on the pre-discretized grids, which is often violated by the off-grid effect. By contrast, atomic norm minimization (ANM) deals with sparse recovery problem directly on continuous space instead of discrete grids. This paper firstly analyzes the off-grid effect in DLSLA 3-D SAR sparse image reconstruction, and then introduces an imaging method applied to off-gird targets reconstruction which combines 3-D pseudo-polar formatting algorithm (pseudo-PFA) with ANM. With the proposed method, wave propagation and along-track image reconstruction are operated with pseudo-PFA, then the cross-track reconstruction is implemented with semidefinite programming (SDP) based on the ANM model. The proposed method holds the advantage of avoiding the off-grid effect and managing to locate the off-grid targets to accurate locations in different imaging scenes. The performance of the proposed method is verified and evaluated by the 3-D image reconstruction of different scenes, i.e., point targets and distributed scene.