Research issues in volume visualization

Volume visualization is a method of extracting meaningful information from volumetric data sets through the use of interactive graphics and imaging. It addresses the representation, manipulation, and rendering of volumetric data sets, providing mechanisms for peering into structures and understanding their complexity and dynamics. Typically, the data set is represented as a 3D regular grid of volume elements (voxels) and stored in a volume buffer (also called a cubic frame buffer), which is a large 3D array of voxels. However, data is often defined at scattered or irregular locations that require using alternative representations and rendering algorithms. There are eight major research issues in volume visualization: volume graphics, volume rendering, transform coding of volume data, scattered data, enriching volumes with knowledge, segmentation, real-time rendering and parallelism, and special purpose hardware     

Image reconstruction from scattered Radon data by weighted positive definite kernel functions

We propose a novel kernel-based method for image reconstruction from scattered Radon data. To this end, we employ generalized Hermite–Birkhoff interpolation by positive definite kernel functions. For radial kernels, however, a straightforward application of the generalized Hermite–Birkhoff interpolation method fails to work, as we prove in this paper. To obtain a well-posed reconstruction scheme for scattered Radon data, we introduce a new class of weighted positive definite kernels, which are symmetric but not radially symmetric. By our construction, the resulting weighted kernels are combinations of radial positive definite kernels and positive weight functions. This yields very flexible image reconstruction methods, which work for arbitrary distributions of Radon lines. We develop suitable representations for the weighted basis functions and the symmetric positive definite kernel matrices that are resulting from the proposed reconstruction scheme. For the relevant special case, where Gaussian radial kernels are combined with Gaussian weights, explicit formulae for the weighted Gaussian basis functions and the kernel matrices are given. Supporting numerical examples are finally presented.     

Hardware-assisted feature analysis and visualization of procedurally encoded multifield volumetric data

We take a new approach to interactive visualization and feature detection of large scalar, vector, and multifield computational fluid dynamics data sets that is also well suited for meshless CFD methods. Radial basis functions (RBFs) are used to procedurally encode both scattered and irregular gridded scalar data sets. The RBF encoding creates a complete, unified, functional representation of the scalar field throughout 3D space, independent of the underlying data topology, and eliminates the need for the original data grid during visualization. The capability of commodity PC graphics hardware to accelerate the reconstruction and rendering and to perform feature detection from this functional representation is a powerful tool for visualizing procedurally encoded volumes. Our RBF encoding and GPU-accelerated reconstruction, feature detection, and visualization tool provides a flexible system for visually exploring and analyzing large, structured, scattered, and unstructured scalar, vector, and multifield data sets at interactive rates on desktop PCs.     

Using Marching Cubes on Small Machines

A simple technique to visualize the isosurfaces extracted from a cell-based volumetric dataset using the Marching Cubes algorithm is proposed. The technique exploits the intrinsic ordering of the triangles produced by the surface extraction algorithm by adopting a Back-to-Front visualization technique. The use of the technique together with the adoption of a simple shading algorithm permits the rendering of high resolution volumetric datasets in computational environments with limited capabilities in terms of memory and graphics hardware.     

基于动态纹理载入的大规模数据场体绘制

为克服图形硬件对传统纹理映射体绘制的限制,提出了一种在普通PC上进行大规模数据场体绘制的有效方法。该方法中,体数据被划分为合适大小的数据块,这些数据块被动态的载入图形硬件,并利用3维纹理映射进行绘制。在整个绘制过程中,仅有一个数据块存储在图形硬件上,有效地提高了对大规模体数据的绘制能力。同时,充分利用目前PC图形硬件成熟的可编程特性,通过对梯度的实时计算来减少在传统纹理映射体绘制中巨大的内存消耗。实验结果表明,该方法在普通PC上可以对超过纹理内存容量的大规模体数据进行交互式体绘制。     

Refraction in volume graphics

Modeling and rendering transparent and translucent objects is one of the most important features of volume graphics. Refraction is a phenomenon closely coupled with such objects, but has largely been overlooked in volume graphics and visualization. There are two main technical difficulties. First, it is expensive to model heterogeneous refractive properties, and to incorporate refractive effects into volume rendering engines that assume light travels only along a straight line. Second, rendering refraction in volume graphics requires smoothly distributed normals to synthesize good-quality visual representations. Such refractive visualization is more susceptible to noise in the data than visualizations that do not involve refraction. In this paper, we present a comprehensive study of modeling and rendering refraction in volume graphics. In particular, we address the need for improving the continuity of voxel gradients in discretely sampled volume datasets using nonlinear diffusion methods, which were originally developed for image denoising. We consider the need for minimizing unnecessary geometrical distortion, detail the functional specification of a volumetric filter for regularized anisotropic nonlinear diffusion (R-ANLD), discuss further improvements of the filter, and compare the efficacy of the filter with an anisotropic nonlinear diffusion (ANLD) filter as well as a Gaussian filter and a linear diffusion filter. Our results indicate that it is possible to make significant improvements in image quality in refractive rendering without excessive distortion. To demonstrate the practical feasibility of modeling and rendering refraction in volume graphics, we describe the implementation of refractive rendering through vlib, a volume graphics API, and discuss the parallelization of vlib in order to meet the increased demands of computational resources imposed by refractive volume rendering.     

Efficient visibility encoding for dynamic illumination in direct volume rendering

We present an algorithm that enables real-time dynamic shading in direct volume rendering using general lighting, including directional lights, point lights, and environment maps. Real-time performance is achieved by encoding local and global volumetric visibility using spherical harmonic (SH) basis functions stored in an efficient multiresolution grid over the extent of the volume. Our method enables high-frequency shadows in the spatial domain, but is limited to a low-frequency approximation of visibility and illumination in the angular domain. In a first pass, level of detail (LOD) selection in the grid is based on the current transfer function setting. This enables rapid online computation and SH projection of the local spherical distribution of visibility information. Using a piecewise integration of the SH coefficients over the local regions, the global visibility within the volume is then computed. By representing the light sources using their SH projections, the integral over lighting, visibility, and isotropic phase functions can be efficiently computed during rendering. The utility of our method is demonstrated in several examples showing the generality and interactive performance of the approach.     

Real-time visualization of large volume datasets on standard PC hardware

In medical area, interactive three-dimensional volume visualization of large volume datasets is a challenging task. One of the major challenges in graphics processing unit (GPU)-based volume rendering algorithms is the limited size of texture memory imposed by current GPU architecture. We attempt to overcome this limitation by rendering only visible parts of large CT datasets. In this paper, we present an efficient, high-quality volume rendering algorithm using GPUs for rendering large CT datasets at interactive frame rates on standard PC hardware. We subdivide the volume dataset into uniform sized blocks and take advantage of combinations of early ray termination, empty-space skipping and visibility culling to accelerate the whole rendering process and render visible parts of volume data. We have implemented our volume rendering algorithm for a large volume data of 512 x 304 x 1878 dimensions (visible female), and achieved real-time performance (i.e., 3-4 frames per second) on a Pentium 4 2.4GHz PC equipped with NVIDIA Geforce 6600 graphics card ( 256 MB video memory). This method can be used as a 3D visualization tool of large CT datasets for doctors or radiologists.     

Atomistic visualization: Space–time multiresolution integration of data analysis and rendering

Time-varying three-dimensional scattered data representing snapshots of atomic configurations produced by molecular dynamics simulations are not illuminating by themselves; gaining insight into them poses a tremendous challenge. In order to take the advantage of maximal information offered by these simulations, we have proposed an efficient scheme, which integrates various analysis and rendering tasks together in order to support interactive visualization of the data at space–time multiresolution. Additional data produced by various analytical techniques on the fly represent the atomic system under consideration at diverse length- (e.g., nearest neighbor, next-nearest neighbor or beyond) and time- (e.g., instantaneous, finite intervals or overall averages) scales. In particular, the radial distribution functions, coordination environments, clusters and rings are computed and visualized to understand the structural behavior whereas a variety of displacement data and covariance matrices are explored to understand the dynamical behavior. While the spatial distributions of atoms need to be reproduced correctly during rendering, we take the advantage of high flexibility in rendering other attributes because of the lack of their direct physical relevance. A combination of different techniques including animation, color maps, pathlines, different types of glyphs, and graphics hardware accelerated approach is exploited to render the original and extracted data. First-principles molecular dynamics simulation data for liquid systems are used to justify the effectiveness and usefulness of the proposed scheme.     

Interactive exploration of tensor fields in geosciences using volume rendering

Volume rendering methods enable the user to explore interactively scalar data on regularly spaced three-dimensional grids. This article discusses how to use this method to explore and analyse three-dimensional tensor fields. The proposed visualization makes use of the programmability of modern graphics hardware and of “Line Integral Convolution”, a texture-based technique for the visualization of vector fields. While an example from geomechanics is used for presentation purposes, the rendering methods introduced are generic and would suit other application areas that involve volumetric data with several attributes equally well.     

基于PC硬件的大规模数据场快速可视化方法

科学可视化技术在众多领域具有十分广泛的应用,然而直接体绘制技术却有着计算量大、计算时间长的缺点,在普通的PC机上很难实现对大规模数据的实时交互绘制。目前的三维可视化系统通常需要架构在高端的图形工作站或转用计算机上。随着计算机软硬件技术的发展,普通的PC机图形处理器GPU(Graphic Processing Unit)具有了可编程功能。正是借助GPU的可编程功能及其强大的并行处理能力,研究并实现了一种基于普通PC硬件的体会之方法。最后应用该方法对工业、医学等体数据进行可视化,结果证明该方法可以在普通PC上实现较大规模数据的快速可视化。     

Incremental Volume Rendering Using Hierarchical Compression

We present a new algorithm here for efficient incremental rendering of volumetric datasets. The primary goal of this algorithm is to give average workstations the ability to efficiently render volume data received over relatively low bandwidth network links in such a way that rapid user feedback is maintained. Common limitations of workstation rendering of volume data include: large memory overheads, the requirement of expensive rendering hardware, and high speed processing ability. The rendering algorithm presented here overcomes these problems by making use of the efficient Shear-Warp Factorisation method which does not require specialised graphics hardware. However the original Shear-Warp algorithm suffers from a high memory overhead and does not provide for incremental rendering which is required should rapid user feedback be maintained. Our algorithm represents the volumetric data using a hierarchical data structure which provides for the incremental classification and rendering of volume data. This exploits the multiscale nature of the octree data structure. The algorithm reduces the memory footprint of the original Shear-Warp Factorisation algorithm by a factor of more than two, while maintaining good rendering performance. These factors make our octree algorithm more suitable for implementation on average desktop workstations for the purposes of interactive exploration of volume models over a network. Results from tests using typical volume datasets will be presented which demonstrate the ability of the algorithm to achieve high rendering rates for both incremental rendering and standard rendering while reducing the runtime memory requirements.     

Time-varying data visualization using functional representations

In many scientific simulations, the temporal variation and analysis of features are important. Visualization and visual analysis of time series data is still a significant challenge because of the large volume of data. Irregular and scattered time series data sets are even more problematic to visualize interactively. Previous work proposed functional representation using basis functions as one solution for interactively visualizing scattered data by harnessing the power of modern PC graphics boards. In this paper, we use the functional representation approach for time-varying data sets and develop an efficient encoding technique utilizing temporal similarity between time steps. Our system utilizes a graduated approach of three methods with increasing time complexity based on the lack of similarity of the evolving data sets. Using this system, we are able to enhance the encoding performance for the time-varying data sets, reduce the data storage by saving only changed or additional basis functions over time, and interactively visualize the time-varying encoding results. Moreover, we present efficient rendering of the functional representations using binary space partitioning tree textures to increase the rendering performance.     

立体可视化——新兴的灵境技术

立体可视化是９０年出现的可视化及计算机图形学的一个重要领域。立体可视化质变计算机图形学带来了一场革命,并在其众多的应用领域中取得了突破性进展,不仅容易实现图形演示的虚拟真实性（灵境）,而且可以将视野深入至复杂物体的内部世界,文语文介绍立体可视化技术的原理,立体数据的生成,处理及演示。     

GPU加速的台风可视化方法

自然现象的可视化是计算机图形学和虚拟现实领域的重要研究内容。对传统光线投射算法分析的基础上进行改进,提出基于球壳体的光线投射算法。将GPU运用于球壳体数据场的体绘制,设计了基于球壳体数据场的顶点着色程序和像素着色程序。同时,对台风源数据格式进行解析,生成了用于台风可视化的体数据,采用提出的算法实现了台风云层和因子的可视化。实验结果表明,本文基于GPU的球壳体光线投射算法在球体表面较好地实现了实时台风可视化效果。     

Efficient reconstruction from non-uniform point sets

We propose a method for non-uniform reconstruction of 3D scalar data. Typically, radial basis functions, trigonometric polynomials or shift-invariant functions are used in the functional approximation of 3D data. We adopt a variational approach for the reconstruction and rendering of 3D data. The principle idea is based on data fitting via thin-plate splines. An approximation by B-splines offers more compact support for fast reconstruction. We adopt this method for large datasets by introducing a block-based reconstruction approach. This makes the method practical for large datasets. Our reconstruction will be smooth across blocks. We give reconstruction measurements as error estimations based on different parameter settings and also an insight on the computational effort. We show that the block size used in reconstruction has a negligible effect on the reconstruction error. Finally we show rendering results to emphasize the quality of this 3D reconstruction technique.     

Interactive Visualization with Programmable Graphics Hardware

One of the main scientific goals of visualization is the development of algorithms and appropriate data models which facilitate interactive visual analysis and direct manipulation of the increasingly large data sets which result from simulations running on massive parallel computer systems, from measurements employing fast high‐resolution sensors, or from large databases and hierarchical information spaces. This task can only be achieved with the optimization of all stages of the visualization pipeline: filtering, compression, and feature extraction of the raw data sets, adaptive visualization mappings which allow the users to choose between speed and accuracy, and exploiting new graphics hardware features for fast and high‐quality rendering. The recent introduction of advanced programmability in widely available graphics hardware has already led to impressive progress in the area of volume visualization. However, besides the acceleration of the final rendering, flexible graphics hardware is increasingly being used also for the mapping and filtering stages of the visualization pipeline, thus giving rise to new levels of interactivity in visualization applications. The talk will present recent results of applying programmable graphics hardware in various visualization algorithms covering volume data, flow data, terrains, NPR rendering, and distributed and remote applications.     

A comparison of the von Mises and Gaussian basis functions for approximating spherical acoustic scatter

This paper compares the approximation accuracy of two basis functions that share a common radial basis function (RBF) neural network architecture used for approximating a known function on the unit sphere. The basis function types considered are that of a new spherical basis function, the von Mises function, and the now well-known Gaussian basis function. Gradient descent learning rules were applied to optimize (learn) the solution for both approximating basis functions. A benchmark approximation problem was used to compare the performance of the two types of basis functions, in this case the mathematical expression for the scattering of an acoustic wave striking a rigid sphere.     

协同分布式图形硬件的混合并行体绘制

由于一般的共享存储并行机缺乏图形硬件,其上产生的3维科学计算数据,无法采用硬件加速的并行体绘制来就地进行数据可视化。为此基于本地并行机和分布式图形工作站,给出了一种混合并行绘制模型。该模型的工作原理是先将源数据存留在并行机,然后通过并行机的多处理器发布远程绘制命令流,进而通过操控工作站的图形硬件完成绘制;后期图像合成在并行机上执行,以发挥共享存储通信优势。通过负载平衡优化,并行绘制流水线有效实现了绘制、合成与显示的重叠。实验结果显示,该方法能以1024×1024图像分辨率,交互绘制并行机上的大规模数据场。