四面体体数据高效可视化技术研究
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摘要
体可视化能有效展示三维数据场中有意义的结构或信息,被广泛应用于三维医学影像分析、地质数据可视化和流体计算仿真等领域。常规的体数据结构可分为两类：规则数据和不规则数据。规则体数据常常用三维数组表示,在等间距的网格点处进行采样。这种数据虽然表示简单、操作容易,非常适合处理均匀的数据场。但是大部分物理模拟计算(如计算流体力学或偏微分方程求解)生成的三维数据场分布极不均匀,如果采用规则数据表示,将会产生精度问题和极大的存储冗余。因此这类不规则体数据采用多面体或其他不规则数据单元来表示,其中最常见的是四面体。三维数据场的不规则体表示提高了表示精度,降低了存储需求,同时也增加了在计算和绘制方面的代价。如何提高绘制效率,如何提高绘制结果的精度,是不规则数据体绘制的两个主要挑战。针对这两个问题,本文做了一系列的改进和提高,具体如下：
·规则数据的组织方式比较简单,利于并行,而且不需要求交计算,可以节省大量的计算代价。因此将不规则数据规则化是提高性能的最直接的解决方案。已有工作将基于四面体的体数据被转换为八叉树结构,使用基于纹理的方法完成绘制。但是当不规则数据比较精细的时候,就会造成八叉树的层次比较深,极大地增加数据存储和绘制查找时间。针对这个问题,本文提出了一种双结构化的解决方案。处理结果为使用GPU的两个纹理结构。这种结构即节省空间,又能充分地利用GPU,提高绘制的效率。
·规则化是一种精度有损的方法。因此本文的主要工作是关于直接可视化不规则体数据,代表性方法是投影法,而其中的效率瓶颈在于逐帧实施的四面体单元的排序操作。采用四面体重心深度值进行排序,将几何排序转换成浮点数排序,简单方便。目前这种排序都是采用一些已有的通用方法,而本文考虑到四面体数据在空间上的连贯性。预计算不同采样视点下,四面体集合在不同深度区间上的分布。绘制时保证四面体集合快速地划分到对应区间上独立排序,各区间负载均衡。实验证明,本文的方法极大地提高了重心排序的效率。
·重心排序的方法是不精确的,在有些情况下会产生顺序错误,从而导致错误的绘制结果。基于精确遮挡关系的排序可以解决这个问题,但对并行提出了极大的挑战。本文采用分层的方式实现并行化的目的,但在确定层次的顺序时依旧受到串行处理的困扰。物理切割可以打破层间的顺序性,本文将四面体数据组织到一个空间k-d树的结构中,将处于分割面上的四面体进行切割,每个节点内的四面体单独排序。极大地提高了排序的效率。但物理切割的计算代价比较大,预处理时间较长,数量上的增加也带来了存储和绘制方面的压力。本文进一步改善了该方法,提出一种逻辑切割的方式。即在逻辑上将数据划分到不同的深度区间,但不进行真正的切割,绘制时只是对相应区间范围内的部分进行积分。实验证明,这种方法在不增加存储压力情况下极大的提高了精确排序的效率。
·除了排序效率的问题,绘制结果质量的提高也是不规则数据体绘制的一个重要方面。当前的方法大都是假设数据在四面体内部是线性分布的,表达的精度有限。本文将数据采用7方向盒样条函数进行了重构,建立了高次连续的数据场。然后在数据场中提取二次四面体,采用有限元的方法绘制了基于二次插值函数的结果。实验结果显示,基于二次插值函数的绘制结果不仅绘制精度更高,而且能够强化特征、显示更多的模式、消除四面体之间的裂缝。极大地提高了绘制质量。
本文工作集中在不规则体数据的可视化。具体方法分为两大类,一是将不规则数据转换为规则数据再绘制；二是在不规则数据上直接进行体绘制。本文在第一类方法中主要提出一种双结构化的架构,保证存储容量和绘制精度的平衡。而在第二类方法中,基于四面体投影法,提出了一个完整的框架。在这个框架下,将排序过程和绘制过程分开。先利用体数据的空间连贯性改进了不精确排序的效率；然后分别用物理分割和逻辑分割两种方法降低了精确排序的时间。在绘制方面,将原有的线性分布的数据进行了重构,采用二次插值函数提高了绘制的精度。整个系统比较完善,既有绘制效率的提高,又有绘制质量的改善。对科学计算结果的特征识别和提取带来了极大地帮助。大量实验证明了本文方法的可靠性。
Volume visualization can represent the significant interior structure or information of data field in three dimensions. It has been implemented in medical image analysis, geological data vi-sualization, computational fluid dynamics simulation, and so on. General volume data structure can be divided into two categories:regular datasets and unstructured datasets. Regular datasets often has been constructed by an array in three dimensions, sampling on grid points which have same span with each other. Regular datasets can be shown simply and handled easily, being ap-propriate to uniform data field. But most physical simulations, for example computational fluid dynamics simulation or partial differential equations, generate data field which is nonuniform. Us-ing regular datasets will bring about accuracy problem and redundant storage. So unstructured datasets have been represented by polyhedron or other unstructured data elements, and tetrahedra has been used popularly. Unstructured volume representation of data field in three dimensions im-proves accuracy and reduces requirement in storage, but it also increases the cost in computation and rendering. How to improve the rendering efficiency and enhance the rendering accuracy, are two primary challenges in rendering unstructured datasets. This paper made a lot of improvements as following:
Regular datasets can reduce a lot of computation cost because its structure is simple and easy to handle in parallel. It also does not need intersection computation. Therefore, regu-larization is the most direct scheme to solve this problem. Some works transform tetrahedral datasets into octree structure and render it based on texture. If the unstructured datasets have higher accuracy, regularization will generate the octree with more layers which increase the time to store and find. We propose a dual-structure scheme to decompose the datasets in-to two components, which can be represented as two GPU-friendly textures. The new data structure is memory-efficient, GPU-friendly, and thus allows for effective GPU-based vol-ume visualization.
Regularization is a method with accuracy loss. The main work of this paper is still about rendering directly on unstructured datasets. Projection is a typical method. Its bottleneck of rendering is sorting. Sorting value of tetrahedral centroids transform geometry sorting into float value sorting, which is easy and convenient. Until now, this kind of sorting has been handled by general sorting method. But our method considers the spatial coherence of tetrahedral datasets. We pre-compute the distribution of tetrahedral datasets in different deep blocks under different views. Tetrahedral datasets have been divided into corresponding block quickly with load balancing. The efficiency of sorting centroids increases with our method.
Sorting centroids is not accurate. It will produce some rendering error because of wrong order. Sorting on exact occlusion relationship can solve this problem, but it is a great chal-lenge to parallel. We solve this problem by layering the datasets, but the order of the layers is still processed seriously. The order between layers can be broken by physical partition. The tetrahedral datasets have been organized into a spatial octree structure. The tetrahedra on the partition plane has been divided into small ones. The tetrahedra in different node has been sorted independently, that increases the sorting efficiency. The physical partition needs more calculation and the more tetrahedra after partition produces many difficulties in storage and rendering. We improves this method and proposes a scheme named logical partition, which divides the tetrahedral datasets into different deep block without real partition. Only corresponding area has been integrated when rendering. This method increases the efficiency without more storage requirement.
The quality of rendering unstructured datasets is another important challenge. Most of ren-dering systems on unstructured datasets suppose that the interpolation in one element is linear, whose accuracy is limited. This paper reconstructs datasets with7direction box s-pline and builds a data field with high-order continuity. Then quadratic tetrahedra has been extracted and rendered by finite element methods. The experiments show that rendering with quadratic interpolation can increase the accuracy of result image, enhance the features and reduce the crack between tetrahedra. The quality of result image has been improved a lot.
The contributions of this paper are on visualization of unstructured datasets. The content has been divided two categories:one is transforming unstructured datasets into regular datasets; the other is rendering directly on unstructured datasets. In the former part, this paper proposes a dual-structure scheme which can balance between storage and accuracy. In the later part, this paper proposes a complete frame based on tetrahedra projection. The sort and the rendering have been separated. The efficiency of sorting tetrahedral centroids has been improved by using spatial coherence. The time of accurate sorting has been reduced by physical partition and logical parti-tion. In rendering aspect, this paper reconstructs the linear data field and improves the accuracy by using quadratic interpolation. This frame is complete, improving both rendering efficiency and quality. It brings great help to identifying and extracting feature in scientific computation. A lot of experiments identify the reliability of our system.
·规则数据的组织方式比较简单,利于并行,而且不需要求交计算,可以节省大量的计算代价。因此将不规则数据规则化是提高性能的最直接的解决方案。已有工作将基于四面体的体数据被转换为八叉树结构,使用基于纹理的方法完成绘制。但是当不规则数据比较精细的时候,就会造成八叉树的层次比较深,极大地增加数据存储和绘制查找时间。针对这个问题,本文提出了一种双结构化的解决方案。处理结果为使用GPU的两个纹理结构。这种结构即节省空间,又能充分地利用GPU,提高绘制的效率。
·规则化是一种精度有损的方法。因此本文的主要工作是关于直接可视化不规则体数据,代表性方法是投影法,而其中的效率瓶颈在于逐帧实施的四面体单元的排序操作。采用四面体重心深度值进行排序,将几何排序转换成浮点数排序,简单方便。目前这种排序都是采用一些已有的通用方法,而本文考虑到四面体数据在空间上的连贯性。预计算不同采样视点下,四面体集合在不同深度区间上的分布。绘制时保证四面体集合快速地划分到对应区间上独立排序,各区间负载均衡。实验证明,本文的方法极大地提高了重心排序的效率。
·重心排序的方法是不精确的,在有些情况下会产生顺序错误,从而导致错误的绘制结果。基于精确遮挡关系的排序可以解决这个问题,但对并行提出了极大的挑战。本文采用分层的方式实现并行化的目的,但在确定层次的顺序时依旧受到串行处理的困扰。物理切割可以打破层间的顺序性,本文将四面体数据组织到一个空间k-d树的结构中,将处于分割面上的四面体进行切割,每个节点内的四面体单独排序。极大地提高了排序的效率。但物理切割的计算代价比较大,预处理时间较长,数量上的增加也带来了存储和绘制方面的压力。本文进一步改善了该方法,提出一种逻辑切割的方式。即在逻辑上将数据划分到不同的深度区间,但不进行真正的切割,绘制时只是对相应区间范围内的部分进行积分。实验证明,这种方法在不增加存储压力情况下极大的提高了精确排序的效率。
·除了排序效率的问题,绘制结果质量的提高也是不规则数据体绘制的一个重要方面。当前的方法大都是假设数据在四面体内部是线性分布的,表达的精度有限。本文将数据采用7方向盒样条函数进行了重构,建立了高次连续的数据场。然后在数据场中提取二次四面体,采用有限元的方法绘制了基于二次插值函数的结果。实验结果显示,基于二次插值函数的绘制结果不仅绘制精度更高,而且能够强化特征、显示更多的模式、消除四面体之间的裂缝。极大地提高了绘制质量。
本文工作集中在不规则体数据的可视化。具体方法分为两大类,一是将不规则数据转换为规则数据再绘制；二是在不规则数据上直接进行体绘制。本文在第一类方法中主要提出一种双结构化的架构,保证存储容量和绘制精度的平衡。而在第二类方法中,基于四面体投影法,提出了一个完整的框架。在这个框架下,将排序过程和绘制过程分开。先利用体数据的空间连贯性改进了不精确排序的效率；然后分别用物理分割和逻辑分割两种方法降低了精确排序的时间。在绘制方面,将原有的线性分布的数据进行了重构,采用二次插值函数提高了绘制的精度。整个系统比较完善,既有绘制效率的提高,又有绘制质量的改善。对科学计算结果的特征识别和提取带来了极大地帮助。大量实验证明了本文方法的可靠性。
Volume visualization can represent the significant interior structure or information of data field in three dimensions. It has been implemented in medical image analysis, geological data vi-sualization, computational fluid dynamics simulation, and so on. General volume data structure can be divided into two categories:regular datasets and unstructured datasets. Regular datasets often has been constructed by an array in three dimensions, sampling on grid points which have same span with each other. Regular datasets can be shown simply and handled easily, being ap-propriate to uniform data field. But most physical simulations, for example computational fluid dynamics simulation or partial differential equations, generate data field which is nonuniform. Us-ing regular datasets will bring about accuracy problem and redundant storage. So unstructured datasets have been represented by polyhedron or other unstructured data elements, and tetrahedra has been used popularly. Unstructured volume representation of data field in three dimensions im-proves accuracy and reduces requirement in storage, but it also increases the cost in computation and rendering. How to improve the rendering efficiency and enhance the rendering accuracy, are two primary challenges in rendering unstructured datasets. This paper made a lot of improvements as following:
Regular datasets can reduce a lot of computation cost because its structure is simple and easy to handle in parallel. It also does not need intersection computation. Therefore, regu-larization is the most direct scheme to solve this problem. Some works transform tetrahedral datasets into octree structure and render it based on texture. If the unstructured datasets have higher accuracy, regularization will generate the octree with more layers which increase the time to store and find. We propose a dual-structure scheme to decompose the datasets in-to two components, which can be represented as two GPU-friendly textures. The new data structure is memory-efficient, GPU-friendly, and thus allows for effective GPU-based vol-ume visualization.
Regularization is a method with accuracy loss. The main work of this paper is still about rendering directly on unstructured datasets. Projection is a typical method. Its bottleneck of rendering is sorting. Sorting value of tetrahedral centroids transform geometry sorting into float value sorting, which is easy and convenient. Until now, this kind of sorting has been handled by general sorting method. But our method considers the spatial coherence of tetrahedral datasets. We pre-compute the distribution of tetrahedral datasets in different deep blocks under different views. Tetrahedral datasets have been divided into corresponding block quickly with load balancing. The efficiency of sorting centroids increases with our method.
Sorting centroids is not accurate. It will produce some rendering error because of wrong order. Sorting on exact occlusion relationship can solve this problem, but it is a great chal-lenge to parallel. We solve this problem by layering the datasets, but the order of the layers is still processed seriously. The order between layers can be broken by physical partition. The tetrahedral datasets have been organized into a spatial octree structure. The tetrahedra on the partition plane has been divided into small ones. The tetrahedra in different node has been sorted independently, that increases the sorting efficiency. The physical partition needs more calculation and the more tetrahedra after partition produces many difficulties in storage and rendering. We improves this method and proposes a scheme named logical partition, which divides the tetrahedral datasets into different deep block without real partition. Only corresponding area has been integrated when rendering. This method increases the efficiency without more storage requirement.
The quality of rendering unstructured datasets is another important challenge. Most of ren-dering systems on unstructured datasets suppose that the interpolation in one element is linear, whose accuracy is limited. This paper reconstructs datasets with7direction box s-pline and builds a data field with high-order continuity. Then quadratic tetrahedra has been extracted and rendered by finite element methods. The experiments show that rendering with quadratic interpolation can increase the accuracy of result image, enhance the features and reduce the crack between tetrahedra. The quality of result image has been improved a lot.
The contributions of this paper are on visualization of unstructured datasets. The content has been divided two categories:one is transforming unstructured datasets into regular datasets; the other is rendering directly on unstructured datasets. In the former part, this paper proposes a dual-structure scheme which can balance between storage and accuracy. In the later part, this paper proposes a complete frame based on tetrahedra projection. The sort and the rendering have been separated. The efficiency of sorting tetrahedral centroids has been improved by using spatial coherence. The time of accurate sorting has been reduced by physical partition and logical parti-tion. In rendering aspect, this paper reconstructs the linear data field and improves the accuracy by using quadratic interpolation. This frame is complete, improving both rendering efficiency and quality. It brings great help to identifying and extracting feature in scientific computation. A lot of experiments identify the reliability of our system.
引文
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