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The Mixture Graph-A Data Structure for Compressing, Rendering, and Querying Segmentation Histograms
arXiv - CS - Graphics Pub Date : 2020-09-06 , DOI: arxiv-2009.02702
Khaled Al-Thelaya and Marco Agus and Jens Schneider

In this paper, we present a novel data structure, called the Mixture Graph. This data structure allows us to compress, render, and query segmentation histograms. Such histograms arise when building a mipmap of a volume containing segmentation IDs. Each voxel in the histogram mipmap contains a convex combination (mixture) of segmentation IDs. Each mixture represents the distribution of IDs in the respective voxel's children. Our method factorizes these mixtures into a series of linear interpolations between exactly two segmentation IDs. The result is represented as a directed acyclic graph (DAG) whose nodes are topologically ordered. Pruning replicate nodes in the tree followed by compression allows us to store the resulting data structure efficiently. During rendering, transfer functions are propagated from sources (leafs) through the DAG to allow for efficient, pre-filtered rendering at interactive frame rates. Assembly of histogram contributions across the footprint of a given volume allows us to efficiently query partial histograms, achieving up to 178$\times$ speed-up over na$\mathrm{\"{i}}$ve parallelized range queries. Additionally, we apply the Mixture Graph to compute correctly pre-filtered volume lighting and to interactively explore segments based on shape, geometry, and orientation using multi-dimensional transfer functions.

中文翻译:

混合图——一种用于压缩、渲染和查询分割直方图的数据结构

在本文中,我们提出了一种新的数据结构,称为混合图。这种数据结构允许我们压缩、渲染和查询分段直方图。在构建包含分段 ID 的卷的 mipmap 时会出现此类直方图。直方图 mipmap 中的每个体素都包含分割 ID 的凸组合(混合)。每个混合代表 ID 在相应体素的孩子中的分布。我们的方法将这些混合分解为恰好两个分割 ID 之间的一系列线性插值。结果表示为一个有向无环图 (DAG),其节点是按拓扑顺序排列的。修剪树中的复制节点然后压缩使我们能够有效地存储结果数据结构。在渲染过程中,传递函数从源(叶)通过 DAG 传播,以允许以交互式帧速率进行高效的预过滤渲染。在给定体积的足迹中组装直方图贡献使我们能够有效地查询部分直方图,比 na$\mathrm{\"{i}}$ve 并行范围查询实现高达 178$\times$ 的加速。此外,我们应用混合图来计算正确的预过滤体积照明,并使用多维传递函数以交互方式探索基于形状、几何形状和方向的段。{i}}$ve 并行范围查询。此外,我们应用混合图来计算正确的预过滤体积照明,并使用多维传递函数以交互方式探索基于形状、几何形状和方向的段。{i}}$ve 并行范围查询。此外,我们应用混合图来计算正确的预过滤体积照明,并使用多维传递函数以交互方式探索基于形状、几何形状和方向的段。
更新日期:2020-09-08
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