Multi-Resolution computation and presentation of Contour Trees
Multi-Resolution computation and presentation of Contour Trees
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发表时间：
2005
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通讯作者：
Valerio Pascucci;K. Cole-McLaughlin;G. Scorzelli
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作者：
Valerio Pascucci;K. Cole-McLaughlin;G. Scorzelli
标量场的等高线树是将场的水平集的所有连通分量收缩为点而得到的图。这是一个强大的抽象表示的领域的结构与明确的描述其水平集的拓扑变化。它已被证明是一种有效的数据结构，用于快速提取等值面，其应用程序已被提倡作为一个用户界面组件，指导交互式数据探索会议。在实践中，这种使用已经非常有限，这是由于呈现的图的问题，该图可能在尺寸上是压倒性的，并且其中平面嵌入可能由于自相交而令人困惑。拓扑简化技术有助于缓解这一问题。这项工作是在美国能源部的赞助下，由加州大学劳伦斯利弗莫尔国家实验室根据合同号W-7405-Eng-48进行的。这是一个问题，因为它们允许减少图形的大小。我们提出了一个多分辨率的数据结构表示轮廓树和算法的建设。此外，我们提供了一个分层的布局，允许粗略到精细的渲染树在一个渐进的用户界面。我们的多分辨率模型的构建仅比标准树稍微昂贵，但在根据不同度量的重要性对数据的拓扑进行统一和自适应过滤时，引入了更大的灵活性。我们已经测试的方法，使用拓扑持久性（这是一对关键点之间的功能值的差异被简化）作为主要指标，用于构建拓扑层次结构，并使用几何位置（包含在一个边界框）作为二级指标自适应细化。
The Contour Tree of a scalar field is the graph obtained by contracting all the connected components of the level sets of the field into points. This is a powerful abstraction for representing the structure of the field with explicit description of the topological changes of its level sets. It has proven effective as a data-structure for fast extraction of isosurfaces and its application has been advocated as a user interface component guiding interactive data exploration sessions. In practice, this use has been very limited due the problem of presenting a graph that may be overwhelming in size and in which a planar embedding may be confusing due to self-intersections. Topological simplification techniques have helped in relieving this ∗This work was performed under the auspices of the U.S. Department of Energy by University of California Lawrence Livermore National Laboratory under contract No. W-7405-Eng-48. problem since they allow reducing the size of the graph. We present a multi-resolution data-structure for representing contour trees and an algorithm for its construction. Moreover, we provide a hierarchical layout that allows coarse-to-fine rendering of the tree in a progressive user interface. Construction of our multi-resolution model is only slightly more expensive than the standard tree, but introduces far greater flexibility when filtering, both uniformly and adaptively, the topology of the data by importance with respect to different metrics. We have tested the approach using topological persistence (that is the difference in function value between a pair of critical points that are simplified) as the main metric for constructing the topological hierarchy, and using geometric position (containment in a bounding box) as a secondary metric for adaptive refinement.