标量场拓扑的一种渐进方法
A Progressive Approach to Scalar Field Topology
摘要：
本文介绍了标量数据拓扑分析的渐进算法。我们的方法是基于一个分层表示的输入数据和拓扑不变的顶点，这是顶点，没有影响的数据的拓扑描述，我们表明，不需要计算，因为它们是在层次结构中引入的快速识别。这使得有效的粗到细拓扑算法的定义，利用普通顶点的快速更新机制，避免计算拓扑不变的。我们证明了我们的方法与两个例子的拓扑算法（临界点提取和持久性图计算），产生可解释的输出中断请求后，逐步完善他们，否则。现实生活中的数据集上的实验表明，我们的渐进式策略，除了连续的视觉反馈，它提供了，甚至提高了运行时间性能方面的非渐进式算法，我们描述了进一步的加速与共享内存并行。我们说明了我们的方法在批处理模式和交互式设置中的实用性，它分别能够控制完整拓扑管道的执行时间以及数据集中发现的拓扑特征的预览，并在交互时间内提供渐进式更新。
英文摘要：
This paper introduces progressive algorithms for the topological analysis of scalar data. Our approach is based on a hierarchical representation of the input data and the fast identification of topologically invariant vertices, which are vertices that have no impact on the topological description of the data and for which we show that no computation is required as they are introduced in the hierarchy. This enables the definition of efficient coarse-to-fine topological algorithms, which leverage fast update mechanisms for ordinary vertices and avoid computation for the topologically invariant ones. We demonstrate our approach with two examples of topological algorithms (critical point extraction and persistence diagram computation), which generate interpretable outputs upon interruption requests and which progressively refine them otherwise. Experiments on real-life datasets illustrate that our progressive strategy, in addition to the continuous visual feedback it provides, even improves run time performance with regard to non-progressive algorithms and we describe further accelerations with shared-memory parallelism. We illustrate the utility of our approach in batch-mode and interactive setups, where it respectively enables the control of the execution time of complete topological pipelines as well as previews of the topological features found in a dataset, with progressive updates delivered within interactive times.
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