An image-space Morse decomposition for 2D vector fields
An image-space Morse decomposition for 2D vector fields
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DOI：
10.1117/12.2080196
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
Guoning Chen;Shuyu Xu
中科院分区：
文献类型：
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作者：
Guoning Chen;Shuyu Xu
莫尔斯分解被用来计算和表示稳定向量场的拓扑结构。与传统的差分拓扑结构相比，莫尔斯分解和得到的莫尔斯连接图（MCG）具有数值稳定性。然而，原始莫尔斯分解的粒度受到底层空间离散化的分辨率的限制，这通常导致非光滑表示。在这项工作中，提出了一个图像空间莫尔斯分解（ISMD）框架来解决这个问题。与原始方法相比，ISMD首先将原始矢量场投影到图像平面上，然后基于投影场以像素为最小元素计算莫尔斯分解。因此，可以实现像素级精度。该ISMD框架已应用于许多合成和现实世界的稳定矢量场，以证明其实用性。ISMD的性能被仔细研究和报道。最后，利用ISMD可以研究和可视化集成莫尔斯分解，这有助于可视化莫尔斯集相对于数值计算中引入的误差和输入向量场的扰动的稳定性。
Morse decompositions have been proposed to compute and represent the topological structure of steady vector fields. Compared to the conventional differential topology, Morse decomposition and the resulting Morse Connection Graph (MCG) is numerically stable. However, the granularity of the original Morse decomposition is constrained by the resolution of the underlying spatial discretization, which typically results in non-smooth representation. In this work, an Image-Space Morse decomposition (ISMD) framework is proposed to address this issue. Compared to the original method, ISMD first projects the original vector field onto an image plane, then computes the Morse decomposition based on the projected field with pixels as the smallest elements. Thus, pixel-level accuracy can be achieved. This ISMD framework has been applied to a number of synthetic and real-world steady vector fields to demonstrate its utility. The performance of the ISMD is carefully studied and reported. Finally, with ISMD an ensemble Morse decomposition can be studied and visualized, which is shown useful for visualizing the stability of the Morse sets with respect to the error introduced in the numerical computation and the perturbation to the input vector fields.