具有经验收敛分离矩阵的二维图像的组合梯度场
Combinatorial Gradient Fields for 2D Images with Empirically Convergent Separatrices
摘要：
本文提出了一种有效的概率方法，计算组合梯度场的二维的图像数据。与现有的算法相比，这种方法产生了一个几何Morse-Smale复杂的收敛几乎肯定其连续对应的图像分辨率增加时。这种方法的动机是使用概率论的基本思想，并建立在具有强大数学基础的离散Morse理论的算法之上。虽然只是暗示了一个正式的证明，我们提供了一个彻底的数值评估我们的方法，并比较它建立的算法。
英文摘要：
This paper proposes an efficient probabilistic method that computes combinatorial gradient fields for two dimensional image data. In contrast to existing algorithms, this approach yields a geometric Morse-Smale complex that converges almost surely to its continuous counterpart when the image resolution is increased. This approach is motivated using basic ideas from probability theory and builds upon an algorithm from discrete Morse theory with a strong mathematical foundation. While a formal proof is only hinted at, we do provide a thorough numerical evaluation of our method and compare it to established algorithms.
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