论文标题
离散摩尔斯的功能和流域切割的梯度矢量场
Gradient Vector Fields of Discrete Morse Functions and Watershed-cuts
论文作者
论文摘要
在本文中，我们研究了一类来自离散的摩尔斯理论的离散摩尔斯函数，这些功能等同于来自数学形态的一类简单堆栈。我们表明，与离散的莫尔斯理论一样，我们可以将简单堆栈的梯度向量字段（视为离散函数）视为我们应该考虑的唯一相关信息。最后但并非最不重要的一点是，我们还表明，简单堆栈的双图的最小跨越森林是由初始函数的梯度向量场诱导的。该结果允许从梯度矢量场计算流域切割。
In this paper, we study a class of discrete Morse functions, coming from Discrete Morse Theory, that are equivalent to a class of simplicial stacks, coming from Mathematical Morphology. We show that, as in Discrete Morse Theory, we can see the gradient vector field of a simplicial stack (seen as a discrete Morse function) as the only relevant information we should consider. Last, but not the least, we also show that the Minimum Spanning Forest of the dual graph of a simplicial stack is induced by the gradient vector field of the initial function. This result allows computing a watershed-cut from a gradient vector field.
