Any watershed, when defined on a stack on a normal pseudomanifold of dimension d, is a pure (d -- 1)-subcomplex that satisfies a drop-of-water principle. In this paper, we introduce Morse stacks, a class of functions that are equivalent to discrete Morse functions. We show that the watershed of a Morse stack on a normal pseudomanifold is uniquely defined, and can be obtained with a linear-time algorithm relying on a sequence of collapses. Last, we prove that such a watershed is the cut of the unique minimum spanning forest, rooted in the minima of the Morse stack, of the facet graph of the pseudomanifold.

翻译：任何定义在d维正规伪流形上的堆栈中的分水岭，都是一个满足"水滴原理"的纯(d-1)维子复形。本文引入Morse堆栈——一类等价于离散Morse函数的函数类。我们证明，正规伪流形上Morse堆栈的分水岭具有唯一性，并可通过依赖一系列坍塌的线性时间算法获取。最后，我们证明该分水岭恰为以Morse堆栈极小点为根的伪流形面图唯一最小生成森林的割。