Hierarchical Morse-Smale Complex in 3D
نویسندگان
چکیده
This paper investigates the topology of piecewise linear scalar functions, such as the interpolation function over a tetrahedralized volumetric grid. An algorithm is presented that creates a hierarchical representation of a Morse-Smale complex based on persistence. We show the correctness of our approach and discuss the applications. 1
منابع مشابه
Morse-Smale Decompositions for Modeling Terrain Knowledge
In this paper, we describe, analyze and compare techniques for extracting spatial knowledge from a terrain model. Specifically, we investigate techniques for extracting a morphological representation from a terrain model based on an approximation of a Morse-Smale complex. A Morse-Smale complex defines a decomposition of a topographic surface into regions with vertices at the critical points and...
متن کاملModeling Three-Dimensional Morse and Morse-Smale Complexes
Morse and Morse-Smale complexes have been recognized as a suitable tool for modeling the topology of a manifold M through a decomposition of M induced by a scalar field f defined over M. We consider here the problem of representing, constructing and simplifying Morse and Morse-Smale complexes in 3D. We first describe and compare two data structures for encoding 3D Morse and Morse-Smale complexe...
متن کاملHierarchical Video Segmentation using Morse-Smale Complexes
In this paper, we regard a space-time block of video data as a piecewise-linear 3-manifold, and we interpret video segmentation as the computation of the Morse-Smale complex for the block. In the generic case, this complex is a decomposition of space-time data into 3-dimensional cells shaped like crystals, and separated by quadrangular faces. The vertices of these are Morse critical points. In ...
متن کاملVideo Segmentation using Morse-Smale Complexes
In this paper, we regard a space-time block of video data as a piecewise-linear 3-manifold, and we interpret video segmentation as the computation of the Morse-Smale complex for the block. In the generic case, this complex is a decomposition of space-time data into 3-dimensional cells shaped like crystals, and separated by quadrangular faces. The vertices of these are Morse critical points. In ...
متن کاملParallel Computation of 3D Morse-Smale Complexes
The Morse-Smale complex is a topological structure that captures the behavior of the gradient of a scalar function on a manifold. This paper discusses scalable techniques to compute the Morse-Smale complex of scalar functions defined on large three-dimensional structured grids. Computing the Morse-Smale complex of three-dimensional domains is challenging as compared to two-dimensional domains b...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004