Morse-smale complexes for piecewise linear 3-manifolds

Edelsbrunner, Herbert; Harer, John; Natarajan, Vijay; Pascucci, Valerio

doi:10.1145/777792.777846

Cited by 191 publications

(108 citation statements)

References 17 publications

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“…In order to capture the structure of a Morse-Smale complex of a manifold M , without making reference to a function f , a notion of a cell complex called a quasi-Morse complex in 2D and 3D has been introduced in [15] and [14], respectively. The idea was to define a discrete counterpart of the Morse-Smale complex.…”

Section: Morse and Morse-smale Complexesmentioning

confidence: 99%

“…Almost all existing methods extract critical points of f as a first step. The characterization and classification of critical points in 2D [2,23] and 3D [14] is done locally, based on the values of the elevation function f at a point p and at the points in some neighborhood of p.…”

Section: Related Workmentioning

confidence: 99%

“…The Morse-Smale complex describes the subdivision of M into parts, characterized by uniform flow of the gradient of f . Morse and Morse-Smale complexes have been applied in terrain modeling for segmenting the graph of a 2D scalar field, and, recently, some algorithms have been developed for segmenting three-dimensional scalar fields through Morse-Smale complexes [9,14,18].…”

Section: Introductionmentioning

confidence: 99%

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Multi-Scale 3D Morse Complexes

Čomić

Floriani

2008

2008 International Conference on Computational Sciences and Its Applications

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Morse theory studies the relationship between the topology of a manifoldM and the critical points of a scalar function f defined over M . Morse and Morse-Smale complexes, defined by critical points and integral lines of f , induce a subdivision of M into regions of uniform gradient flow, representing the morphology of M in a compact way. Function f can be simplified by canceling its critical points in pairs, thus simplifying the morphological representation of M , given by Morse and Morse-Smale complexes of f . Here, we propose a compact representation for the two Morse complexes in 3D, which is based on encoding the incidence relations of their cells, and on exploiting the duality among the complexes. We define cancellation operations, and their inverse expansion operations, on the Morse complexes and on their dual representation. We propose a multi-scale representation of the Morse complexes which provides a description of such complexes, and thus of the morphology of a 3D scalar field, at different levels of abstraction. This representation allows us also to perform selective refinement operations to extract description of the complexes which varies in different parts of the domain, thus improving efficiency on large data sets, and eliminating the noise in the data through topology simplification.

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Section: Morse and Morse-smale Complexesmentioning

confidence: 99%

Section: Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multi-Scale 3D Morse Complexes

Čomić

Floriani

2008

2008 International Conference on Computational Sciences and Its Applications

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“…Common approaches are based on PL framework. The main idea is to march from maxima and minima to form the ascending and descending manifolds, and then the MS complex is computed by intersecting these manifolds (Edelsbrunner et al, 2001(Edelsbrunner et al, , 2003. Due to the noise in the data and rounding off, there are many redundant critical points extracted by the former methods.…”

Section: Introductionmentioning

confidence: 99%

High-quality topological structure extraction of volumetric data on C2-continuous framework

Fang

2015

Computer Aided Geometric Design

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“…The smoothness may be simulated on discrete data via an interpolation by a generic function. Among most systematic studies of that kind one could point out the work of Edelsbrunner et al [5,6]. This approach is natural in many geometric modeling problems but there are other types of applications where the simulation of smoothness and non-degeneracy is not desirable.…”

Section: Introductionmentioning

confidence: 99%