Controlled-topology filtering

Yotam I. Gingold, Denis Zorin

Research output: Contribution to journalArticle

Abstract

Many applications require the extraction of isolines and isosurfaces from scalar functions defined on regular grids. These scalar functions may have many different origins: from MRI and CT scan data to terrain data or results of a simulation. As a result of noise and other artifacts, curves and surfaces obtained by standard extraction algorithms often suffer from topological irregularities and geometric noise. While it is possible to remove topological and geometric noise as a post-processing step, in the case when a large number of isolines are of interest there is a considerable advantage in filtering the scalar function directly. While most smoothing filters result in gradual simplification of the topological structure of contours, new topological features typically emerge and disappear during the smoothing process. In this paper, we describe an algorithm for filtering functions defined on regular 2D grids with controlled topology changes, which ensures that the topological structure of the set of contour lines of the function is progressively simplified.

Original languageEnglish (US)
Pages (from-to)676-684
Number of pages9
JournalCAD Computer Aided Design
Volume39
Issue number8
DOIs
StatePublished - Aug 2007

Fingerprint

Filtering
Topology
Scalar
Topological Structure
Smoothing
Contour Lines
Grid
Isosurface
Computerized tomography
Curves and Surfaces
Irregularity
Post-processing
Simplification
Filter
Processing
Simulation

Keywords

  • Computational topology
  • Critical points
  • Filtering
  • Isosurfaces

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Industrial and Manufacturing Engineering
  • Geometry and Topology

Cite this

Controlled-topology filtering. / Gingold, Yotam I.; Zorin, Denis.

In: CAD Computer Aided Design, Vol. 39, No. 8, 08.2007, p. 676-684.

Research output: Contribution to journalArticle

Gingold, Yotam I. ; Zorin, Denis. / Controlled-topology filtering. In: CAD Computer Aided Design. 2007 ; Vol. 39, No. 8. pp. 676-684.
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