Controlled-Topology Filtering

Yotam I. Gingold, Denis Zorin
Originally in Proceedings of SPM 2006, Cardiff, Wales, June 2006 (Best Paper Award, 2nd).
Expanded as: Computer-Aided Design, Volume 39, Issue 8, August 2007.

Paper: CAD (5.5M PDF)
Presentation: SPM 2006 (21M PDF)


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.

Surface evolution with and without topology control.


  title    = "Controlled-topology filtering",
  author   = "Yotam I. Gingold and Denis Zorin",
  journal  = "Computer-Aided Design",
  volume   = "39",
  number   = "8",
  pages    = "676--684",
  year     = "2007",
  note     = "Solid and Physical Modeling 2006",
  issn     = "0010-4485",
  doi      = "10.1016/j.cad.2007.05.010",
  url      = "",
  keywords = "Computational topology",
  keywords = "Critical points",
  keywords = "Filtering",
  keywords = "Isosurfaces"

BibTeX for the SPM paper can be found on the ACM page.