Texture mapping using surface flattening via multidimensional scaling

Gil Zigelman, Ron Kimmel, Nahum Kiryati

Research output: Contribution to journalArticlepeer-review

Abstract

We present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from a given surface point in O(n lg n) operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multidimensional scaling (MDS). MDS is a family of methods that map a set of points into a finite dimensional flat (Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distance between the corresponding points. We then solve an "inverse" problem and map a flat texture patch onto the curved surface while preserving the structure of the texture.

Original languageEnglish
Pages (from-to)198-207
Number of pages10
JournalIEEE Transactions on Visualization and Computer Graphics
Volume8
Issue number2
DOIs
StatePublished - Apr 2002

Keywords

  • Euclidean distance
  • Fast marching method
  • Geodesic distance
  • Multidimensional scaling
  • Texture mapping

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