Computational surface flattening: A voxel-based approach

Ruth Grossmann*, Nahum Kiryati, Ron Kimmel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


A voxel-based method for flattening a surface in 3D space into 2D while best preserving distances is presented. Triangulation or polyhedral approximation of the voxel data are not required. The problem is divided into two main parts: Voxel-based calculation of the minimal geodesic distances between points on the surface and finding a configuration of points in 2D that has Euclidean distances as close as possible to these distances. The method suggested combines an efficient voxel-based hybrid distance estimation method, that takes the continuity of the underlying surface into account, with classical multidimensional scaling (MDS) for finding the 2D point configuration. The proposed algorithm is efficient, simple, and can be applied to surfaces that are not functions. Experimental results are shown.

Original languageEnglish
Pages (from-to)433-441
Number of pages9
JournalIEEE Transactions on Pattern Analysis and Machine Intelligence
Issue number4
StatePublished - Apr 2002


  • Geodesic distance estimation
  • Multidimensional scaling
  • Surface flattening
  • Texture mapping
  • Voxel representation


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