Constrained 3D shape reconstruction using a combination of surface fitting and registration

Yang Liu*, Helmut Pottmann, Wenping Wang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We investigate 3D shape reconstruction from measurement data in the presence of constraints. The constraints may fix the surface type or set geometric relations between parts of an object's surface, such as orthogonality, parallelity and others. It is proposed to use a combination of surface fitting and registration within the geometric optimization framework of squared distance minimization (SDM). In this way, we obtain a quasi-Newton like optimization algorithm, which in each iteration simultaneously registers the data set with a rigid motion to the fitting surface and adapts the shape of the fitting surface. We present examples to show the applicability of our method to constrained 3D shape fitting for reverse engineering of CAD models and to high accuracy fitting with kinematic surfaces, which include surfaces of revolution (reconstructed from fragments of archeological pottery) and spiral surfaces, which are fitted to 3D measurement data of shells. Our optimization algorithm can combine registration of multiple scans of an object and model fitting into a single optimization process which is shown to be superior to the traditional procedure, which first registers the data and then fits a model to it.

Original languageEnglish (US)
Pages (from-to)572-583
Number of pages12
JournalCAD Computer Aided Design
Issue number6
StatePublished - Jun 2006
Externally publishedYes


  • Constrained surface fitting
  • Digital reconstruction
  • Registration
  • Squared distance minimization

ASJC Scopus subject areas

  • Industrial and Manufacturing Engineering
  • Computer Science Applications
  • Computer Graphics and Computer-Aided Design


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