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

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...

• Type: Journal
• Year: 2006
• Where: CAD
• Authors: Yang Liu, Helmut Pottmann, Wenping Wang
• Keywords: CAD 2006, Fitting Surface, Geometric Optimization Framework, Measurement Data, Theoretical Computer Science