1.  In many cases the reconstructed model contains too many elements (triangles, edges, vertices) to be amenable for further processing. A widely used method decimates the model by contracting edges with their incident triangles. We study this edge contraction process with the goal that the topology of the model is preserved. This guarantee can be extended to two dimensional simplicial complexes and to three dimensional manifolds with our method. No prior method can guarantee this. This is a joint work with Herbert Edelsbrunner based on which Raindrop Geomagic has developed the decimator software.

2.  In another approach we decimate the sample before reconstructing a surface out of it. This has the advantage of automatic topology and feature preservations over the model simplification method. Also, one does not need to worry about self intersection. After decimating the sample we employ our Cocone algorithm to reconstruct the surface. 

Topology preserving edge contraction.

Decimating Sample.

Decimation of samples at different levels
 

Decimation of sample Foot at three diffrent levels (nearly 80% data reduction is achieved). Reconstruction is performed with Cocone

For  Shuffle see