Topologically Correct 3D Surface Reconstruction and Segmentation from Noisy Samples

Abstract. Existing theories on 3D surface reconstruction impose strong constraints on feasible object shapes and often require error-free measurements. Moreover these theories can often only be applied to binary segmentations, i.e. the separation of an object from its background. We use the Delaunay complex and α-shapes to prove that topologically correct segmentations can be obtained under much more realistic conditions. Our key assumption is that sampling points represent object boundaries with a certain maximum error. We use this in the context of digitization, i.e. for the reconstruction based on supercover and m-cell intersection samplings.