Fish Scales: Representing Fuzzy Manifolds

We address the problem of automatically reconstructing m-manifolds of unknown topology from unorganized points in metric p-spaces obtained from a noisy measurement process. The point set is first approximated by a collection of oriented primitive fuzzy sets over a range of resolutions. Hierarchical multiresolution representation is then computed based on the relation of relative containment defined on the collection. Finally, manifold structure is recovered by establishing connectivity between these primitives based on proximity, compatibility of position and orientation, and local topological constraints. The method has been successfully applied to the problem of surface reconstruction from polynocular-stereo data with many outliers.