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The Medial Scaffold for 3D Shape Representation and some Recent Applications in Archaeology and Sculpting

Dr. Frederic Leymarie University of London

December 17, 2004 at  11:00 AM
Zames Seminar Room - MC437

I will discuss my recent work on the representation of 3D shape involving collaborations with artists and scientists, including mathematicians, engineers, sculptors, archaeologists. In the last few years I have developed, with Prof. Ben B. Kimia of Brown University and Prof. Peter J. Giblin of Liverpool University, a new technology to represent 3D pieces of spatial data, for example using point clouds from laser scanners used to sample the surfaces of objects in a scene. The representation is called a Medial Scaffold: it is a 3D graph structure formally derived from another representation that was proposed in pattern recognition in the 1960's, called the Medial Axis. It also represents an extension to 3D of shock graphs defined by Siddiqi, Kimia et al. for 2D problems. The graph structure for a given set of input samples (e.g., points, polygons, curved surface patches) is built from special medial nodes taken as the centers of maximal contact spheres and located at singularities of a certain flow obtained from propagating geometric waves initiated at the input loci. The theory is related to the geometry of spheres and singularity theory.

These graphs are "flexible" in that small perturbations or deformationsv of the input sets do not modify their topology; however sudden transition changes in the graph structure can occur for sufficiently large deformations. These topological events have been recently entirely understood and I will report on their use in simplifying the medial scaffolds to elicit what may be thought of as qualitative versus quantitative shape descriptions. This represents a major step toward object recognition by a cybernetic system. The result of recent collaborations, with applications to archaeology and sculpting.will be presented.