Boolean 2D Shape Similarity for Surface Reconstruction

BOOLEAN 2D SHAPE SIMILARITY FOR SURFACE RECONSTRUCTION Assoc. Prof. Dr. Oscar E. Ruiz (CAD / CAM / CG Laboratory. Mech. Eng. Dept.) Assoc. Prof. Dr. Carlos A. Cadavid (Basic Sciences Dept.) EAFIT University, Medellin, COLOMBIA Abstract Surface reconstruction problem (SRP) from planar samples has been traditionally approached by either (i) using local proximity between data points in adjacent layers, or by (ii) classifying the topological transitions that may explain the evolution of the cross sections. Strategy (i) is robust in the sense that it has answers for every possible case, although in some scenarios renders counterintuitive surfaces, commented below. Approach (ii) has mainly remained in the theoretical terrain. The present work follows on aspect (ii), by using a Morse-based topological classification of the transitions, and complementing it with reasoning based on the geometry of the evolving cross sections to determine a high level description of the transitions from m to n contours (m:n transitions). This reasoning of shape similarity is performed by boolean operators. Finally, the surface is synthesized using the m:n transitions. This conjunction of topological and geometrical reasoning renders highly intuitive results, and allows for the incorporation of methods derived from the area of machine vision.