Boolean 2D Shape Similarity for Surface Reconstruction

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, which we comment 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.
KEY WORDS: 2D shape similarity, surface reconstrucion.