Codon constraints on closed 2D shapes

Abstract

Codons are simple primitives for describing plane curves. They thus are primarily image-based descriptors. Yet they have the power to capture important information about the 3D world, such as making part boundaries explicit. The codon description is highly redundant (useful for error-correction). This redundancy can be viewed as a constraint on the number of possible codon strings. For smooth closed strings that represent the bounding contour (silhouette) of many smooth 3D objects, the constraints are so strong that sequences containing 6 elements yield only 33 generic shapes as compared with a possible number of 15,625 combinations.