Codon constraints on closed 2D shapes

Codons are simple primitives for describing plane curves. They thus are primarily C.:0 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 LLL 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 . LA.. bounding contour (silhouette) of many smooth 3D objects, the constraints are so strong that sequences containing 6 elements yield only 33 generic shal~es as compared with a possible number of 15,625 combinations. 4 A4 ' ." -'I 4&45 Acknowledgments: This report describes research done at the Department of Psychology and the Artificial Intelligence Laboratory of the Massachusetts Institute of Technology. Support for this work is provided by AFOSR under a grant for Image Understanding, contract F49620-83-C-0135. William Gilson helped with the preparation of the manuscript. The comments of Aaron Bobick and John Rubin were appreciated. Chris Fitch and Steve Schad broke the combination that made Appendix III possible. *D.D. Hoffman is now at the University of California, Irvine. © 1984 Massachusetts Institute of Technology djatrl '