Matching a surface to a given sectional curve.
We describe an algorithm to position a rigid surface so as to make its cross-section by a given plane match a given curve in that plane, a problem relevant to model-based medical imaging. After building an atlas of cross-sections of the surface and searching it for a best position to start from, each iteration of the algorithm (1) determines a vector field along the intersection curve that will improve its matching with the target curve, and (2) computes and applies a small displacement of the surface whose effect on the intersection will approximate best the required vector field. Computations use least-square techniques, an exponential formula for Lie groups of transformations, and generic properties of cross-sections. Experiments with an implementation are reported and theoretical tools for justifying and improving the algorithm, some of them based on Catastrophe Theory, are outlined.
Kergosien
Yannick L
YL
Département d'informatique, université de Cergy-Pontoise, 2, av. Adolphe-Chauvin, 95302 Cergy-Pontoise, France. yannick.kergosien@libertysurf.fr
D000465:Algorithms; D000715:Anatomy / Q000379:methods; D006801:Humans; D007091:Image Processing, Computer-Assisted / Q000379:methods*; D016018:Least-Squares Analysis; D013499:Surface Properties