Curve smoothing and matching

We present a new approach to the problem of matching 3D curves . The approach has an algorithmic complexity sublinear with the number of models, and can operate in the presence of noise and partial occlusions . Our method buids upon the seminal work of [27, 28], where curves are first smoothed using B-splines, with matching based on hashing using curvature and torsion measures . However, we introduce two enhancements * Ce travail a été en partie financé par Digital Equipment Corporation .We present a new approach to the problem of matching 3D curves . The approach has an algorithmic complexity sublinear with the number of models, and can operate in the presence of noise and partial occlusions . Our method buids upon the seminal work of [27, 28], where curves are first smoothed using B-splines, with matching based on hashing using curvature and torsion measures . However, we introduce two enhancements * Ce travail a été en partie financé par Digital Equipment Corporation . We present a new approach to the problem of matching 3D curves . The approach has an algorithmic complexity sublinear with the number of models, and can operate in the presence of noise and partial occlusions . Our method buids upon the seminal work of [27, 28], where curves are first smoothed using B-splines, with matching based on hashing using curvature and torsion measures . However, we introduce two enhancements * Ce travail a été en partie financé par Digital Equipment Corporation . we make use of non-uniform B-spline approximations, which permits us to better retain information at high curvature locations . The spline approximations are controlled (i.e ., regularized) by making use of normal vectors to the surface in 3-D on which the curves lie, and by an explicit minimization of a bending energy . These measures allow a more accurate estimation of position, curvatue, torsion and Frénet frames along the curve ; • the computational complexity of the recognition process is considerably decreased with explicit use of the Frénet frame for hypotheses generation . As opposed to previous approaches, the method better copes with partial occlusion . Moreover, following a statistical study of the curvature and torsion covariances, we optimize the hash table discretization and discover improved invariants for recognition, différent than the torsion measure. Finally, knowledge of invariant uncertainties is used to compute an optimal global transformation using an extended Kalman filter . We present experimental results using synthetic data and also using characteristic curves extracted front 3D medical images .Nous présentons une solution originale au problème de la reconnaissance et du recalage d'une courbe gauche discrète. La spécificité du problème est la nécessité de conserver une faible complexité algorithmique en présence d'un très grand nombre de modèles, d'être robuste au bruit et aux occultations partielles. Notre approche est une continuation logique des travaux de [27, 28] fondés sur un lissage des points par une courbe régulière puis par une reconnaissance à l'aide d'une table d'indexation mais présente deux innovations importantes: . pour une détermination plus fiable du modèle et de ses dérivées, les points discrets sont lissés par des splines en utilisant un critère d'erreur mixte et une distribution non uniforme de nœuds fondée sur la courbure locale et une régularisation exploitant la connaissance de la normale à la surface sur laquelle la courbe est inscrite et minimisant explicitement la variation de la courbure..