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Acquiring an anatomical map from position data is important for medicalapplications where catheters interact with soft tissues. To improve autonomousnavigation in these settings, we require information beyond nonparametric mapstypically available. We present an algorithm for local surface approximationfrom position data with automatic surface order selection. The traditionalsurface fitting objective function is derived from a Bayesian perspective.Posterior probabilities from the occupancy map are incorporated as weights onpoints selected for surface fitting. Our novel iterative algorithm incorporatessurface order selection using the Bayesian information criterion. Simulationsdemonstrate the ability to automatically select surface order consistent withthe latent surface in the presence of noise. Results on human procedure dataare also presented.

Local Parametric Surface Approximation With Automatic Order Selection From Position Data