Local Parametric Surface Approximation With Automatic Order Selection From Position Data

Acquiring an anatomical map from position data is important for medical applications where catheters interact with soft tissues. To improve autonomous navigation in these settings, we require information beyond nonparametric maps typically available. We present an algorithm for local surface approximation from position data with automatic surface order selection. The traditional surface fitting objective function is derived from a Bayesian perspective. Posterior probabilities from the occupancy map are incorporated as weights on points selected for surface fitting. Our novel iterative algorithm incorporates surface order selection using the Bayesian information criterion. Simulations demonstrate the ability to automatically select surface order consistent with the latent surface in the presence of noise. Results on human procedure data are also presented.