Efficient estimation of tissue thicknesses using sparse approximation for Gaussian processes

Highly accurate localization of the human skull is vital in cranial radiotherapy. Marker-less optical head tracking provides a fast and accurate way to monitor this motion. Recent research has given evidence that marker-less tracking of the forehead benefits from tissue thickness information in addition to the 3D surface geometry. Using Gaussian Processes (GPs) tissue thickness is determined from optical backscatter of a sweeping laser. However, the computational complexity of the GPs scales cubically with the number of training samples. A full head scan contains 1024 points, whereas scans from several perspectives may be required for a comprehensive model for each subject. In five subjects, we thus evaluate sparse approximation methods to reduce the computational effort. We found a better - computation time versus root mean square error (RMSE) - tradeoff for a simple subset of data (SoD) technique. The increase of RMSE when dropping data was not found steep enough to justify the computational overhead of a better approximation by inducing point methods (namely FITC). Promising results were, however, obtained when clustering the training data before selecting the subset.