A Novel Point Based Non-rigid Registration Method and Its Application on Brain Shift∗

This paper presents a novel point based non-rigid registration (NRR) method. We overcome the limitations of the traditional point-based NRR methods by using a biomechanical model with a Robust Point Matching framework. Our new framework relies on robust regression technique to handle sparse point sets which are partially correlated. The non-rigid registration problem is formulated as a two variables (Correspondence and Mapping) functional minimization problem. The functional is decomposed into stress and similarity components. Linear Finite Element method using a patient-specific biomechanical model along with Expectation Maximization method are used for the simultaneous computation/approximation of both Correspondence and Mapping function. Gaussian distribution-based search range is used to improve the computational efficiency and robustness of the method. The combination of the search range with Least Trimmed Squared can effectively detect outliers in both source and target point sets. Preliminary performance data from an experimental evaluation for brain shift compensation shows the effectiveness of this method for sparse and even partially correlated source and target point sets.