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

 

Yixun Liu, Andriy Fedorov, Ron Kikinis and Nikos Chrisochoides.

 

Published in SPIE Medical Imaging, 2010

 

Abstract

 

This paper presents a novel point based non-rigid registration (NRR) method. The purpose of point based NRR is to find mapping function, which generally requires to know correspondence. One kind of methods are to use some specific algorithm to find the correspondence and then solve mapping function. The other kind of methods do not rely on any specific algorithms to find correspondence, but solve them (correspondence and mapping function) simultaneously. The representative of this kind of methods is point matching method (RPM), which is an extension of well-known iterative closest point (ICP) algorithm. However, RPM employs thin-plate splines (TPS) as mapping function and therefore is incapable of estimating the deformation given sparse data because TPS is not compact support. Furthermore, RPM cannot deal with the outliers existing in both source and target point sets. To overcome these limitations, we combine biomechanical model with RPM framework to deal with sparse point sets and employ robust regression technique to to deal with partially overlapping point sets. We formulate this registration problem as a two variables (Correspondence C and Mapping function F) functional minimization problem, which can be decomposed into a stress energy of biomechanical model and a similarity energy. Finite element method is used to discretize this functional and Expectation Maximization method is used to solve these two variables simultaneously. For the consideration of computational efficiency and robustness again outliers, a Gaussian distribution-based search range is defined. Combined the search range with Least Trimmed Squared(LTS), this method can be effectively used to detect the outliers in both source and target point sets. The experiment for compensating for brain shift shows the effectiveness of this method as dealing with the non-rigid registration only given sparse and even partially overlapping point sets.