Local Regression Learning via Forest Classification for 2D/3D Deformable Registration

Abstract

Recent 2D/3D deformable registration methods have achieved real-time computation of 3D lung deformations by learning global regressions that map projection intensities to deformation parameters globally in a shape space. If the mapping matrices are specialized to a specific local region of the shape space, the linear mappings will perform better than mappings trained to work on the global shape space. The major contribution of this paper is presenting a novel method that supports shape-space-localized learning for 2D/3D deformable registration and uses regression learning as an example. The method comprises two stages: training and application. In the training stage, it recursively finds normalized graph cuts that best separate the training samples given the number of desired training partitions. Second, in each training partition the projection mapping matrices are learned by linear regressions locally. Third, the method trains a decision forest for deciding into which training partition a target projection image should be classified, on the basis of projection image intensity and gradient values in various image regions. In the application stage, the decision forest classifies a target projection image into a training partition and then the learned linear regressions for that training partition are applied to the target projection image intensities to yield the desired deformation. This local regression learning method is validated on both synthetic and real lung datasets. The results indicate that the forest classification followed by local regressions yields more accurate and yet still real-time 2D/3D deformable registration than global regressions.