A statistical deformation model (SDM) based regularizer for non-rigid image registration: application to registration of multimodal prostate MRI and histology

Abstract

Free form deformation (FFD) is a popular algorithm for non-linear image registration because of its ability to accurately recover deformations. However, due to the unconstrained nature of elastic registration, FFD may introduce unrealistic deformations, especially when differences between template and target image are large, thereby necessitating a regularizer to constrain the registration to a physically meaning transformation. Prior knowledge in the form of a Statistical Deformation Model (SDM) in a registration scheme has been shown to function as an effective regularizer. With a similar underlying premise, in this paper, we present a novel regularizer for FFD that leverages knowledge of known, valid deformations to train a statistical deformation model (SDM). At each iteration of the FFD registration, the SDM is utilized to calculate the likelihood of a given deformation occurring and appropriately influence the similarity metric to limit the registration to only realistic deformations. We quantitatively evaluate robustness of the SDM regularizer in the framework of FFD through a set of synthetic experiments using brain images with a range of induced deformations and 3 types of multiplicative noise - Gaussian, salt and pepper and speckle. We demonstrate that FFD with the inclusion of the SDM regularizer yields up to a 19% increase in normalized cross correlation (NCC) and a 16% decrease in root mean squared (RMS) error and mean absolute distance (MAD). Registration performance was also evaluated qualitatively and quantitatively in spatially aligning <i>ex vivo </i>pseudo whole mount histology (WMH) sections and <i>in vivo </i>prostate MRI in order to map the spatial extent of prostate cancer (CaP) onto corresponding radiologic imaging. Across all evaluation measures (MAD, RMS, and DICE), regularized FFD performed significantly better compared to unregularized FFD.