Statistically-Constrained High-Dimensional Warping Using Wavelet-Based Priors

In this paper, a Statistical Model of Deformation (SMD) that captures the statistical prior distribution of highdimensional deformations more accurately and effectively than conventional PCA-based statistical shape models is used to regularize deformable registration. SMD utilizes a wavelet-based representation of statistical variation of a deformation field and its Jacobian, and it is able to capture both global and fine shape detail without overconstraining the deformation process. This approach is shown to produce more accurate and robust registration results in MR brain images, relative to the registration methods that use Laplacian-based smoothness constraints of deformation fields. In experiments, we evaluate the SMD-constrained registration by comparing the performance of registration with and without SMD in a specific deformable registration framework. The proposed method can potentially incorporate various registration algorithms to improve their robustness and stability using statistically-based regularization.

1. Introduction

Many registration methods have been proposed for finding the deformation field between two 3D images by maximizing the image-similarity measure and, at the same time, properly constraining/regularizing the deformation field [7], [9], [15], [16], [17]. In these methods, a variety of smoothness constraints are used, such as Laplacian-based regularization, or physically-based constraints, e.g. elasticity and vis-coelasticity. Statistical models have also been utilized to regularize the registration procedure to improve the registration performance [18]. Compared to the conventional methods, statistically-constrained deformable registration can achieve more robust performance, because the statistical regularization constraints reflect the relatively complex nature of the respective deformation fields.