  Objective: Non-rigid image registration with high accuracy and efficiency is
still a challenging task for medical image analysis. In this work, we present
the spatially region-weighted correlation ratio (SRWCR) as a novel similarity
measure to improve the registration performance. Methods: SRWCR is rigorously
deduced from a three-dimension joint probability density function combining the
intensity channels with an extra spatial information channel. SRWCR estimates
the optimal functional dependence between the intensities for each spatial bin,
in which the spatial distribution modeled by a cubic B-spline function is used
to differentiate the contribution of voxels. We also analytically derive the
gradient of SRWCR with respect to the transformation parameters and optimize it
using a quasi-Newton approach. Furthermore, we propose a GPU-based parallel
mechanism to accelerate the computation of SRWCR and its derivatives. Results:
The experiments on synthetic images, public 4-D thoracic computed tomography
(CT) dataset, retinal optical coherence tomography (OCT) data, and clinical CT
and positron emission tomography (PET) images confirm that SRWCR significantly
outperforms some state-of-the-art techniques such as spatially encoded mutual
information and Robust PaTch-based cOrrelation Ration. Conclusion: This study
demonstrates the advantages of SRWCR in tackling the practical difficulties due
to distinct intensity changes, serious speckle noise, or different imaging
modalities. Significance: The proposed registration framework might be more
reliable to correct the non-rigid deformations and more potential for clinical
applications.
