Recent image registration methods built upon unsupervised learning have achieved promising diffeomorphic image registration performance. However, the bijective consistency of spatial transformations is not sufficiently investigated in existing image registration studies. In this study, we develop a multi-level image registration framework to achieve diffeomorphic image registration in a coarse-to-fine manner. A novel stationary velocity field computation method is proposed to integrate forward and inverse stationary velocity fields so that the image registration result is invariant to the order of input images to be registered. Moreover, a new bijective consistency regularization is adopted to enforce the bijective consistency of forward and inverse transformations at different time points along the stationary velocity integration paths. Validation experiments have been conducted on two T1-weighted magnetic resonance imaging (MRI) brain datasets with manually annotated anatomical structures. Compared with four state-of-the-art representative diffeomorphic registration methods, including two traditional diffeomorphic registration algorithms and two unsupervised learning-based diffeomorphic registration approaches, our method has achieved better image registration accuracy with superior topology preserving performance.
Large deformation diffeomorphic metric mapping (LDDMM) is one of the state-of-the-art deformable image registration algorithms that has been shown to be of superior performance, especially for brain images. LDDMM was originally proposed for matching intra-modality images, with the Sum of Squared Difference (SSD) being used as the matching cost function. Extension of LDDMM to other types of matching cost functions has been very limited. In this paper, we systematically evaluated three different matching cost functions, the SSD, the Mutual Information (MI), and the Cross Correlation (CC) in the LDDMM-image setting, based on 14 subcortical and ventricular structures in a total of 120 pairs of brain images. In addition, we proposed an efficient implementation for those three LDDMM-image settings via GPU-base parallel computing and quantitatively compared with the standard open source implementation of LDDMM-SSD in terms of both registration accuracy and computational time. The proposed parallelization and optimization approach resulted in an acceleration by 28 times, relative to the standard open source implementation, on a 4-core machine with GTX970 card (29.67 mins versus 828.35 mins on average), without sacrificing the registration accuracy. Comparing the three matching cost functions, we observed that LDDMM-CC worked the best in terms of registration accuracy, obtaining Dice overlaps larger than 0.853 for a majority of structures of interest.
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