In this paper, we proposed an efficient approach for large deformation diffeomorphic metric mapping (LDDMM) for brain images by utilizing GPU-based parallel computing and a mixture automatic step size estimation method for gradient descent (MAS-GD). We systematically evaluated the proposed approach in terms of two matching cost functions, including the Sum of Squared Differences (SSD) and the Cross-Correlation (CC). The registration accuracy and computational efficiency on two datasets inducing respective 120 and 1,560 registration maps were evaluated and compared between CPU-based LDDMM-SSD and GPU-based LDDMM-SSD both utilizing backtracking line search for gradient descent (BLS-GD), GPU-based LDDMM (BLS-GD) and GPU-based LDDMM (MAS-GD) with each of the two matching cost functions being used. In addition, we compared our GPU-based LDDMM-CC (MAS-GD) with another widely-used state-of-the-art image registration algorithm, the symmetric diffeomorphic image registration with CC (SyN-CC). The GPU-based LDDMM-SSD was about 94 times faster than the CPU-based version (8.78 mins versus 828.35 mins) without sacrificing the Dice accuracy (0.8608 versus 0.8609). The computational time of LDDMM with MAS-GD for SSD and CC were shorter than that of LDDMM with BLS-GD (5.29 mins versus 8.78 mins for SSD and 6.69 mins versus 65.87 mins for CC), and the corresponding Dice scores were higher, especially for CC (0.8672 versus 0.8633). Compared with SyN-CC, the proposed algorithm, GPU-based LDDMM-CC (MAS-GD) had a higher registration accuracy (0.8672 versus 0.8612 and 0.7585 versus 0.7537 for the two datasets) and less computational time (6.80 mins versus 25.97 mins and 6.58 mins versus 26.23 mins for the two datasets).
Keywords: Automatic step-size estimation; Brain image registration; Cross-Correlation; Gradient descent optimization; LDDMM; Parallelization.