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. Author manuscript; available in PMC: 2023 Mar 20.
Published in final edited form as: Med Phys. 2020 Nov 9;47(12):6366–6380. doi: 10.1002/mp.14545

Table 2:

Comparison of SSIM, MSE, and the number and percentage of pixel locations with non-positive Jacobian determinant among the proposed method (UnsupConvNet), SyN, and VoxelMorph. The top three results in SSIM and MSE are shown in bold, underline, and italics, respectively. Evaluations were done on 2D images with size 384 × 384.

Method SSIM MSE |Jϕ| ≤ 0 (counts) % of |Jϕ| ≤ 0 (%)
Affine only 0.83 ± 0.008 69.2 ± 2.7 - -
VoxelMorph (MSE)22 0.88 ± 0.003 47.0 ± 2.4 685 ± 185 0.5 ± 0.1
VoxelMorph (CC)22 0.92 ± 0.006 43.5 ± 4.8 2754 ± 370 1.9 ± 0.3
SyN (MSE)20 0.88 ± 0.011 52.0 ± 4.1 - -
SyN (MI)20 0.88 ± 0.011 55.1 ± 4.0 - -
SyN (CC)20 0.89 ± 0.011 52.8 ± 4.1 - -
UnsupConvNet (w/o regularization) 0.96 ± 0.007 37.3 ± 5.1 21082 ± 3938 14.3 ± 2.7
UnsupConvNet
(w/ diffusion regularization)		 0.93 ± 0.008 42.6 ± 5.4 1202 ± 225 0.8 ± 0.1
UnsupConvNet
(w/ diff. + None-neg. Jac. reg.)		 0.92 ± 0.009 44.8 ± 4.9 518 ± 74 0.4 ± 0.1
UnsupConvNet
(w/ TV regularization)		 0.87 ± 0.030 54.7 ± 9.3 659 ± 459 0.4 ± 0.3
UnsupConvNet
(w/ Gaussian filtering)		 0.94 ± 0.008 41.5 ± 5.4 8500 ± 1829 5.7 ± 1.3