TABLE 1.

Average Dice score, number and percentage of voxels with non‐positive Jacobian determinant for affine alignment, NiftyReg, ANTs (SyN), VoxelMorph, ProbMultilayer, LapIRN, and the proposed method (referred to as MDReg‐Net) on different testing datasets

Methods	MALC			Mindboggle‐101
	Avg. Dice	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (#)	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (%)	Avg. Dice	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (#)	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (%)
Affine	0.429 (0.182)	–	–	0.347 (0.093)	–	–
NiftyReg	0.576 (0.184)	–	–	0.471 (0.126)	–	–
ANTs‐c1	0.597 (0.187)	9,571 (3,384)	0.58 (0.21)	0.538 (0.130)	4,349 (1,081)	0.74 (0.18)
ANTs‐c2	0.568 (0.188)	126 (187.7)	7.6e−3 (1.1e−2)	0.482 (0.130)	29 (49.1)	4.9e−3 (8.3e−3)
VoxelMorph (PING)	0.572 (0.182)	3.68 (7.7)	2.2e−4 (4.7e−4)	0.472 (0.117)	0.58 (1.98)	9.8e−5 (3.3e−4)
VoxelMorph (ADNI1)	0.568 (0.182)	4.53 (9.8)	2.7e−4 (6.0e−4)	0.476 (0.113)	0.32 (2.33)	5.4e−5 (3.9e−4)
ProbMultilayer (PING)	0.578 (0.181)	0.26 (1.54)	1.6e−5 (9.4e−5)	0.486 (0.106)	0.03 (0.3)	5.1e−6 (5.1e−5)
ProbMultilayer (ADNI1)	0.573 (0.181)	0.35 (1.89)	2.1e−5 (1.1e−4)	0.482 (0.105)	0 (0)	0 (0)
LapIRN (PING)	0.546 (0.186)	2,642 (2,088)	0.16 (0.13)	0.475 (0.097)	2,009 (920)	0.34 (0.16)
LapIRN (ADNI1)	0.547 (0.185)	2,585 (2,074)	0.16 (0.13)	0.477 (0.097)	1,533 (665)	0.26 (0.11)
MDReg‐Net (PING)	0.588 (0.180)	0.089 (0.515)	5.4e−6 (3.1e−5)	0.534 (0.094)	0 (0)	0 (0)
MDReg‐Net (ADNI1)	0.587 (0.172)	0.029 (0.172)	1.8e−6 (1.0e−5)	0.530 (0.092)	0.07 (0.7)	1.2e−5 (1.2e−4)

Note: The performance of VoxelMorph, ProbMultilayer, LapIRN, and MDReg‐Net trained using ADNI 1 dataset are also presented. The SDs are shown in parentheses. The average and standard deviation of Dice score were calculated over all anatomical structures and subjects. The statistics of voxels with non‐positive Jacobian determinant were calculated within brain region.