TABLE 3.

Average dice score, number, and percentage of voxels with non‐positive Jacobian determinant for the proposed MDReg‐Net without/with spatial smoothing layer on two testing datasets

Methods	MALC			Mindboggle‐101
	Avg. Dice	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (#)	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (%)	Avg. Dice	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (#)	$\left|J_{\mathrm{\Phi }}\right|\le 0$ (%)
MDReg‐Net w/o s ($\lambda =0.5$, PING)	0.592 (0.181)	19.18 (20.85)	1.2e−3 (1.3e−3)	0.539 (0.099)	2.59 (3.79)	4.4e−4 (6.4e−4)
MDReg‐Net w/o s ($\lambda =0.5$, ADNI1)	0.590 (0.181)	15.5 (11.5)	9.4e−4 (7.0e−4)	0.543 (0.095)	1.28 (2.17)	2.2e−4 (3.7e−4)
MDReg‐Net w/o s ($\lambda =1.0$, PING)	0.583 (0.181)	0.029 (0.172)	1.8e−6 (1.0e−5)	0.527 (0.095)	0.14 (1.14)	2.4e−5 (1.9e−4)
MDReg‐Net w/o s ($\lambda =1.0$, ADNI1)	0.580 (0.180)	0.088 (0.515)	5.4e−6 (3.1e−5)	0.523 (0.094)	0 (0)	0 (0)
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)
MDReg‐Net (PING, inverse)	0.586 (0.180)	0.235 (0.855)	1.4e−5 (5.2e−5)	0.534 (0.092)	0.05 (0.359)	8.7e−6 (6.2e−5)
MDReg‐Net (ADNI1, inverse)	0.585 (0.178)	0.029 (0.172)	1.8e−6 (1.0e−5)	0.532 (0.091)	0 (0)	0 (0)

Note: The registration performance on images registered with the deformation fields computed in the opposite direction based on the same velocity fields are referred as MDReg‐Net (inverse). 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.