. Author manuscript; available in PMC: 2016 Oct 1.

Published in final edited form as: Med Image Anal. 2015 Apr 17;25(1):72–85. doi: 10.1016/j.media.2015.04.002

Table 2.

Synthetic data. Estimated parameters, and the recall, precision, Dice coefficient, relative volume difference (RVD), average surface distance (ASD), and ICVF root-mean-squared error (RMSE). Format: mean±std [min,max].

(a) Estimated parameters corresponding to different ground-truth values of the SUV scaling parameter (α).

	D_x, D_y, D_z (mm²/day, 10⁻³)			β (day⁻¹, 10⁻²)	γ (kPa)		α (mm³/g/day)

Ground truth	2.00	1.00	0.00	2.00	2.00	Ground truth	2.50	3.00	3.50	4.00
N-RMSEVD	1.71±0.37 [1.48,2.26]	0.89±0.19 [0.73,1.07]	0.03±0.03 [0.01,0.08]	2.08±0.83 [0.83,2.50]	1.98±0.03 [1.95,2.01]	N-RMSEVD	3.04	3.61	4.16	2.50
N-VD	1.74±1.10 [0.59,3.24]	0.83±0.58 [0.22,1.63]	0.13±0.12 [0.01,0.25]	2.45±0.10 [2.31,2.50]	2.35±0.72 [1.97,3.43]	N-VD	2.69	3.61	4.19	4.17
N-RMSE	1.50±0.65 [0.65,2.23]	0.70±0.31 [0.28,1.01]	0.14±0.22 [0.00,0.46]	2.08±0.83 [0.83,2.50]	2.41±1.06 [1.67,3.98]	N-RMSE	2.50	3.61	4.17	2.50
L-RMSEVD	1.64±0.38 [1.30,2.18]	0.86±0.17 [0.73,1.07]	0.04±0.05 [0.00,0.10]	2.08±0.83 [0.83,2.50]	4.47±0.20 [4.22,4.68]	L-RMSEVD	3.04	3.61	4.17	2.51

(b) Estimated parameters corresponding to different ground-truth values of the force scaling parameter (γ).

	D_x, D_y, D_z (mm²/day, 10⁻³)			β (day⁻¹, 10⁻²)	α (mm³/g/day)		γ (kPa)

Ground truth	2.00	1.00	0.00	2.00	3.50	Ground truth	1.00	2.00	3.00	4.00
N-RMSEVD	1.62±0.04 [1.58,1.66]	0.74±0.01 [0.73,0.74]	0.03±0.02 [0.01,0.06]	2.49±0.01 [2.48,2.50]	4.13±0.02 [4.11,4.16]	N-RMSEVD	0.99	1.95	2.98	3.89
N-VD	1.52±0.05 [1.47,1.57]	0.73±0.04 [0.67,0.76]	0.01±0.01 [0.01,0.02]	2.50±0.01 [2.49,2.51]	4.20±0.02 [4.17,4.23]	N-VD	0.99	1.97	2.97	3.89
N-RMSE	1.54±0.05 [1.48,1.58]	0.74±0.02 [0.73,0.77]	0.01±0.00 [0.00,0.01]	2.50±0.01 [2.49,2.51]	4.17±0.01 [4.16,4.17]	N-RMSE	0.99	1.97	2.98	3.88
L-RMSEVD	1.89±0.50 [1.57,2.64]	0.92±0.25 [0.73,1.27]	0.08±0.13 [0.00,0.27]	2.51±0.03 [2.50,2.56]	4.16±0.03 [4.12,4.19]	L-RMSEVD	2.43	4.55	5.00	4.91

(c) Overall prediction performances.

	Recall (%)	Precision (%)	Dice (%)	RVD (%)	ASD (mm)	RMSE (%)
N-RMSEVD	98.43±0.81 [97.44,99.91]	99.67±0.25 [99.22,99.95]	99.04±0.36 [98.50,99.56]	1.44±0.57 [0.70,2.16]	0.04±0.02 [0.02,0.07]	0.93±0.24 [0.57,1.26]
N-VD	96.52±6.85 [81.02,99.58]	99.27±0.55 [98.38,99.68]	97.77±3.90 [88.94,99.54]	3.14±6.48 [0.24,17.81]	0.09±0.16 [0.02,0.45]	1.76±1.28 [0.97,4.55]
N-RMSE	93.65±12.15 [66.17,99.63]	99.76±0.29 [99.12,99.95]	96.21±7.32 [79.62,99.38]	6.26±12.16 [0.52,33.79]	0.12±0.21 [0.03,0.61]	2.89±4.96 [0.94,14.14]
L-RMSEVD	97.30±1.39 [94.40,98.90]	97.89±3.45 [90.18,99.78]	97.57±1.91 [93.80,99.13]	2.88±2.62 [0.48,8.35]	0.19±0.22 [0.08,0.67]	1.48±1.08 [0.71,3.80]