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

Published in final edited form as: Med Image Anal. 2014 Aug 7;19(1):30–45. doi: 10.1016/j.media.2014.07.004

Table 3.

Comparison of theoretical magnification and estimated magnification factors for 4 clinical cases. The value of t_i,j=0 indicates the start of video acquisition. The units for t_i,j is seconds. (ε_H = 10.0, ε_∇ = 0.02)

		Theoretical		Algorithm
t_i	t_j	$α_{i}^{j}$	$α_{0}^{k}$	$\tilde{α_{i}^{j}}$	$\tilde{α_{k}^{0}}$	$Δ α_{i}^{j}$	$Δ α_{k}^{0}$
Full-length Clinical Case 1

0	0	-	1.00	-	1.00	-	-
4.50	6.75	1.28	1.28	1.28	1.28	0.00	0.00
290.25	412.25	1.19	1.52	1.21	1.55	0.02	0.03
1122.75	1197.00	0.933	1.42	0.980	1.50	0.047	0.08
2002.00	2139.00	1.07	1.52	1.02	1.51	0.05	0.01
2633.25	2637.75	0.954	1.45	0.911	1.40	0.043	0.05
2640.00	2646.75	0.925	1.34	0.870	1.24	0.055	0.10
2646.75	2655.75	1.33	1.78	1.35	1.68	0.02	0.10

Full-length Clinical Case 2

0	0	-	1.00	-	1.00	-	-
893.90	894.92	0.988	0.988	1.02	1.02	0.027	0.027
928.47	929.49	1.24	1.23	1.24	1.18	0.0004	0.046
935.59	936.61	1.12	1.38	1.11	1.32	0.008	0.061
2862.71	2863.73	1.13	1.55	1.19	1.52	0.069	0.024
2881.02	2882.03	1.02	1.58	1.05	1.60	0.028	0.018
3702.71	3703.73	1.15	1.82	1.11	1.78	0.04	0.037
3703.73	3704.75	1.39	2.53	1.32	2.35	0.07	0.184
3722.03	3724.07	0.630	1.60	0.633	1.49	0.003	0.108
3735.25	3737.29	0.856	1.37	0.871	1.30	0.015	0.070
3751.53	3753.56	1.65	2.25	1.69	2.19	0.04	0.067
3769.83	3771.86	0.800	1.80	0.798	1.75	0.002	0.057

Clinical Case 3

0	0	-	1.00	-	1.00	-	-
6809.49	6810.51	0.613	0.613	0.580	0.580	0.033	0.033
6856.27	6859.32	1.72	1.06	1.74	1.01	0.02	0.05
6865.42	6866.44	1.23	1.29	1.17	1.18	0.06	0.11
6871.53	6873.56	0.711	0.920	0.718	0.850	0.007	0.07
6878.64	6879.66	0.722	0.664	0.710	0.603	0.012	0.061

Clinical Case 4

0	0	-	1.00	-	1.00	-	-
3917.97	3923.39	0.903	0.903	0.912	0.912	0.008	0.008
3923.39	3924.75	0.612	0.553	0.631	0.575	0.019	0.022
3936.27	3939.66	1.50	0.829	1.43	0.826	0.065	0.003
3950.51	3951.19	1.12	0.926	1.12	0.921	0.001	0.005
3960.00	3968.14	1.29	1.20	1.30	1.19	0.002	0.005
3979.66	3982.37	1.23	1.48	1.17	1.40	0.055	0.072
3990.51	3992.54	0.465	0.687	0.462	0.648	0.003	0.038
4007.46	4008.81	1.35	0.927	1.32	0.853	0.033	0.073

Root Mean Square Error						0.044	0.062