5-dimensional CSFs: spatial and temporal frequency, luminance, size and eccentricity

Fitting error

Dataset	Fitting error		Sensitivity adjustment
Dataset	stelaCSF	FovVideoVDP CSF	stelaCSF	FovVideoVDP CSF
Average training	4.15 [dB]	9.15 [dB]	N/A	N/A
modelfest	3.05 [dB]	6.04 [dB]	1.000	1.000
hdrvdp_csf	3.69 [dB]	5.18 [dB]	1.283	1.310
hdr_csf	3.54 [dB]	5.60 [dB]	0.694	0.945
rovamo1993	2.79 [dB]	6.62 [dB]	1.472	1.956
robson1966	2.80 [dB]	10.43 [dB]	0.970	0.651
laird2006	5.41 [dB]	6.20 [dB]	0.801	1.002
snowden1995	5.04 [dB]	14.38 [dB]	0.641	0.305
virsu1979	6.84 [dB]	9.26 [dB]	1.072	1.170
virsu1982	5.69 [dB]	8.89 [dB]	1.175	1.072
wright1983	2.71 [dB]	7.15 [dB]	0.678	0.502
anderson1991	6.90 [dB]	11.83 [dB]	2.938	1.793

Model comparison statistics

Model	Sum of Square Errors (SS)	Degrees of freedom (df)	F-test		AIC
Model	Sum of Square Errors (SS)	Degrees of freedom (df)	F-statistic	p-value	AIC
stelaCSF (Reference Model)	41.769	826	N/A	N/A	-2527.24
FovVideoVDP CSF	199.958	845	164.644	0.0000 ✓	-1223.22

We use AIC and F-test to test whether the difference in fitting error is statistically significant at alpha=0.05 level. Both statistical metrics take the number of optimized parameters into account.

F-test: For F-test, we compare the fitting results from stelaCSF with those of other models. The F-static is calculated using the residual sum of squares and degrees of freedom (number of data points - number of optimized parameters) from both models. The corresponding p-value indicates whether or not the null hypothesis is rejected, where H₀: the stelaCSF does not provide significant better fit than the other model. The p-values less than 0.05 indicates that stelaCSF provides a better fit to the data at the significance level of 0.05 (marked with ✓). We performed the F-test for all individual datasets as well as for all datasets combined. For smaller datasets, where the number of data points are comparable to the number of model parameters, F-test can not provide any results since it indicates there is more variance within the models' fits than between.

AIC: Akaike information criterion is a statistical estimator of prediction error and relative quality of the models, which accounts for the number of parameters of each model. The model with the lower AIC score is considered to be better and with a good balance of error value and the number of parameters.

The sensitivity adjustment column contains a multiplier that is used to adjust the sensitivity of each datasets. It corresponds to s_d in the paper (Eq. 18).

Model parameters

stelaCSF

p.ach_sust.S_max = [ 68.9501 59.5023 0.164274 7.54866e-07 7.77268e+09 ]; p.ach_sust.f_max = [ 1.62144 36.6565 0.255823 ]; p.ach_sust.bw = 0.000219263; p.ach_sust.a = 0.103686; p.ach_trans.S_max = [ 0.500846 57.3469 ]; p.ach_trans.f_max = 0.0267489; p.ach_trans.bw = 1.75147; p.ach_trans.a = 0.000273289; p.sigma_trans = 0.12314; p.sigma_sust = 5.79336; p.ecc_drop = 0.0296662; p.ecc_drop_nasal = 0.0113638; p.ecc_drop_f = 0.0190062; p.ecc_drop_f_nasal = 0.0193858;

FovVideoVDP CSF

p.S_0 = 1; p.k_cm = 1;