4-dimensional CSFs: spatial frequency, luminance, size and eccentricity

Fitting error

DatasetFitting errorSensitivity adjustment
stelaCSFVDP CSFRovamo 1995 CSFFovVideoVDP CSFstelaCSFVDP CSFRovamo 1995 CSFFovVideoVDP CSF
Average training4.08 [dB]8.76 [dB]5.63 [dB]6.36 [dB]N/AN/AN/AN/A
modelfest3.26 [dB]3.69 [dB]3.44 [dB]2.21 [dB]1.0001.0001.0001.000
hdrvdp_csf3.26 [dB]8.72 [dB]6.35 [dB]3.15 [dB]1.2551.6750.9570.990
hdr_csf3.40 [dB]5.94 [dB]5.15 [dB]3.97 [dB]0.7190.4870.6150.713
rovamo19932.77 [dB]6.38 [dB]1.91 [dB]4.81 [dB]1.6362.5771.8881.506
virsu19795.11 [dB]9.73 [dB]6.24 [dB]7.91 [dB]1.2101.3730.9060.995
virsu19823.33 [dB]8.72 [dB]5.12 [dB]7.84 [dB]0.7100.3750.5070.872
anderson19916.31 [dB]12.53 [dB]7.81 [dB]10.58 [dB]1.0061.8482.5161.624

Model comparison statistics

ModelSum of Square Errors (SS)Degrees of freedom (df)F-testAIC
F-statisticp-value
stelaCSF (Reference Model)18.032366N/AN/A-1157.08
VDP CSF81.37138185.70420.0000 ✓-594.893
Rovamo 1995 CSF34.13537925.1410.0000 ✓-932.288
FovVideoVDP CSF48.07738532.09470.0000 ✓-809.698

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 sd in the paper (Eq. 18).

Model parameters

stelaCSF
p.ach_sust.S_max = [ 52.4592 3.81915 0.222862 7.27366e-07 1.15157e+10 ]; p.ach_sust.f_max = [ 1.52743 14.5391 0.257662 ]; p.ach_sust.bw = 0.0163998; p.ach_sust.a = 0.00677941; p.ach_trans.S_max = [ 1.17739 57.6281 ]; p.ach_trans.f_max = 0.00220211; p.ach_trans.bw = 2.07562; p.ach_trans.a = 0.000273289; p.sigma_trans = 0.141447; p.sigma_sust = 32.2325; p.ecc_drop = 0.0322032; p.ecc_drop_nasal = 0.0199422; p.ecc_drop_f = 0.0243679; p.ecc_drop_f_nasal = 0.0162802;
VDP CSF
p.P = 256.183; p.ob = 1.00787; p.k = 0.300253; p.epsilon = 1.19203; p.a_l_m = 38.4614; p.b_l_m = 1.64298;
Rovamo 1995 CSF
p.ach_sust.S_0 = 38.6286; p.ach_sust.f_max = 9.73821; p.ach_sust.f0 = 0.503634; p.ach_trans.S_0 = 35836.4; p.ach_trans.f_max = 13.8597; p.ach_trans.f0 = 9.23544e-05; p.cm_e2 = 1.43973; p.cm_e2_nasal = 2.83047;
FovVideoVDP CSF
p.S_0 = 2.12826; p.k_cm = 1.02008;

CSF model: stelaCSF


CSF model: VDP CSF


CSF model: Rovamo 1995 CSF


CSF model: FovVideoVDP CSF


Legend

To keep the plots legible, only up to 3 models are plotted.

Dataset: [modelfest] ModelFest

Achroatic CSF as a function of frequency

Dataset: [hdrvdp_csf] HDR-VDP CSF

Achromatic CSF as a function of frequency

Achromatic CSF as a function of size

Dataset: [hdr_csf] High Dynamic Range CSF

CSF as the function of frequency at different luminance levels (fixed number of cycles)

CSF for different number of cycles

Dataset: [rovamo1993] Rovamo et al. 1993

CSF as the funcation of stimulus area

Dataset: [virsu1979] Virsu & Rovamo 1979

Contrast sensitivity of central and peripheral vision as a function of spatial frequency and eccentricity

Dataset: [virsu1982] Virsu et al. 1982

Contrast sensitivity as the function of frequency

Contrast sensitivity as the function of eccentricity

Dataset: [anderson1991] Anderson et al. 1991

Contrast sensitivity as the function of retinal visual field (at 8 Hz)