CSF models as functions of spatial and temporal frequency, luminance and area

Fitting error

Dataset Fitting error Sensitivity adjustment
castleCSF original Barten's CSF (1999) stelaCSF castleCSF original Barten's CSF (1999) stelaCSF
Average training 3.38 ± 0.09 [dB] 3.83 ± 0.09 [dB] 4.21 ± 0.09 [dB] N/A N/A N/A
Average testing 3.48 ± 0.35 [dB] 3.87 ± 0.35 [dB] 4.37 ± 0.37 [dB] N/A N/A N/A
modelfest 2.48 [dB] 2.54 [dB] 2.55 [dB] 0.914 1.229 1.231
hdrvdp_csf 2.28 [dB] 3.83 [dB] 2.24 [dB] 1.209 1.732 1.628
rovamo1993 3.06 [dB] 2.84 [dB] 3.04 [dB] 1.539 2.309 2.075
laird2006 5.43 [dB] 6.20 [dB] 5.98 [dB] 0.818 0.895 0.961
snowden1995 4.15 [dB] 4.51 [dB] 5.64 [dB] 1.053 1.203 1.197
robson1966 2.40 [dB] 2.43 [dB] 2.90 [dB] 0.941 1.131 1.128
virsu1979 4.17 [dB] 4.68 [dB] 4.76 [dB] 1.368 1.902 1.707
virsu1982 2.09 [dB] 1.98 [dB] 3.19 [dB] 0.901 1.143 1.225
wright1983 2.79 [dB] 3.55 [dB] 2.80 [dB] 0.847 1.015 1.027
colorfest 2.95 [dB] 2.87 [dB] 2.94 [dB] 0.925 0.877 0.853
hdr_csf 3.46 [dB] 4.09 [dB] 3.53 [dB] 1.000 1.000 1.000
hdr_csf_disc 1.85 [dB] 2.20 [dB] 1.39 [dB] 1.121 1.160 0.859

Model comparison statistics

Model No. of free parameters Sum of Square Errors (SS) Degrees of freedom (df) F-test AIC
F-statistic p-value
castleCSF (Reference Model) 53 16.759 526 N/A N/A -1945.04
original Barten's CSF (1999) 13 21.032 566 3.35297 0.0000 ✓ -1893.53
stelaCSF 21 26.093 558 9.15527 0.0000 ✓ -1752.69

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 castleCSF 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 castleCSF does not provide significant better fit than the other model. The p-values less than 0.05 indicates that castleCSF 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.

Model parameters

castleCSF
M_lms2acc = 1.0000 1.0000 0 1.0000 -2.3112 0 -1.0000 -1.0000 50.9875 p.rg.sigma_sust = 16.5442; p.rg.beta_sust = 1.15463; p.rg.ch_sust.S_max = [ 621.872 38.001 0.445858 ]; p.rg.ch_sust.f_max = 0.0154857; p.rg.ch_sust.bw = 1.93605; p.rg.A_0 = 2850.03; p.rg.f_0 = 0.0690099; p.rg.ecc_drop = 0.0591431; p.rg.ecc_drop_nasal = 2.89648e-05; p.rg.ecc_drop_f = 2.04986e-69; p.rg.ecc_drop_f_nasal = 0.180118; p.yv.sigma_sust = 7.91906; p.yv.beta_sust = 0.998701; p.yv.ch_sust.S_max = [ 79.899 62.6796 0.402931 ]; p.yv.ch_sust.f_max = 0.00303902; p.yv.ch_sust.bw = 1.42105; p.yv.A_0 = 2.83319e+07; p.yv.f_0 = 0.000637474; p.yv.ecc_drop = 0.00357397; p.yv.ecc_drop_nasal = 5.85804e-141; p.yv.ecc_drop_f = 0.0080878; p.yv.ecc_drop_f_nasal = 0.0147658; p.ach.ach_sust.S_max = [ 62.2205 3.79547 0.165478 5.54618e-07 1.52174e+10 ]; p.ach.ach_sust.f_max = [ 1.55633 39.3923 0.272818 ]; p.ach.ach_sust.bw = 0.000213192; p.ach.ach_sust.a = 0.174327; p.ach.ach_sust.A_0 = 157.103; p.ach.ach_sust.f_0 = 0.702338; p.ach.ach_trans.S_max = [ 0.216511 2741.3 ]; p.ach.ach_trans.f_max = 0.000326823; p.ach.ach_trans.bw = 2.67165; p.ach.ach_trans.a = 0.000241177; p.ach.ach_trans.A_0 = 3.31793; p.ach.ach_trans.f_0 = 3.14133; p.ach.sigma_trans = 0.0824625; p.ach.sigma_sust = 10.3141; p.ach.omega_trans_sl = 2.44328; p.ach.omega_trans_c = 4.83666; p.ach.ecc_drop = 0.0259781; p.ach.ecc_drop_nasal = 0.0452708; p.ach.ecc_drop_f = 0.0217926; p.ach.ecc_drop_f_nasal = 0.0068348; Parameters for Ach component: p.ach_sust.S_max = [ 62.2205 3.79547 0.165478 5.54618e-07 1.52174e+10 ]; p.ach_sust.f_max = [ 1.55633 39.3923 0.272818 ]; p.ach_sust.bw = 0.000213192; p.ach_sust.a = 0.174327; p.ach_trans.S_max = [ 0.216511 2741.3 ]; p.ach_trans.f_max = 0.000326823; p.ach_trans.bw = 2.67165; p.ach_trans.a = 0.000241177; p.ach_trans.A_0 = 3.31793; p.ach_trans.f_0 = 3.14133; p.sigma_trans = 0.0824625; p.sigma_sust = 10.3141; p.omega_trans_sl = 2.44328; p.omega_trans_c = 4.83666; p.ecc_drop = 0.0259781; p.ecc_drop_nasal = 0.0452708; p.ecc_drop_f = 0.0217926; p.ecc_drop_f_nasal = 0.0068348; Parameters for RG component: p.ch_sust.S_max = [ 621.872 38.001 0.445858 ]; p.ch_sust.f_max = 0.0154857; p.ch_sust.bw = 1.93605; p.A_0 = 2850.03; p.f_0 = 0.0690099; p.sigma_sust = 16.5442; p.beta_sust = 1.15463; p.ecc_drop = 0.0591431; p.ecc_drop_nasal = 2.89648e-05; p.ecc_drop_f = 2.04986e-69; p.ecc_drop_f_nasal = 0.180118; Parameters for YV component: p.ch_sust.S_max = [ 79.899 62.6796 0.402931 ]; p.ch_sust.f_max = 0.00303902; p.ch_sust.bw = 1.42105; p.A_0 = 2.83319e+07; p.f_0 = 0.000637474; p.sigma_sust = 7.91906; p.beta_sust = 0.998701; p.ecc_drop = 0.00357397; p.ecc_drop_nasal = 5.85804e-141; p.ecc_drop_f = 0.0080878; p.ecc_drop_f_nasal = 0.0147658;
original Barten's CSF (1999)
p.k = 6.79262; p.eta0 = 0.0373135; p.sigma0 = 0.317603; p.eg = 3.3; p.u00 = 3.73259; p.Phi00 = 3e-08; p.T = 0.0664566; p.Xmax0 = 19.3648; p.Nmax = 7.1407; p.tau10 = 0.0396901; p.tau20 = 0.0372527; p.n1 = 5.11908; p.n2 = 1.24924;
stelaCSF
p.ach_sust.S_max = [ 43.4249 0.5001 0.286464 7.28816e-07 8.54798e+09 ]; p.ach_sust.f_max = [ 1.63018 57.679 0.262735 ]; p.ach_sust.bw = 0.000219131; p.ach_sust.a = 0.0611494; p.ach_trans.S_max = [ 0.432997 446.224 ]; p.ach_trans.f_max = 0.00029198; p.ach_trans.bw = 2.8167; p.ach_trans.a = 0.000273289; p.sigma_trans = 0.140939; p.sigma_sust = 11.773; p.ecc_drop = 0.0296662; p.ecc_drop_nasal = 0.0113638; p.ecc_drop_f = 0.0190062; p.ecc_drop_f_nasal = 0.0193858;

↸CSF model: castleCSF

L+M

↸CSF model: original Barten's CSF (1999)

L+M

↸CSF model: stelaCSF

L+M

Legend

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

↸Dataset: [modelfest] ModelFest

Achromatic 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: [rovamo1993] Rovamo et al. 1993

CSF as the funcation of stimulus area

CSF as the function of spatial frequency

↸Dataset: [laird2006] Laird et al. 2006

Achromatic CSF as a function of temporal frequency for different spatial frequencies

↸Dataset: [snowden1995] Snowden et al. 1995

Temporal contrast sensitivity at different spatial frequencies and luminance levels

↸Dataset: [robson1966] Robson 1966

Spatial CSF for different temporal frequencies

Temporal CSF for different spatial frequencies

↸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

↸Dataset: [wright1983] Wright and Johnson 1983

CSF as function of eccentricity

↸Dataset: [colorfest] ColorFest

Chromatic CSF as a function of frequency

↸Dataset: [hdr_csf] High Dynamic Range CSF

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

↸Dataset: [hdr_csf_disc] High Dynamic Range Disc CSF

CSF as the function of size at different luminance levels