Photoreceptor non-linearities can account for the MacAdam ellipses D.Alleysson & J. Hérault T.I.R.F - I.N.P. Grenoble France [email protected] in collaboration with C.S.E.M Neuchâtel

Model of photoreceptor non linearity Michaelis-Menten’s law

x

x= α

ε

1 2

X X + X0

Adaptation

α

X0 ≈ X

ε X0

∆ X2

∆ X1

X

Same Perception threshold different stimulation

ε → ∆ X1 ≠ ∆ X 2

Measure of just noticeable difference (jnd) of color Cone excitatory space LMS

CIE xy space

y

S

x

L-M x   L  0.15 0.54 − 0.03   M  = Y y  − 0.15 0.46 0.03   y        S   0 0 0.001  1 − x − y 

Smith & Pokorny

Model principle Cone transduction space

Cone excitation space

X X + X0

s

S

l

φε

m

M

L

perceptual jnd l= αl

m= αm

L L + L0 M M + M0

S s= αs S + S0

y

x

Parameters Adjustment α i X / ( X + X0 i )

For each MacAdam’s ellipse i : X 0i

: depend on adaptation states L0 = 66   M 0 = 33  S0 = 016 . 

α

i

: gain related to cones (density, response, ...) MacAdam’s ellipses

Model’s ellipses best α

i

 α l = α m = 1665   α s = 226

α = α

i

Results & conclusion

- MacAdam - Model y

- biological model (non ad-hoc function) - 1st stage can explain the phenomenon (≠ Guth)

- Still to improve : influence of light adaptation on the non linearity

x