
White balance 171
preference φ ∈ [0, π) can be modeled with the following PDE [108]:
∂a(r, φ, t)
∂t
= −αa(r, φ, t)+µ
Z
π
0
Z
R
2
ω(r, φkr
0
, φ
0
)σ(a(r
0
, φ
0
, t))dr
0
dφ
0
+h(r, φ, t),
(7.31)
where α, µ are coupling coefficients, h(r, φ, t) is the external input (visual
stimuli), ω(r, φkr
0
, φ
0
) is a kernel that decays with the differences |r−r
0
|, |φ−φ
0
|
and σ is a sigmoid function. If we ignore the orientation φ and assume that
the input h is constant in time, it can be shown that Equation 7.31 is closely
related to the gradient descent equation of 7.30, where neural activity a plays
the role of image value I, sigmoid function σ behaves as the derivative of
the absolute ...