More specifically, orientation is encoded in a bank of orientation-tuned channels φ (
N = 60, equally spread) defined as von Mises (circular normal) distributions
\begin{eqnarray}{\varphi _i}\left( \theta \right) \sim V\left( {{\mu _i},{\kappa _\varphi }} \right), \quad \end{eqnarray}
where µ
i is the preferred orientation of channel φ
i and κ
φ is the channel's spread. Each channel produces a response
n to a stimulus
s depending on the orientation θ
s and contrast
cs of the stimulus. When contrast is maximum (i.e.,
cs = 1), the response of each channel
ni is computed from a von Mises distribution
\begin{eqnarray}{n_i}\left( {{\theta _s},{c_s} = 1} \right) = V\left( {{\theta _s}{\rm{|}}{\mu _i},{\kappa _\varphi }} \right), \quad \end{eqnarray}
where θ
s is the orientation of the stimulus and κ
φ is the spread at maximum contrast. The response distribution is normalized to [0, 1], where 1 indicates maximum response of a channel and 0 no response at all. As contrast decreases, the response of a channel is calculated from
\begin{eqnarray}{n_i}\left( {{\theta _s},{c_s}} \right) = \frac{{c_s^{{c_{exp}}}}}{{c_{50}^{{c_{exp}}} + c_s^{{c_{exp}}}}}V\left( {{\theta _s}{\rm{|}}{\mu _i},{\kappa _c}} \right), \quad \end{eqnarray}
where
c50 is the semi-saturation constant,
cexp is the exponent, and κ
c is the spread at contrast
c. While it is usually assumed that orientation bandwidth is contrast invariant, it has been shown to decrease with contrast especially for stimuli presented at variable contrasts (
Nowak & Barone, 2009). We used a saturation function for the decrease in tuning width so that κ
c is calculated from
\begin{eqnarray}{\kappa _c} = \frac{{c_s^\varepsilon }}{{w_{50}^\varepsilon + c_s^\varepsilon }}{\kappa _\varphi }, \quad \end{eqnarray}
where
w50 is the semi-saturation constant, ε is the exponent, and κ
φ is the spread at maximum contrast.