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The Retina

Processing in the retina was modeled by filtering the logarithm of the input image \( \ln (I_{(i,j)}) \), where \( I_{(i,j)} \) represents image intensity at the retinal position \( (i,j) \), with the two-dimensional Mexican-hat function

$\displaystyle m_{(x,y)}$ $\textstyle =$ $\displaystyle \left[ \partial ^{2}_{x}+\partial ^{2}_{y}\right] \, \exp (-0.5*(x^{2}+y^{2})/\sigma ^{2})$  
  $\textstyle =$ $\displaystyle \frac{1}{\sigma ^{4}}(x^{2}+y^{2}-2*\sigma ^{2})\, \exp (-0.5*(x^{2}+y^{2})/\sigma ^{2})\, .$ (4)

The filter operation
e_{(k,l)}=\sum _{i,j}m_{(i,j)}\cdot \ln (I_{(k-i,l-j)})
\end{displaymath} (5)

is quite effective in removing relative contrast variations between the two stereo images.

In the simulations, \( \sigma ^{2}=2.0 \) is used, and the result \( e_{(k,l)} \) of this retinal filter operation is fed forward into the simple cell layer.