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Complex Cells

Complex cells \( c_{(i,j)}(\varphi ,s) \) sample input from the simple cell layer by adding the responses of paired cells. In the reported simulations, data is sampled from a small patch of neighboring simple cells, so a complex cell has the response

c_{(i,j)}(\varphi ,s)=\sum _{k,l}b_{k}b_{l}[s_{(i-k,j-l)}^{a}(\varphi ,s)+s^{b}_{(i-k,j-l)}(\varphi ,s)]\, ,
\end{displaymath} (9)

with the filter kernel \( b_{k}=(0.0625,0.25,0.375,0.25,0.0625) \). Depending on the value of \( \varphi \), a complex cells responds to different relative shifts of images patches in left or right retinal image; we use the values \( \varphi =-\pi /4 \), \( +\pi /4 \), and 0. This corresponds to ``left'', ``right'' and ``no'' image motion. Thus, for \( \varphi =0 \), a complex cell measures local image contrast.