Computational mechanisms underlying the second-order structure of cortical complex cells

We investigate what computational mechanisms give rise to the nonlinearity of the complex cell receptive field in the primary visual cortex. Complex cells are characterized by their nonlinear spatial properties such as spatial phase invariance and nonlinear response to multiple bar presentations. We carry out network simulations to estimate the second-order Wiener-Like kernels for several different models. Models with nonlinear spatial pooling of simple-cell-like linear subunits reproduce the :second-order kernels in good agreement with physiologically estimated kernels, while models without the pooling mechanism fail to reproduce the kernel. The structure of the kernels is independent of specific nonlinear transfer functions such as half-wave rectification and squaring. The results support the cascade mechanism consisting of simple cells' local feature extraction followed by nonlinear spatial pooling.