Analysis of natural images by independent quadratic forms and temporally coherent quadratic forms

Several studies have succeeded to correlate natural image statistics with receptive field properties of neurons in the primary visual cortex such as simple cells. However, complex cell properties have not fully explained by previous studies of natural image statistics. In this study, we deal with quadratic forms. Because they form a class of functions that includes complex cell responses and many other functions. We employ two criteria for learning parameters of quadratic forms. They are independence of output and temporal coherence of output. By independence criterion, squared responses of simple cells were obtained and complex cell properties were not reproduced. On the other hand, by maximizing the sparseness of difference of output, we obtained complex cell properties among other kind of quadratic forms.