Jarmo Hurri, Aapo Hyvärinen
We show that two important properties of the primary visual cortex emerge when the principle of temporal coherence is applied to natural image sequences. The properties are simple-cell-like receptive ﬁelds and complex-cell-like pooling of simple cell outputs, which emerge when we apply two different approaches to temporal coherence. In the ﬁrst approach we extract receptive ﬁelds whose outputs are as temporally co- herent as possible. This approach yields simple-cell-like receptive ﬁelds (oriented, localized, multiscale). Thus, temporal coherence is an alterna- tive to sparse coding in modeling the emergence of simple cell receptive ﬁelds. The second approach is based on a two-layer statistical generative model of natural image sequences. In addition to modeling the temporal coherence of individual simple cells, this model includes inter-cell tem- poral dependencies. Estimation of this model from natural data yields both simple-cell-like receptive ﬁelds, and complex-cell-like pooling of simple cell outputs. In this completely unsupervised learning, both lay- ers of the generative model are estimated simultaneously from scratch. This is a signiﬁcant improvement on earlier statistical models of early vision, where only one layer has been learned, and others have been ﬁxed a priori.