Hierarchical Learning from Natural Images

In this paper, we apply unsupervised learning methods to construct response functions for V1 simple cells, V1 complex cells, and V2 simple cells from a set of natural images. To support this, we reimplement existing sparse coding methods with the use of commercial optimization software. Introduction The human visual cortex contains a small number of self-contained functional units that fit together in reasonably well-understood pathways. The ventral pathway, which is concerned with object recognition, has four stages: V1, V2, V4, and IT (the inferior temporal lobule). V1 consists of simple cells that resemble localized, oriented Gabor filters and complex cells that respond to identical stimuli independent of phase. V1 outputs information to V2, which contains cells thought to respond to broader image contours. Since the landmark paper of Field & Olshausen (1996), it has been known that linear filters learned as sparse codings on datasets of natural images correspond almost exactly to the receptive fields of V1 simple cells. Hoyer & Hyvärinen (2000), among others, realized that learning an additional layer of nonlinear energies replicated the behavior of V1 complex cells. V1 has received the great majority of research focus in this area because its behavior is well understood and, perhaps, of suspicion that simple information-theoretic elements should not apply to higher levels. However, Hoyer & Hyvärinen (2002) demonstrates that similar sparse-coding techniques may yield the contour activation patterns one would expect in V2. In this paper, we expand on these results in two ways. First, we introduce learned features at every level, feeding forward from the image to V1 and from V1 to V2. This is in contrast to the hand-coded V1