Abstract:
Ever since the seminal experiments by Hubel and Wiesel (Journal of Physiology, 1968), cells in V1 are usually conceived as edge detectors. These cells are commonly categorized as simple and complex cells based on their degree of invariance with respect to phase shift of their preferred stimulus. Further physiological studies revealed additional receptive field properties such as orientation and frequency selectivity (De Valois et al, Vision Research, 1982; De Valois et al, Vision Research, 1982).
Recently, Berkes and Wiskott (Journal of Vision, 2005) demonstrated that the unsupervised learning principle of temporal slowness can account for a wide range of complex cell properties, including optimal stimuli, phase shift invariance, and orientation and frequency selectivity. Their simulations showed that the properties of the simulated receptive fields crucially depend on the transformations present in the image sequences used for training while being largely independent of the statistics of natural images.
We will present a mathematical framework for their simulations, which is based on the Lie group of the transformations used in the simulations. It allows to analytically derive non-linear receptive fields whose properties are in agreement with the simulations and with physiological data.
Apart from showing that the results of the simulations can be largely understood analytically, our theory provides an intuitive understanding of the self-organization mechanism in the principle of temporal slowness. The success of the theory confirms the conclusion of Berkes and Wiskott that the properties of the functions, which optimize temporal slowness are not adaptations to the content of the images used for training but to the transformations present in the training data. The agreement of the model with physiological data suggests that the structure of receptive fields in V1 may be the results of an adaptation to dominant transformations in natural visual scenes.