Abstract:
Slow Feature Analysis (SFA) [1] is an algorithm for extracting slowly varying features from a quickly varying signal. If applied to image sequences generated from natural images using a range of spatial transformations, SFA yields units that share many properties with complex and hypercomplex cells of early visual areas [2]. All units are responsive to Gabor stimuli with phase invariance, some show sharpened or widened orientation or frequency tuning, secondary response lobes, end/side-inhibition, or selectivity for direction of motion. Interestingly, the results do not depend on the higher-order statistics of natural images. We get virtually identical results with colored noise images. This permits a clear formulation of the conditions under which complex cell properties emerge and makes the problem amenable to an analytical treatment. Here we show that important complex cell properties can be derived by means of variational calculus from first principles and a few basic assumptions.
[1] Wiskott, L. and Sejnowski, T.J. (2002). Slow Feature Analysis: Unsupervised Learning of Invariances. Neural Computation, 14(4):715-770. http://itb.biologie.hu-berlin.de/~wiskott/Abstracts/WisSej2002.html
[2] Berkes, P. and Wiskott, L. (2005). Slow feature analysis yields a rich repertoire of complex cell properties. Journal of Vision, 5(6):579-602. http://journalofvision.org/5/6/9/