Abstract:
Slow feature analysis (SFA) is a new algorithm for extracting slowly varying features from a quickly varying signal [Wiskott & Sejnowski, 2002]. In the work presented here we apply SFA to 2D image sequences with translation, zoom, and rotation. The response properties of the emerging units are characterized firstly by the optimal excitatory stimuli S+ and the optimal inhibitory stimuli S- and secondly by the primary invariances, i.e. those variations of S+ to which the unit is most insensitive.
The optimal excitatory stimuli S+ we found are typically localized and oriented textures resembling Gabor wavelets. Their response is largely invariant to changes in the phase of the wavelet, which corresponds to the complex cell's insensitivity to exact location of a bar stimulus. These two properties have already been reproduced with earlier models and can be easily explained with a quadrature-pair of Gabor filters.
In addition we found functionally more complicated response properties that have, to our knowledge, not been found in other modelling studies, but which are typical for complex cells. The orientation tuning varied a lot between different units either due to S- stimuli that were non-orthogonal to S+, resulting in sharpened or even bimodal orientation tuning, or due to invariances to orientation changes, resulting in flat orientation tuning curves. We found similar sharpening or flattening effects also for the frequency tuning curves. In some cases the S- stimulus was adjacent to the S+ stimulus but aligned, resulting in the well known end-stopping behavior. We also found units tuned to corners or T-shapes.
Our model makes predictions about additional invariances, not yet found in physiological experiments, and about the relation between complex cell properties and the time scale of response variation.
Wiskott, L. and Sejnowski, T.J. (2002). Slow Feature Analysis: Unsupervised Learning of Invariances. Neural Computation, 14(4):715-770.
Keywords: primary visual cortex, complex cell properties, computational model, slow feature analysis