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Nonlinear spatio-temporal model based on the geometry of the visual input

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E. Barth and A.B. Watson

NASA Ames Research Center, Moffet Field, CA.
**Abstract:**
__Purpose__: We propose a nonlinear model of spatio-temporal
processing which leads to an hierarchical visual representation and can
account for some basic psychophysical and neurophysiological results. __Methods__:
The model is inspired by the differential geometry of the spatio-temporal
hypersurface (STHS) corresponding to image intensity . The Riemann tensor
of the STHS involves computations which can be expressed as non-linear
combinations of spatio-temporal filters. __Results__: The visual
information load is sequentially reduced by extracting intrinsic 2D- and
3D features derived from the Riemannian and Gaussian curvatures respectively.
The Riemann tensor of the STHS is shown to incorporate the computation
of the optical flow under the constant-gradient assumption, as well as
the spatial properties of orientation and end-stopping. Our model further
involves the computation of two-dimensional space-time curvatures which
are implemented as "and"-type combinations of sustained and transient units.
Finally, we suggest top-down strategies for selecting the spatio-temporal
locations which contribute to the global motion percept such as to avoid
erroneous local motion estimates like those due to the aperture problem.
__Conclusions__: We argue that important properties of the visual
system may be understood as resulting from basic geometric processing of
the spatio-temporal visual input, as opposed to through terms such as "orientation
selectivity", "end-stopping", and "motion".
Supported by DFG grant Ba 1176/4-1 to EB
and NASA grant 199-06-12-39 to ABW.