As opposed to dealing with the geometry of objects in the 3D world, this paper considers the geometry of the visual input itself, i.e. the geometry of the spatio-temporal hypersurface defined by image intensity as a function of two spatial coordinates and time. The Riemann curvature tensor of this hypersurface can be used to estimate speed and direction of motion in four different ways. While this four motion vectors are equal for pure translations, they differ otherwise, e.g. for discontinuous motion. The differences can be used to build confidence measures. Applications demonstrate that the approach can improve the computation of motion by avoiding the aperture problem, discontinuous motions, and occlusions. Moreover, the approach allows to predict global motion percepts and properties of MT neurons and it is argued that important aspects of early and middle level visual coding may be understood as resulting from basic geometric processing of the spatio-temporal visual input.
Keywords: vision models, motion, flow-field, nonlinear features, curvature tensor

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