Abstract

We describe a procedure for recovering the global, two-dimensional velocity of translation of an image by incorporating spatial filtering, and, optionally, temporal filtering, into a scheme that employs a novel and generalized version of the gradient algorithm of motion detection. Motion within a patch is analyzed in parallel by six different spatiotemporal filters derived from two linearly independent spatiotemporal kernels. Advantageous features of this scheme are that (a) the average velocity within the patch is determined in a single step and without recourse to constraints imposed by neighboring calculations or assumptions about the global structure of the pattern; (b) there is no need to impose a smoothness constraint on the optical flow; (c) the need to compute spatial derivatives directly is obviated by our combining the outputs of the kernel filters with the outputs of other filters whose weighting functions are partial derivatives, in space, with respect to the first set; (d) there is no need to compute second derivatives, and thus the scheme is potentially more resistant to noise than certain other schemes; (e) the spatiotemporal kernels can be chosen almost completely arbitrarily and can therefore be tailored to maximize signal reliability; and (f) the measurement of velocity can be made as local or as global as desired by altering the size of the patch that is viewed by the filters. The validity of the scheme is demonstrated on a computer by application to a variety of real, moving images.

© 1991 Optical Society of America

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