R.O. Dror. Accuracy of visual velocity estimation by Reichardt correlators. Master's thesis, University of Cambridge, 1998.
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Abstract

While the Reichardt correlator and its mathematical equivalents do not signal true image velocity, a great deal of experimental evidence establishes them as mechanisms for visual motion detection in insects, humans, and other animals. This study examines the accuracy with which Reichardt correlators can provide velocity estimates in an organism's natural visual environment. I develop an analytical method which predicts the mean response of a correlator to moving broad-band images. Combined with recent findings that natural images have highly stereotyped power spectra, my analysis predicts a consistent correspondence between mean correlator response and velocity. This predictable relationship, confirmed by simulations using a set of natural images, allows the otherwise ambiguous Reichardt correlator to act as a velocity estimator in the natural environment. My analysis and simulations also suggest that processes commonly found in visual systems, such as prefiltering, saturation, integration, and adaptation, improve the reliability of velocity estimation and expand the range of velocities which the correlator can code. Experimental recordings of the responses of wide-field neurons to moving broad-band images confirm my analytical predictions. By explaining how visual systems overcome the shortcomings of the Reichardt correlator to take advantage of its simplicity, generality, and robustness to noise, this work illuminates the functional significance of elements of biological motion detection systems as well as their potential relevance to machine vision.