Elaborated Reichardt detectors

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Abstract
The elaborated Reichardt detector (ERD) proposed by van Santen and Sperling [ J. Opt. Soc. Am. A 1, 451 ( 1984)], based on Reichardt’s motion detector [ Z. Naturforsch. Teil B 12, 447 ( 1957)], is an opponent system of two mirror-image subunits. Each subunit receives inputs from two spatiotemporal filters (receptive fields), multiplies the filter outputs, and temporally integrates the product. Subunit outputs are algebraically subtracted to yield ERD output. ERD’s can correctly indicate direction of motion of drifting sine waves of any spatial and temporal frequency. Here we prove that with a careful choice of either temporal or spatial filters, the subunits can themselves become quite similar or equivalent to the whole ERD; with suitably chosen filters, the ERD is equivalent to an elaborated version of a motion detector proposed by Watson and Ahumada [NASA Tech. Memo. 84352 (1983)]; and for every choice of filters, the ERD is fully equivalent to the detector proposed by Adelson and Bergen [ J. Opt. Soc. Am. A 2, 284– 299 ( 1985)]. Some equivalences between the motion detection (in x, t) by ERD’s and spatial pattern detection (in x, y) are demonstrated. The responses of the ERD and its variants to drifting sinusoidal gratings, to other sinusoidally modulated stimuli (on–off gratings, counterphase flicker), and to combinations of sinusoids are derived and compared with data. ERD responses to two-frame motion displays are derived, and several new experimental predictions are tested experimentally. It is demonstrated that a system containing ERD’s of various sizes can solve the correspondence problem in two-frame motion of random-bar stimuli and shows the predicted phase dependencies when confronted with displays composed of triple sinusoids combined either in amplitude modulation phase or in quasi-frequency modulation phase. Finally, it is shown that, while the ERD may in some instances give larger responses to nonrigid than to rigid displacements, the subunits (and hence the ERD) are especially well behaved with continuous movement of rigid or smoothly deforming objects.