1. We have analyzed receptive fields (RFs) of directionally selective (DS) complex cells in the striate cortex of the cat. We determined the extent to which the DS of a complex cell depends on spatially identifiable subunits within the RF by studying responses to an optimally oriented, three-luminance-valued, gratinglike stimulus that was spatiotemporally randomized. 2. We identified subunits by testing for nonlinear spatial RF interactions. To do this, we calculated Wiener-like kernels in a spatial superposition test that depended on two RF positions at a time. The spatial and temporal separation of light and dark bars at these two positions varied over a spatial range of 8 degrees and a temporal range of +/- 112 ms in increments of 0.5 degree and 16 ms, respectively. 3. DS responses in complex cells cannot be explained by their responses to single light or dark bars because any linear superposition of responses whose time course is uniform across space shows no directional preference. 4. Nonlinear interactions between a flashed reference bar that is fixed in position and a second bar that is flashed at surrounding positions help explain DS by showing multiplicative-type facilitation for bar pairs that mimic motion in the preferred direction and suppression for bar pairs that mimic motion in the null direction. Interactions in the preferred direction have an optimal space/time ratio (velocity), exhibited by elongated, obliquely oriented positive domains in a space-time coordinate frame. This relationship is inseparable in space-time. The slope of the long axis specifies the preferred speed, and its negative agrees with the most strongly suppressed speed in the opposite direction. 5. When the reference bar position is moved across the RF, the spatiotemporal interaction moves with it. This suggests the existence of a family of nearly uniform subunits distributed across the RF. We call the subunit interaction, as averaged across the RF, the "motion kernel" because its spatial and temporal variables are those necessary to specify the velocity, the only parameter that distinguishes a moving image from a temporally modulated stationary image. The nonlinear interaction shows a spatial periodicity, which suggests a mechanism of velocity selectivity for moving extended images.(ABSTRACT TRUNCATED AT 400 WORDS)

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1. Directionally asymmetric (DA) units respond preferentially to one direction of image movement. If that preferred direction is independent of stimulus contrast then the DA unit is considered directionally selective (DS). We have analyzed receptive-field (RF) properties of striate units with these properties by presenting bar-shaped stimuli that are moved in a stepwise sequence. Short interstimulus durations for certain ranges of step size elicit DA responses similar to those from smooth movement, while still allowing identification of on- and off-components of the response. 2. We have been able to isolate three mechanisms underlying DA and DS. The simplest, superposition, explains the dependence of preferred direction on stimulus contrast found in some DA units. It relies completely on asymmetries in static RF regions to provide an advantage for one direction of image motion by means of the simultaneity of image elements leaving an apparently inhibitory region and entering an excitatory one. 3. For all DA and DS units we have encountered forward inhibition of otherwise excitatory influences that reduces the responsiveness in the antipreferred direction. The spatial specificity of inhibitory target RF regions and the nonlinearity of the effect suggest that lateral inhibition may be transmitted via sequence-detecting subunits. 4. Units that do not show superposition in the preferred direction exhibit forward facilitation of responses in a nonlinear and target-specific way which suggests that facilitation may also be transmitted via sequence-detecting subunits. 5. Each of these mechanisms depends on short-lived influences that are laterally transmitted between 0.125 and 0.5 degrees in visual space. These spatial and temporal values are appropriate for the analysis of smooth movement by the visual system. 6. Stepwise movement sequences using dark bars on a bright background demonstrate for some DA units exactly the same mechanisms as demonstrated using bright-bar sequences in other units or, in the case of DS units, in the same units. In such DS units, which do not normally exhibit strong stationary RF asymmetries, differential sensitivity of the nonlinear DS mechanisms to stimulus elements of either contrast will yield an effective preferred movement direction for complex stimuli.

Complex cells in the cat's visual cortex show nonlinearities in processing of image luminance and movement. To study mechanisms, initially we have represented the chain of neurons from retina to cortex as a black-box model. Independent information about the visual system has helped us cast this "Wiener-kernel" model into a dynamic-linear/static-nonlinear/dynamic-linear (LNL) cascade. We then use system identification techniques to define the nature of these transformations directly from responses of the neuron to a single presentation of a stimulus composed of a sequence of white-noise-modulated luminance values. The two dynamic linear filters are mainly low-pass, and the static nonlinearity is mainly of even polynomial degree. This approximate squaring function may be effected in the animal by soft-thresholding each of the linear ON- and OFF-channel signals and then summing them, which account for "ON-OFF" responses and for the squaring operation needed for computation of "motion energy", both observed in these neurons.