Introduction. The purpose of the study was to determine the local processing structure for the depth form in complex visual scenes. We approached this issue by evaluating the detection of sinusoidal ripples in the stereoscopic disparity of a noise field. Local processing structure may be understood as the effective receptive fields for processing the form information in a disparity field. The local disparity detectors provide the information as to the depth profile over space, together with a ‘depth-cleaning’ stage to resolve the ambiguities of multiple correspondence among the large number of dots in a random element stereogram. The result is (usually) a unitary depth surface. But having obtained the surface, the visual system is face with the problem of ‘understanding’ or processing the form of this surface. There are four general approaches that the brain might take to this problem.

1. An attentional tracking system. One may envisage an attentional focus tracking the derived depth surface, encoding its properties in the fashion that an aeroplane navigator might encode the topography of some countryside over which the aeroplane is flying. The encoding would form some sort of list of coordinate for features of interest. Depth processing would thus be entirely local and would exhibit no extended summation field.

2. A single channel system of summation fields across the cyclopean retina, reporting in parallel some property such as local curvature of the depth image, from which the form of the depth image could be adduced. The summation fields should then have simple properties that are uniform with orientation.

3. An adaptive channel system that can adjust itself for an ideal match to whatever disparity profile information is available in the depth image. Such a mechanism should exhibit ideal observer summation behavior under all conditions. That is, once threshold is established for the smallest cyclopean Gabor patch, detection should improve with the square root of area of the Gabor envelope, regardless of its shape.

4. A multiple channel system of form processing where the form is processed by arrays of cyclopean receptive fields specific to particular aspects of the form of the depth image.

Methods. Sinusoidal Gabor patches of cyclopean depth modulation (disparity wavelets).were generated in a stereoscopic display. To obtain subpixel resolution of disparity, the random base stimulus was filtered noise with a 7’ blur function and an r.m.s. contrast of 50%. Disparity thresholds for front/back depth discrimination were determined by our maximum likelihood Psi staircase as a function of width and height of the cyclopean Gabor, for both horizontal and vertical cyclopean bar carriers, over a full range of carrier spatial frequencies.

Disparity thresholds were measured for cyclopean Gabor targets with an envelope width of one cycle (width at half-height) in both directions, one cycle vertically by eight cycles horizontally, and eight cycles vertically by one horizontally. The same paradigm was employed for cyclopean Gabor targets with horizontal ripples and those with vertical ripples.

Results. The thresholds as a function of spatial frequency of the vertical ripples are shown for one observer in Fig. 1. The functions are indistinguishable within the range of the measurement noise (+ 0.11 log units of disparity). This result implies that the summation units for vertical ripples are limited to one cycle in both directions, since providing an additional five cycles of width or height generates no improvement in the detectability of the patch.

For horizontal ripples, a very different picture is obtained (Fig. 2). Summation in the vertical direction (across ripples) is substantial, averaging 0.2 log units with no significant variation across spatial frequency. To interpret this result, we need to know whether summation proceeds according to the single channel model (log slope of -1) or the ideal observer model of multiple receptive fields up to the summation size, which proceeds with a log slope of -1/2. Size summation data (not shown) indicate that the ideal-observer model is that one in operation for this system. This means that, as the ripple wavelength varied from 0.5 to 2.8 degrees, summation was available over about 2.5 cycles in all cases. Note that the summation field did not maintain a fixed extent in visual angle, but varied with spatial frequency. The only systems that have this property are either arrays of receptive fields of various scales (scaling uniformly with ripple frequency) or a self-scaling adaptive filter. Any summation filed of fixed size would show a reciprocal variation in numbers of cycles with spatial frequency.

Summation in the horizontal (elongation) direction is different again from that in the vertical direction. Now the improvement in sensitivity extends to 0.4 log units, again uniformly with spatial frequency. On the same ideal observer model, this implies length summation horizontally up to about 6 cycles worth of elongation. Thus, the cyclopean receptive fields are surprisingly elongated in one direction, implying an anisotropic receptive field structure for horizontal ripples, but an isotropic one for vertical ripples.

The most extended summation fields for stereoscopic form may be depicted geometrically in a mesh plot (Fig. 3). For horizontal cyclopean ripples (H), vertical summation was minimal but horizontal summation extended to about 6 (half-cycle) bar widths. The ellipticity of the summation field scaled across spatial frequency. For vertical cyclopean ripples (V), both length and width summation were minimal beyond one cycle.

Fig. 3. Depiction of cyclopean receptive field structure for horizontal (H) and vertical (V) disparity ripples.

Conclusion. There is specialized processing for patterns of cyclopean disparity structure. It does not correspond to a fixed summation field but varies in size with spatial frequency and in shape with orientation of the disparity ripples. At the longest, the data support the existence of length summation up to six cycles of horizontal ripples, or 17 degrees of visual angle. The presence of such extended summation fields controvert the notion of local attentional processing (Hypothesis 1). The radical change in summation properties with ripple orientation are incompatible with the idea of single-channel processing of some property of the disparity field (Hypothesis 2). Finally, the limited summation in for vertical ripples and anisotropic summation for horizontal ripples refutes the concept of an adaptive mechanism that can accommodate to any tractable form of disparity image (Hypothesis 3).

Thus, these results validate the existence of a multichannel hypercyclopean level of processing for aspects of cyclopean form. The only hypothesis that seems to account for the diverse summation properties, and self-scaling with ripple frequency, is a set of arrays of Gabor-type filters for the cyclopean form in the depth image, much like the classical receptive fields processing the luminance image in the retinotopic cortical areas.