Vision Res. Vol. 31, No. 12, pp. 2195-2207, 1991 0042-6989/91$3.00 + 0.00 Printed in Great Britain. All rights reserved Copyright 0 1991Pergalnon FVessplc INTEROCULAR CORRELATION, LUMINANCE CONTRAST AND CYCLOPEAN PROCESSING LAWRENCE K. CORMACK, Sco3-r B. STEVENSONand CLIFTON M. SCHOR School of Optometry, University of California, Berkeley, CA 94720, U.S.A. (Received 27 August 1990; in revised form 17 January 1991) Abstract-We have investigated the nature and viability of interocular correlation as a measure of signal strength in the cyclopean domain. Thresholds for the detection of interocular correlation in dynamic random element stereograms were measured as a function of luminance contrast, a more traditional measure of stimulus strength. At high contrasts, correlation thresholds were independent of contrast. At low contrasts, correlation thresholds were inversely proportional to the square of contrast. Stereothresholds were also measured as a function of both contrast and interocular correlation. At low contrasts, stereoacuity was inversely proportional to both interocular correlation and the square of contrast. These results are consistent with an inherently multiplicative mechanism of binocular combi- nation, such as a cross-correlation of the two eye’s inputs. Interocular correlation Contrast Stereopsis INTRODUCTION images, with their generous variety of colors, luminances, etc. interocular correlation is some- In general, interocular correlation can be what difficult to intuit, regardless of the defi- thought of as the degree to which the images in nition employed. It would be unclear, for the two eyes match one another. Intuitively, example, how to change one member of an image interocular correlation, if reasonably defined, pair in order to reduce the interocular corre- should provide a measure of signal strength in lation by some desired amount. In the labora- the cyclopean domain. That is, if the two eye’s tory however, where one can restrict the visual views are almost identical, as is the case with environment to one-bit random dot stereograms binocular fixation of a flat surface, interocular of 50% density, the notion of interocular corre- correlation is very close to the maximum poss- lation is quite intuitive. Under these conditions, ible. On the contrary, if the two eye’s views of the interocular correlation for a given disparity the world are predominantly non-overlapping is simply a linear function of the proportion of then nothing can be predicted about the right dots which match at that disparity, i.e. eye’s image given only the left eye’s image and vice versa. In this case there would be zero IOC(d) = 2P, - 1 (2) interocular correlation and, hence, no cyclopean information available. where Pd is the proportion of matching dots at Formally, interocular correlation can be disparity d. defined as the cross-correlation of the image Examples of different interocular correlations pair comprising the right and left eye’s views of are shown in Fig. 1. The top stereo pair the world. For the simple one-dimensional case illustrates an interocular correlation of + 1 (all the interocular correlation at some disparity d is dots match at 0 disparity) and, when fused, given by: the percept is that of a flat plane. In the middle and bottom panels, the interocular correlation IOC(d) = f(x)h(x + d) dx (1) has been reduced to +OS and 0 respectively, s accompanied by a degradation of the perceived where f(x) and h(x) represent the intensity quality of the plane. It should be noted that the profiles (or some derivative of them) along the phenomenology of these static examples differs horizontal meridian of the right and left eye’s somewhat from that of dynamic displays such as retinae. were employed in our experiments. Specifically, This definition is simple, quantitative, and the dynamic displays of interocular correlations works for any given image pair. For “natural” less than unity give rise to a percept much like 2195 2196 LAWRENCE K. C‘ORMACK el (11. b. C. Fig. 1, Examples of random noise with various amounts of interocular correlation. These examples can either be free-fused or viewed through a stereoscope. In (a). the interocular correlation is 100% at 0 dn, parity, and the percept is one of a Aat plane. In (b) the interocular correlation has been reduced to SO” ,I while a flat plane is still perceived, it appears less robust and accompanied by dots both in front of :III~! behind the plane of fixation. In (c), the interocular correlation is 0, and no percept of a coherent plani. : extant. In dynamic versions of these stimuli, such as were employed in the experiments, the phenomtr; ology is somewhat different. Lower interocular correlations in particular appear as semi-transparct!t volumes when dynamic, whereas. when static, they appear as opaque surfaces with chaotic topograph? a dirty window embedded in fog; as correlation was the appearance of’s pstchwork 01 cc)-plan;lr increases, the window grows dirtier and the fop dots imbedded in a ri~Hlrousllustr_c,a- b:~l\ grows thinner. Absent in the dynamic displays t‘cv-ound, such as is seen in thcw stalk ;-tarl~pie~ lnterocular correlation, luminance contrast and cyclopean processing 2197 Yet Fig. 1 does illustrate a basic point, which is that as one decreases the interocular corre- lation of the stimulus, the salience of the flat plane also decreases. In this sense, interocular correlation could represent a metric of signal amplitude in the cyclopean domain analogous to the manner in which luminance contrast provides a metric of signal amplitude in the spatial domain. * The generation of a cyclopean signal does not occur in parallel with the gener- ation of a spatial (contrast) signal however; the presence of a contrast signal is a necessary precursor to the generation of a cyclopean signal. Given this ordinal relationship, and the fact that contrast is already known to influence Fig. 2. Schematic illustration of the experimental apparatus. such hypercyclopean functions as stereoacuity Random bit streams were hardware generated and sent to a pair of video monitors, which were viewed through a (Halpern & Blake, 1988; Legge & Gu, 1989; mirror haploscope. Disparities were created by delaying the Heckman & Schor, 1989), it might be possible sync to one monitor. Interocular correlation was manipu- to control the amplitude of a cyclopean signal lated by driving the monitors with a single dot generator, by manipulating luminance contrast. For independent dot generators, or a combination thereof (see example, if the luminance contrast of a cy- text for details). The psychophysics (stimulus presentation, data aquisition, etc.) were all under computer control. clopean stimulus is reduced, it might be possible to compensate for the resulting decrease in signal strength by increasing the interocular 7 MHz and was displayed on a pair of matched correlation, thereby maintaining a constant (e.g. TSD monitors (p4 phosphor, 60 Hz non- threshold) level of performance on some task. interlaced) viewed through a mirror haploscope. Thus, given a threshold level of performance on The viewing distance was 53.7 cm and the said task, a trading relation would be expected haploscope mirrors were adjusted for each between contrast and interocular correlation. subject to the corresponding convergence Moreover, the form of this trading relation angle, thus obviating any mismatch between would reflect the manner in which cyclopean convergence and accommodation or “higher signals are derived from monocular contrast level” distance cues. Mean luminance was signals. Accordingly, we measured the effect 80cd/m2. The displays were viewed through of contrast on the detection of interocular 7 deg circular apertures in an otherwise black correlation in the first experiment. Based on surround. the results of this experiment, a model was Horizontal disparities were produced by de- developed to generate predictions concerning laying the horizontal video sync to one monitor. hypercyclopean functions such as stereoacuity. This was accomplished via a programmable Predictions of this model were then tested delay chip (Digital Delay Devices model PDU- in Experiment 2 by measuring stereoacuity as 13256-0.5), which allowed us to delay the noise a function of both contrast and interocular stimulus to one eye in 0.5 nsec (corresponding to correlation. 2 arc set) increments. Interocular correlation was simply the pro- GENERAL METHODS portion of the dots which were “forced” to match in the two images; the remainder of the The experiments were performed using dy- dots then had a 50% chance of matching. Thus, namic random-element stereograms of 50% el- in a display which had an interocular corre- ement density. A diagram of the basic apparatus lation of 0, half of the dots in the right image is shown in Fig. 2. A random noise signal was were matched by dots in the left image. In a hardware generated via shift registers running at display which had an interocular correlation of - 1 (“anticorrelation”), the right image was simply the opposite contrast version of the left *In this paper, we will use the term “cyclopean” to refer to the site and/or processes of binocular combination itself image and no matches existed. For an inter- and the term “hypercyclopean” to refer to processes ocular correlation of + 1, of course, the two occurring after or beyond the cyclopean stage. images were identical. 2198 LAWRENCEK. CORMACKet al Thus, rearranging equation (2), the pro- be placed under software (Experiment 1) or portion of matching dots is, on average, simply hardware (Experiment 2) control.* (IOC + 1)/2; the two are linearly related, as is Thus, to create an interocular correlation of somewhat demanded by intuition. 0.75, the duty cycle of the rectangular wave Interocular correlation was varied through switching pulse was such that the subject was the use of two independent noise generators. To viewing a fully correlated display 75% of the produce an interocular correlation of + 1, the space/time, and viewing an uncorrelated display output of a single noise generator was sent for the remainder.