RESPONSE CLASSIFICATION IMAGES FOR PARAFOVEAL VERNIER ACUITY

B. L. Beard, A. J. Ahumada, Jr.

NASA Ames Research Center

Abstract

Purpose. Linear image features were determined for a parafoveal two-line vernier task using the response classification technique described in Beard & Ahumada (SPIE, 1998).

Methods. Observers fixated 5 degrees to the right of two short, horizontally oriented vernier line features. Line contrast was set to maintain an error rate near 25%. Stimulus duration was 0.5 sec with abrupt onset and offset. The vernier stimulus was added to, and centrally located within, a 40 by 40-min (128 by 128 pixels) noise display area. Alignment thresholds were obtained using a two interval forced choice (2IFC) method of constant stimuli with one vernier offset value. On a given trial, the right vernier line was randomly either aligned with the left line or upwardly offset by 0.31 arc min. The observers were instructed to report if the two lines were aligned or vertically offset. After each trial, a tone gave the observer feedback. Trials were run in blocks of 100. There were four observers. On each trial the observers response, the stimulus type and the particular noise sample were tabulated. In two observers, the proportion of internal noise was determined. The noises were then averaged separately for each of the either four or six stimulus-response trials. These averaged noises were combined with appropriate signs to form a classification image illustrating the contribution of each noise image pixel to the decision.

Results. In fovea, although there are individual differences, all observers show discrete bipolar distributions as seen in our earlier research. Peripheral classification images showed one or more of the following characteristics: (1) a broader spatial spread in the vertical direction (2) an extension of relevant noise pixels toward the point of fixation (3) relevant noise pixels for the left reference line were clustered near the offset region.

Conclusions. The classification images for peripheral vernier acuity have greater spatial spread than do foveal classification images.

Slide Presentation

INTRODUCTION

Changing stimulus parameters to uncover visual mechanism properties may induce changes in the stimulus features used to categorize or classify the stimulus.

Here we let the trial-by-trial variations in added noise provide a window to visualize the underlying stimulus classification rules used by observers instead of changing stimulus parameters within an experiment (Ahumada, 1996). The “response classification technique” extracts the linear image features contributing to discrimination by correlating the observer's response on a trial with the noise contrast in each pixel on that trial (Beard & Ahumada, 1997).

Visual performance is often better in the central visual field than peripherally. Vernier acuity performance has been reported to fall off more quickly with eccentricity than does resolution acuity. The factors limiting vernier acuity (i.e., spatial filtering, sampling, uncertainty, attention, masking) may have different importance in the fovea and in the periphery. This could lead to different features being used to make the discrimination.

In the current experiment, we use the response classification technique to compare the linear features being used in the fovea and the periphery. We find that the response classification images for peripheral vernier acuity have greater spatial spread than do foveal classification images; we see no qualitative difference.

METHODS

Stimuli.

Horizontal line stimuli

Abutting

16 min arc long x 0.33 min arc wide 0 min arc separation

Wide Separation

16 min arc long x 0.33 min arc wide 10 min arc separation

Periphery

5 deg

stimulus magnified x 3

observers fixated to right of stimuli

White noise

40 x 40 min arc (128 x 128 pixels)

0.25 peak contrast

Procedure.

Psychophysics

method of constant stimuli

blocks of 100 trials

presentation duration - 0.5 sec

Response Classification Technique

•On each trial tabulate

–observers response

–stimulus type

–particular noise sample

•Noises averaged separately for four stimulus-response trials

•S0 - stimulus is aligned S1 - stimulus is offset

R0 - response “aligned” R1 - response “offset”

Raw Classification Image

These averaged noises are combined with appropriate signs to form a classification image illustrating the contribution of each noise image pixel to the decision.

(-S0 R0) + S0 R1 + (-S1 R0) + S1 R1

[the sum of the two "not aligned" stimulus images is subtracted from the sum of the "aligned" images (proportional to the correlation of each pixel amplitude with the response) to obtain an overall “raw” response correlation image]. The logic is that for a linear response classification rule, the two correlation images for S0 and S1 will be proportional to each other (i.e., estimates of the same image) and can be combined to form a single image. The image polarity for “aligned” responses was reversed to make them compatible with the "not aligned" responses.

Smoothed Image

The image is then smoothed by a 5 x 5 convolution kernel.

Statistical Significance

The spatially smoothed image is then quantized by the expected variability of a filtered random image using a quantization interval of 1.96 standard deviations, so that pixels within a 95% confidence interval on either side of the expected mean value (zero) are coded as a neutral gray.

PREVIOUS WORK

Used the response classification technique to reveal the stimulus features for :

Abutting features

Widely separated features

Spatial filter model predictions.

The difference between two oriented even-symmetric Gabor channels is used for alignment detection for abutting (upper panel) and wide separation (lower panel) vernier conditions.

A local sign model assumes that spatially oriented filters place a position label or 'local sign' by estimating the weighted average or centroid of darkness in a region about each line (Lotze, 1884). The alignment judgment is then based on the difference between these vertical position estimates (Westheimer, 1979; Klein, Stromeyer & Ganz, 1974; Morgan et al., 1990).

Local centroid predictions.

The expected classification image for two odd-symmetric Gabor filters being used to compute the 'local' vertical position, for abutting and wide separation conditions.

In this experiment we were interested in what stimulus classification rules are used for alignment discrimination and whether they change with line separation. It is possible that the stimulus classification rules used by the observer change if a wide spatial separation is introduced between the vernier lines since there is a dramatic elevation in threshold under these conditions.

We find that the two competing theories (i.e., spatial filters versus local centroids) are indistinguishable hypotheses for abutting stimuli.

Classification Images: Raw, Smoothed, Statistical Significance.

PWN Trials = 3300

DNF Trials = 5000 BLB Trials = 3200

Foveal Viewing

CSS Trials = 4800 MPE Trials = 7200

BLB Trials = 4000 DCH Trials = 6000

NSA Trials = 4000 MAJ Trials = 16400

10.23 min arc feature separation.

POLARITY

Use the response classification technique to reveal the stimulus features for opposite polarity features

Opposite polarity stimulus.

Vernier thresholds for abutting line features depend on stimulus polarity (Murphy et al, 1988; O'Shea & Mitchell, 1990; Morgan, 1991; Levi & Waugh, 1994; Beard et al, 1997) and contrast (Watt & Morgan, 1983; Bradley & Skottun, 1987; Wilson, 1986; Klein et al, 1990; Wehrhahn & Westheimer, 1990; Waugh & Levi, 1993a). Within the local sign regime, the separate, coarse position labels placed on each stimulus feature are relatively independent of polarity (Burbeck, 1986; Levi & Westheimer, 1987) and contrast (above four times the detection threshold, Waugh & Levi, 1993a).

We hypothesized that classification images would reflect the dependence on the average luminance level (centroid) of the line features.

Opposite polarity images.

PERIPHERY

The human visual field has been modeled as a set of self-similar, overlapping band-pass detector distributions except for a scale factor where peripheral detectors are tuned to lower frequency, larger stimuli (e.g., Watson, 1985). That positional accuracy declines rapidly as one moves the stimulus into the periphery (Levi, Klein & Yap, 1988; Beard, Levi & Klein, 1997) suggests that response classification images obtained from peripheral viewing would be broader in extent. Here we test this prediction.

Opposite polarity in the periphery.

CONCLUSIONS

Classification images are broader when peripherally viewed even though they have been size scaled to compensate for the cortical magnification factor. Broader images may be due to spatial filter spread or positional uncertainty

Local centroid hypothesis does not account for opposite polarity classification images in the fovea or periphery.