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Influence of correspondence noise and spatial scaling on the upper limit for spatial displacement in fully-coherent random-dot kinematogram stimuli - PubMed

Influence of correspondence noise and spatial scaling on the upper limit for spatial displacement in fully-coherent random-dot kinematogram stimuli

Srimant P Tripathy et al. PLoS One. 2012.

Abstract

Correspondence noise is a major factor limiting direction discrimination performance in random-dot kinematograms. In the current study we investigated the influence of correspondence noise on Dmax, which is the upper limit for the spatial displacement of the dots for which coherent motion is still perceived. Human direction discrimination performance was measured, using 2-frame kinematograms having leftward/rightward motion, over a 200-fold range of dot-densities and a four-fold range of dot displacements. From this data Dmax was estimated for the different dot densities tested. A model was proposed to evaluate the correspondence noise in the stimulus. This model summed the outputs of a set of elementary Reichardt-type local detectors that had receptive fields tiling the stimulus and were tuned to the two directions of motion in the stimulus. A key assumption of the model was that the local detectors would have the radius of their catchment areas scaled with the displacement that they were tuned to detect; the scaling factor k linking the radius to the displacement was the only free parameter in the model and a single value of k was used to fit all of the psychophysical data collected. This minimal, correspondence-noise based model was able to account for 91% of the variability in the human performance across all of the conditions tested. The results highlight the importance of correspondence noise in constraining the largest displacement that can be detected.

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Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.

Figures

Figure 1
Figure 1. The integration of motion information.

Schematic representing the collation of information from local detectors (based upon Reichardt detectors) into a global detector sensitive to a single axis of motion. Solid lines indicate excitatory connections and dashed lines, inhibitory connections. An excitatory summed response from the global detector in this case indicates rightwards motion.

Figure 2
Figure 2. A modified Reichardt detector.

This forms the basis of the local detectors in the module. Output from LD1 is excitatory and indicates rightwards motion. Output from LD2 is inhibitory and indicates leftwards motion. In this modified detector the central catchment area that samples in the neighbourhood of (x,y) in the first-field is shared between LD1 and LD2 (see text).

Figure 3
Figure 3. Effect of dot displacement size on human and model performance.

Direction discrimination performance with an RDK and right vs left motion for three observers (panels A–C) and the correspondence noise model (panel D) as a function of dot displacement size, with dot density as a parameter. Squares and thick solid line: 0.13 dots/deg2, Diamonds and medium solid line: 0.27 dots/deg2, Triangles and thin solid line: 0.53 dots/deg2, Squares and thick dashed line: 1.07 dots/deg2, Diamonds and medium dashed line: 2.13 dots/deg2, Triangles and thin dashed line: 4.27 dots/deg2, Squares and thick dotted line: 8.53 dots/deg2, Diamonds and medium dotted line: 17.07 dots/deg2, Triangles and thin dotted line: 26.67 dots/deg2.

Figure 4
Figure 4. Effect of dot density on human and model Dmax.

A. The value for Dmax derived from the raw direction discrimination performance data. Dmax is plotted as a function of dot density for each of the three observers. Open circle MC; open square SN; open diamond ST. Error bars show the 95% confidence interval for Dmax derived from the fitting procedure. B. Open diamonds show the Dmax values derived from the average performance of the three observers with the filled squares indicating the values of Dmax derived from the model results of direction discrimination performance as a function of displacement size. The error bars are as for the top panel. When error bars are not present, errors are smaller than the symbol size.

Figure 5
Figure 5. Comparison of human and model performance for different dot densities.

Psychophysical (open symbols) and model (closed symbols) direction discrimination performances are plotted as a function of displacement size. Panels, reading from left to right, then top to bottom, display data from dot densities of 0.13, 0.27, 0.53, 1.07, 2.13, 4.27, 8.53, 17.07 and 26.67 dots/deg2. Model k = 1.88; Coherence level = 100%; 1000 random local detectors were incorporated in the model. Psychophysical performances were the average of three human observers and the error bars show the range. Model performances were a result of 1000 trials at each data point and the error bars represent the 95% confidence interval. A fitted cumulative normal function is shown by the solid lines (model data) and dashed lines (human data). The p-value of the χ2 statistic was measured to determine the strength of association between the psychophysical and model data and is displayed for each density.

Figure 6
Figure 6. Comparison of human and model performance across all conditions.

Psychophysical vs model direction discrimination performance pooling data from nine dot density levels and five displacement levels. The thick solid line is the line of equality whilst the thin solid line is the line of best fit, where human performance = 0.79 × model performance +14% (r2 = 0.91).

Figure 7
Figure 7. Effect of number of detectors on model performance.

Modelled direction discrimination performance with an RDK and right vs left motion for two displacement sizes (220 arcmin in panel A; 90 arcmin in panel B) and two dot densities (500 dots – filled triangles and horizontal solid line; 4000 dots – filled squares and horizontal dashed line) as a function of the number of local detectors used to tile the effective stimulus area. Horizontal lines show the performance when the local detectors optimally tiled the stimulus plane. Thin dashed lines represent three repetitions of 1000 trials each for each value of dot number and show repeatable model performance. The thicker curves and the filled symbols represent the means of the three repetitions. Error bars are ± one standard error.

Figure 8
Figure 8. Effect of stimulus-detector mismatch.

Modelled direction discrimination performance with an RDK and right vs left motion for 220 arcmin displacement size and two dot densities (500 dots – filled triangles and solid line; 4000 dots – filled squares and dashed line) as a function of the mismatch between the local detector’s catchment area separations and the stimulus’ dot displacement. Lines are fits of Gaussian functions to the data.

Figure 9
Figure 9. Influence of scaling factor (k) on model performance.

Results for the model performance for a large range of k tested under two different local-detector-tiling conditions: Panel A - optimally positioned local detectors; Panel B - randomly positioned local detectors with the number of local detectors set to 1000. Two dot-densities were used in each tiling condition (500 dots – filled triangles and solid line; 4000 dots – filled squares and dashed line).

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Grants and funding

SNS was supported by an Overseas Research Scholarship at University of Bradford. The publication fee is based on funds agreed by the School of Optometry & Vision Science. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.