Visual perception of texture regularity: Conjoint measurements and a wavelet response-distribution model

Texture regularity, such as the repeating pattern in a carpet, brickwork or tree bark, is a ubiquitous feature of the visual world. The perception of regularity has generally been studied using multi-element textures in which the degree of regularity has been manipulated by adding random jitter to the elements’ positions. Here we used three-factor Maximum Likelihood Conjoint Measurement (MLCM) for the first time to investigate the encoding of regularity information under more complex conditions in which element spacing and size, in addition to positional jitter, were manipulated. Human observers were presented with large numbers of pairs of multi-element stimuli with varying levels of the three factors, and indicated on each trial which stimulus appeared more regular. All three factors contributed to regularity perception. Jitter, as expected, strongly affected regularity perception. This effect of jitter on regularity perception is strongest at small element spacing and large texture element size, suggesting that the visual system utilizes the edge-to-edge distance between elements as the basis for regularity judgments. We then examined how the responses of a bank of Gabor wavelet spatial filters might account for our results. Our analysis indicates that the peakedness of the spatial frequency (SF) distribution, a previously favored proposal, is insufficient for regularity encoding since it varied more with element spacing and size than with jitter. Instead, our results support the idea that the visual system may extract texture regularity information from the moments of the SF-distribution across orientation. In our best-performing model, the variance of SF-distribution skew across orientations can explain 70% of the variance of estimated texture regularity from our data, suggesting that it could provide a candidate read-out for perceived regularity.
Author summary We investigated human perception of texture regularity, in which subjects made comparative judgements of regularity in pairs of texture stimuli with differing levels of three parameters of texture construction—spacing and size of texture elements, and their positional jitter. We analyzed the data using a novel approach involving three-factor Maximum Likelihood Conjoint Measurement (MLCM). We utilized a novel three-way approach in MLCM to evaluate the effect size and significance of the three factors as well as their interactions. We found that all three factors contributed to perceived regularity, with significant main effects and interactions between factors, in a manner suggesting edge-to-edge distances between elements might contribute importantly to regularity judgments. Using a bank of Gabor wavelet spatial filters to model the response of the human visual system to our textures, we compared four types of ways that the distribution of wavelet responses could account for our measured data on perceived regularity. Our results suggest that the orientation as well as spatial frequency (SF) information from the wavelet filters also contributes importantly—in particular, the skew of the variance of the SF-distribution across orientation provides a candidate basis for perceived texture regularity.