Yi xu¹, Akihito Maruya², Qasim Zaidi¹; ¹SUNY college of optometry, ²Zuckerman Institute Columbia University

Plaids formed by the sums of two gratings have been used extensively in vision research, but the perceptual qualities of the large variety of possible plaids have not been studied. Many plaids are seen as the sum of two gratings, but others look like gratings with one or more phase shifts (orthogonal or oblique to the grating orientation), braided patterns, or as discontinuous or wavy gratings. Given that each grating is defined by four parameters (spatial frequency, orientation, phase and contrast), the generative space of plaids is continuous and 8-dimensional. We aim to use perceptual similarities to construct a more tractable space for plaids that would be useful for many purposes, using 37 plaids that covered all the categories above. The space could be topological consisting of discrete clusters, or hierarchically organized into a tree structure, or the similarities could be represented as distances in a multi-dimensional Euclidean, spherical or hyperbolic space. Four observers looked at each plaid as the reference surrounded by the 36 others and indicated the perceptual nearest neighbor (Tversky and Hutchinson, 1986). Observers’ centrality parameters (2.45, 2.13, 2.34, 2.29) indicate a tree structure with around 4 branches, but with 37.4% concordance across observers. To test if a tree can be embedded into a space requires a complete similarity matrix. We used Waraich and Victor’s (2024) method of ranking 8 similarities to efficiently estimate the matrix and compare the log likelihood of Euclidean model spaces (1-10 dimensions) with a random model as the lower bound and distances equal to empirical choice probabilities as the upper bound. The log-likelihood asymptoted at 4 dimensions and DBSCAN indicated a single cluster. A spherical space with minimal curvature provided a slightly better fit, but a hyperbolic space did not. The perceptual space of plaids is thus simpler than the generative space.

Acknowledgements: EY035085, EY035838