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Alan B. Cobo-Lewis; Modeling 1D and 2D non-Fourier motion. Journal of Vision 2002;2(7):652. doi: https://doi.org/10.1167/2.7.652.
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A luminance-gradient mechanism can detect high-order 1D motion (Benton et al., 2001, J Opt Soc Am A, 18, 2204). I examine the response to 1D and 2D motion of a Bayesian gradient-based model whose output is an activation pattern in velocity space (Weiss & Adelson, 1998, AI Memo 1624/CBCL Paper 158, MIT; Cobo-Lewis & Smallwood, in press, Spatial Vision). Using traditional luminance-modulated and contrast-modulated noise carriers, as well as nth-order stimuli (Taub et al., 1997, Vision Res, 37, 1459), I confirm that no front-end nonlinearity is required to detect high-order motion—as long as the model's spatial and temporal resolutions are finer than the carrier's sampling periods. However, because the model is susceptible to static noise, it underestimates the ambiguity in a non-Fourier grating's velocity, fallaciously “solving” the aperture problem. This issue worsens as the carrier's sampling period approaches the model's resolution. The model does correctly account for the velocity ambiguity of second-order gratings—if an appropriate front-end nonlinearity is introduced. Using Fourier and non-Fourier (including high-order) Type 2 plaids, I examine the consequences for 2D motion. The model detects high-order non-Fourier plaid motion, but with large biases toward the vector-sum direction, even when aperture size and stimulus duration are large. This yields a psychophysical prediction that detectable Type 2 plaids of order >2 would be perceived to move close to the vector-sum direction. The large biases can be eliminated for the second-order plaids if an appropriate front-end nonlinearity is introduced. Because contrast-modulated Type 2 plaids behave like luminance-modulated Type 2 plaids (Cropper et al., 1994, Vision Res, 34, 2609), this could suggest that a front-end nonlinearity does participate in the analysis of second-order 2D motion. Alternatively, the model could be rendered more robust to static noise (Johnston et al., 1999, Proc R Soc Lond B, 266, 509). Supported by NIH R15 EY 13362.
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