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Zachary Westrick, Michael Landy; The nonlinearity in texture segregation is not rectification. Journal of Vision 2012;12(9):103. doi: 10.1167/12.9.103.
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© ARVO (1962-2015); The Authors (2016-present)
The filter-rectify-filter (FRF) model has been adopted as a standard explanation of texture segregation. FRF consists of a first stage linear filter (to enhance a constituent texture), nonlinear rectification (computation of "texture energy"), followed by linear filtering tuned to the texture-defined signal. We estimated the spatial-frequency bandwidth of the second filter using two techniques: critical-band masking and 2X2 detection/identification (Watson & Robson, Vis. Res., 1981). The former indicated no 2nd-order tuning, while the latter (along with previous summation results) did find tuning. Including a local winner-takes-most nonlinearity on texture energy can reconcile these seemingly contradictory findings.
Methods. Critical-band masking: 2AFC 2nd-order orientation discrimination. Carrier patterns were 45 and 135 deg gratings. Modulators were vertical or horizontal gratings plus low- or high-pass masking vertical/horizontal plaid noise. Noise cutoff frequency was varied across blocks and 2nd-order threshold modulation contrast was determined by staircase. The derivative of threshold elevation as a function of cutoff yields an estimate of the spatial-frequency channel. 2X2 task: There were two intervals per trial. One contained zero modulation and the other contained a modulator with one of two possible frequencies. Observers indicated both the interval containing the modulator (detection) and its frequency (discrimination). We report channel bandwidth estimates based on maximum-likelihood fits of a 2-channel model to the data.
Results. Critical-band masking indicated no 2nd-order frequency tuning; noise elevated threshold independent of noise frequency relative to signal frequency. The 2X2 experiment yielded bandwidth estimates of 1-1.5 octaves consistent with previous summation experiments. We compare these results to simulated variants of the FRF model. The critical-band masking results differ dramatically from predictions of the standard FRF model. However, untuned response to noise can be explained by an additional nonlinear processing step that computes a local soft-max on texture energy before second-stage filtering (with filter-bandwidth taken from the 2X2 experiment).
Meeting abstract presented at VSS 2012
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