The major cue to shape from texture is the compression of texture as a function of surface curvature [ J. Exp. Psychol. 13, 242 ( 1987); Vision Res. 33, 827 ( 1993)]. A number of computational models have been proposed in which compression is measured by detection of changes in the spatial-frequency spectrum [ Comput. Graphics Image Process. 5, 52 ( 1976)]. We propose that the visual system uses a strategy of characterizing the frequency spectrum by a simple set of measures and of tracking the changes in this characterization rather than determining changes in the shape of the actual spectra. Our evidence is based on a number of psychophysical demonstrations that use stimuli with specifically tailored frequency spectra, constructed from white noise filtered in the frequency domain. Our evidence suggests that the visual system determines the average peak frequency of the spectrum and uses this measure as its characterization. Changes in are strongly correlated with the degree of surface curvature, and, over a range of stimuli, takes account of the variance in local estimates of the frequency spectrum. One computes by determining the peak frequency at each spatial location and then averaging these frequency values over a local spatial region. We show that is related to the second-order moment but is more biologically plausible and shows superior ability to function in the presence of noise. As a test of this model, we have constructed a neural network architecture for computing shape from texture. Our model is limited to orthographically projected, homogeneous textures without in-surface rotation. The early stages of the model consist of multiple simple-cell units tuned to different orientations and spatial frequencies. We show that these simple cells are inadequate for the determination of compression but that the outputs of complex-cell-like units after normalization generate estimates of surface slant and tilt. The network shows qualitative agreement with human perception of shape from texture over a wide range of real and artificial stimuli.
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