Demodulation, predictive coding, and spatial vision.
We argue that some aspects of human spatial vision, particularly for textured patterns and scenes, can be described in terms of demodulation and predictive coding. Such nonlinear processes encode a pattern into local phasors that represent it completely as a modulation, in phase and amplitude, of a prediction associated with the image structure in some region by its predominant undulation(s). The demodulation representation of a pattern is an anisotropic, second-order form of predictive coding, and it offers a particularly efficient way to analyze and encode textures, as it identifies and exploits their underlying redundancies. In addition, self-consistent domains of redundancy in image structure provide a basis for image segmentation. We first provide an algorithm for computing the three elements of a complete demodulation transform of any image, and we illustrate such decompositions for both natural and synthetic images. We then present psychophysical evidence from spatial masking experiments, as well as illustrations of perceptual organization, that suggest a possible role for such underlying representations in human vision. In psychophysical experiments employing masks with more than two oriented Fourier components, we find that peaks of threshold elevation occur at locations in the Fourier plane remote from the orientations and frequencies of the actual mask components. Rather, as would occur from demodulation, these peaks in the frequency plane are related to the vector difference frequencies between the actual masking components and their spectral centers of mass. We offer a neural interpretation of demodulation coding, and finally we demonstrate a practical application of this process in a system for automatic visual recognition of personal identity by demodulation of a facial feature.