The Duality Between Noise And Aliasing And Human Image Understanding

A function and its Fourier transform are related by the "uncertainty inequality" of Heisenberg. The autocorrelation and spectral power density of a function satisfy a similar relation which can be interpreted as a duality between noise and aliasing. This duality can be applied to stochastic collections of image signals that are discretely sampled- either by biological retinas or by pixelated computer displays. It follows that alias artifacts due to sampling an image at less than the Nyquist frequency can be diminished or entirely avoided at the expense of noise introduced by the sampling process. We suggest that the human daylight vision system employs this strategy, in part in order to eliminate inconsistencies in pattern recognition between the foveal high spatial resolution subsystem and the extra-foveal low spatial resolution subsystem. Implications of these ideas for the design of robot and other machine imaging and display systems in the context of limited bandwidth are discussed.