Reconstruction of spatial information in the human visual system

The remarkable capacity of an observer to perceive and recognize objects and forms independent of the exact nature of their components can be described as a process of reconstruction. We have measured the ability of human observers to recognize square-wave or sinusoidal gratings when presented as a pattern of regularly taken spatial samples (see Fig. 1). To recognize the waveforms, the observer must visually reconstruct them from the samples—a process which can be described by the Shannon–Whittaker theorem1,2 of sampling and which Barlow suggests may be carried out by the numerous stellate cells of the visual cortex3. We report here that at low spatial frequencies, relatively more sample lines per spatial cycle were needed for wave recognition than were needed at higher frequencies. However, a square-wave grating was still recognized easily even when it was sampled at a rate at which its third harmonic could not be recognized when presented alone. At high spatial frequencies the square wave was identified when the sampling rate was so low that it caused the third harmonic to be under-sampled. This contradicts the idea that a complex wave is analysed by parallel spatial frequency channels4,5 and emphasizes the capacity of the visual system to use signal features other than the harmonic frequency components of an image to recognize it.