Published in Investigative Opthalmology and Visual Science Supplement (ARVO), vol.29 pp. 408, May 1988.
An image representation is efficiently sampled if the number of coefficients equals the number of degrees of freedom in the represented image. Orthogonal transforms (e.g. the Fourier transform), and some non-orthogonal transforms (e.g. the Gabor transform) are efficiently sampled. Some pyramid representations, such as Burt and Adelson's Laplacian pyramid and Watson's cortex transform, are not efficiently sampled, being oversampled by a factor of 4/3. Recently, efficiently sampled pyramids based on quadrature mirror filters have been developed; they capture a number of useful properties that are similar to those found in the human visual system, such as tuning in SF and orientations, and localization in space. These QMF pyramids perform quite well at image data compression. However, they have some problems with shift-variance that may limit their performance in computational vision and modeling. We argue that a modest amount of oversampling can offer significant advantages in both human and machine vision.