A transformation method for the reconstruction of functions from nonuniformly spaced samples

Variable-Resolution Imagery for Flight Simulation

“…For example, if we had begun with a bandlimited image and applied our variable-resolution procedure to it, the resulting image would no longer be bandlimited. However, because the underlying distortion function, used to alter the spatial distribution of information in the image, is of a form for which an inverse exists (cf, Clark, et al, 1985), that inverse can be used to restore the image to one whose information is distributed uniformly and which is again bandlimited. In this case, the generalized sampling procedure can be applied and the resulting variable-resolution image can be completely represented by a finite set of samples.…”

“…Stated another way, if an image can be projected into the space of BLFs by a transformation along the spatial axis, then it can be adequately represented by a discrete set of samples. The second way of representing a transformed image by a discrete set of samples is to distort and position the interpolation functions (sinc functions) nonuniformly in accordance with the positional distortion function, and then represent the signal even though it is not bandlimited and as such does not satisfy the Nyquist condition (Clark et al, 1985;Zeevi & Shlomot, 1993).…”

“…Intuitively, it is clear that as the data become more sparsely distributed as a result of variable resolution processing, the required density of sampling points decreases. A sampling theorem for images which belong to BO was first introduced by Clark, et al (1985). This theorem was extended by Zeevi and Shlomot (1993) to allow images to be sampled using other than rectilinear patterns.…”

“…Although the processing performed here is not strictly an image magnification, there is some analogy in the change in spatial frequency content of the images resulting from these two procedures. Thus, given that formal procedures have been developed for sampling and generating variable-resolution imagery (Clark et al, 1985;, this imagery may be most useful for producing efficient visual simulation.…”

“…Such imagery is potentially relevant to the design of visual simulators in that it can be madce to appear, to a human observer, to be equivalent to an image whose spatial frequency content is equally high at all points. Once an equivalent 1 variable-resolution image is found, formal procedures (Clark, Palmer, & Lawrence, 1985;Zeevi & Shlomot, 1993) exist for efficiently sampling the image. The more efficient sampled image can then be used in place of the original image in the visual simulator.…”