Abstract

Binary images usually are produced by clipping band-limited images generated through physical systems. We examine the conditions under which a prescribed image can be formed by this process. Obviously, when the desired image has infinitely sharp isolated corners, it cannot be formed by clipping a band-limited image. We show, however, that any desired binary image can be approximated arbitrarily closely. To make this approximation one must find a band-limited function that has approximately the desired level crossings, i.e., contours where the function is equal to the threshold value of the clipping operation. This can be done by defining a band-limited function in terms of a product of functions that define the function’s zero-crossing contours. In a finite region, these zero crossings are defined strictly in terms of the zeros of a two-dimensional polynomial.

© 1989 Optical Society of America

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