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Geometrical approach of the circular harmonic filters

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Abstract

A circular-harmonic (CH) filter contains only one component of the object that gives rotation in variance. But an infinity of objects could have the same center correlation value although most of those are not realistic objects. On the other hand, a CH filter performs the CH expansion of the input about every point in the plane (r,θ). The correlation output can be expressed as where Fm(p) and Gm(p) are the CH functions of the filter and of the input in the Fourier plane respectively, Jm(2πpr) is the Bessel function. This equation shows clearly that apart from the center r = 0 θ = 0, the 2-D correlation of a CH filter of order m depends on the CH components of all the orders and is then unique of a given input. The center output intensity depends only on the order m. But the position of the output peak depends on all the orders.

© 1991 Optical Society of America

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