Abstract
The Mellin radial harmonic filters recently reported are based on the radial Mellin transform of objects in a polar coordinate system. The filters provide scale-invariant pattern recognition by matching the angular information of the object. Phase-only Mellin filters coded similarly in the Fourier plane were also reported. But both filters have only approximative scale invariance. In their definition, a small radius r=0. The r0 remains constant for objects with different sizes, that leads to scale dependence. We show that strict scale invariance can be achieved only when the object function is constant for 0 0. We also consider the behavior of the Mellin filters as a function of the position of the polar coordinate origin. We found that the proper centers for the Mellin filters are usually located outside the object.
© 1990 Optical Society of America
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