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