The Orthonormal Fourier-Mellin Transform For Precision Scale Detection And Range Data Acquisition
John D. McMillen, O. ROBERT MITCHELL · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1988
The Mellin transform converts reference frame scale information into phase information. This property makes the Mellin transform appropriate for determining the scale difference between two signals and for determining features which are invariant to scale change : partial shape recognition, recognition of objects at various distances, speech or brain wave processing, range mapping, processing of doppler shifted signals. A recent study [1] reveals a generalized Mellin transform which, when indexed properly, produces an orthonormal version which is superior to the Mellin transform typically seen in the literature. The orthonormal Mellin transform, the Fourier-Mellin transform and their properties are discussed. The performance of scale detection of digitized curves and its application to monocular range acquisition in a robot vision system are investigated. Key words: Mellin transform, Fourier-Mellin transform, Discrete Mellin Transform, scale detection, range acquisition