INVARIANT SPECTROSCOPIC PATTERN-RECOGNITION USING MELLIN TRANSFORMS

The Mellin transform and its related transforms-the Fourier-Meltin, Mellin-Mellin, and Mellin-Fourier transforms-possess position, scale, and distortion invariance properties that suggest that they might find application in extremely robust spectroscopic instrumentation. In this report, the invariance properties of Mellin transforms have been considered in conjunction with infrared spectra. Findings suggest that the insensitivity of the Mellin transforms toward a variety of optical and experimental defects provides a means of separating differences in recorded spectra that result from instrumental factors, such as drift, misalignment, aberration, and other experimental factors, from those arising from true chemical differences between samples. Furthermore, the invariance properties are useful for robust pattern recognition, where the key features of the spectrum of interest can be recognized despite (i) translation in wavenumber, (ii) both linear and nonlinear scale changes in the wavenumber axis, or (iii) distortion in the amplitude. Normally, pattern matching algorithms are intolerant toward such instrumental factors. It is found that the Mellin correlation algorithm gives better results with discretely sampled data than the full application of the Mellin transforms. Invariant pattern recognition in the presence of translation, scale change, and distortion in the wavenumber axis is illustrated by consideration of spectra of dyes extracted from fabrics. It is demonstrated that a particular dye can be distinguished from very similar dyes despite relatively severe distortion in its infrared spectrum.