Discrimination method of paper by Fourier transform and cross-correlation

Abstract

This paper presents a novel method of identifying a paper sheet by calculating the similarity of the power spectrum of a frequency analysis. Focus has been put on the wire mark in paper as a periodicity in this work. Hand sheets prepared with 5 different commercial wires provided both of 'samples' and 'references'. The two-dimensional fast Fourier transform (FFT) was applied to the light-transmitted images of the sheets to obtain power spectra (PS). Each 'reference' PS file was prepared by averaging 12 PS out of 3 hand sheets per wire. This procedure is to reduce a local variation of paper. The group of the reference PS files can be considered as a database. Another sheet of the same papers was creased intentionally to make a 'sample'. Only a part of the sheet offered a PS for the data. Cross-correlation calculation has been adopted for the quantitative similarity calculation between PS of the samples and of the references. Wavelengths longer than approximately 1.6 mm, herein, have been eliminated for the correlation calculations. Since the periodicity of a wire should be around 0.5 mm and the powers of relatively longer wavelengths are remarkably large comparing to that of the shorter wavelengths, the powers of the wavelengths longer than 1.6 mm lower the correlation precision. Every sample showed the highest similarity when it was coupled with the reference out of the same wire. This implies the possible usefulness of the cross-correlation matching method applied to the power spectrum of FFT analysis of the light-transmitted images in order to distinguish paper.