A Discrimination Method of Paper by Fourier Transform and Cross-Correlation Hitomi Miyata Criminal Investigation Laboratory, Metropolitan Police Department Makoto Shinozaki Advanced Technology Research Laboratory, Oji Paper Co., Ltd. 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 1.6mm 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. Keywords: Fourier transform, power spectrum, cross-correlation, wire mark, image analysis, frequency analysis
wire A hand sheets: a1 through a4 wire B hand sheets: b1 through b4 Table 1 Mesh counts and yarn materials of the forming wires *mesh count: strands per inch wire E hand sheets: e1 through e4 Fig. 1 Five different commercial forming wires providing four hand sheets each. The center of the sheet has the wire-mark of its original wire.
wire A wire D wire A wire D wire B wire E wire B wire E wire C Fig. 2 Light-reflected images of commercial wires with a dimension of 32.5mm wide by 30.5 mm high. wire C Fig. 3 Light-transmitted images of hand sheets out of the commercial wires, A thru E, shown in Fig. 2. The dimension was of the same size with that of the wires. Note that each image shows mirror-reflected wire-mark of its original wire.
Four parts a sheet and three sheets a wire were Fourier-Transformed and produced 12 Power Spectra (PS) for a wire. 5-1; PS of paper 'a' 5-2; PS of creased paper 'a' 5-3; PS of paper 'b' Fig. 4 Method to determine 'reference' power Fig. 5 The FFT power spectra of two paper 'a' and spectra as a database. b' and of creased 'a'. Our eyes can see that 5-2 looks more similar to 5-1 than to 5-3.
Table 2 Cross correlation 'E' between the power spectra of the 'samples' and of the 'refernces' Each sample (written in lower case letters; a through e) showed the highest similarity (i.e. the cross correlation E) when it was compared with the reference (written in upper letters ; A through E) prepared with the same wire. (underlined pairs; a is with A, b is with B and so forth). 7) Sugita, Suzuki "Discrimination of paper by macro -and microscopic Observation", INTERNA- TIONAL WORKSHOP ON THE FORENSIC OF TRACE EVIDENCE Proceeding (1998)
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