ABSTRACT
The periodic woven structures of fabrics can be defined on the basis of the convolution theorem. Here an elementary unit with the minimum number of thread crossings and a nonrectangular two-dimensional comb function for the pattern of repetition is used to define woven structures. The expression derived is more compact than the conventional diagram for weaving, and the parameters that one needs to determine a given fabric can easily be extracted from its Fourier transform. Several results with real samples of the most common structures-plain, twill, and satin-are presented.
ABSTRACT
A Fourier-domain-based recognition technique is proposed for periodic and quasiperiodic pattern recognition. It is based on the angular correlation of the moduli of the sample and the reference Fourier spectra centered at the maximum central point. As in other correlation techniques, recognition is achieved when a high correlation peak is obtained, and this result occurs when the two spectra coincide. The angular correlation is a one-dimensional function of the rotation angle. The position of the correlation peak indicates the rotation angle between two similar patterns in the original images. Some optimizations for the discrete calculation of the Fourier-domain-based angular correlation are also proposed. Some applications of this technique to web inspection tasks, such as pattern recognition and classification, damaged web evaluation, and detection of defects, are presented and discussed.
