Applying Fourier and Associated Transforms to Pattern Characterization in Textiles

Abstract

The regular periodic nature of many textile patterns permits Fourier transform techniques in image processing to be used to measure their visual characteristics. In carpets, the patterns may be due to either the arrangement of the pile or the repetition of a colored design. The Fourier power spectrum provides a useful description of the spatial frequency content in a digital image, and in particular the coarseness of any texture present. It is also an intermediate step in deriving the two-dimensional auto correlation function, which graphically describes the translational and rotational sym metry of an image. The cross-correlation function enables comparisons of similar patterns to be made and gives a means of measuring the changes in pattern definition that arise from wear. The low or high frequency components in an image can be suppressed with appropriate Fourier masks, allowing the pile texture or the colored pattern in a patterned carpet to be enhanced. This sort of transformation permits image processing methods that have proved useful in measuring the pile texture in plain carpets to be applied to patterned types.