Quantifying Surface Roughness of Carpets by Fractal Dimension

Abstract

Surface roughness of carpets refers to the degree of irregularity in the terrain of a carpet surface, and reflects the severity of appearance change with wear, such as pilling, untwisting, tuft matting and crushing. An irregular, rough surface can be represented by a fractal function, and quantified by its fractal dimension. This study used a specially-developed imaging system, including a CCD camera, a frame grabber and a computer, as an analytical tool for capturing and processing carpet images. The study applied the fractal dimension to quantifying surface roughness of carpets, and to analyzing appearance loss in carpets owing to mechanical wear. One algorithm for computing fractal dimensions, "reticular cell counting ", was illustrated. It was found from a trial test that the fractal dimension of a carpet surface corresponds to a visual assessment of the surface wear, and a change in fractal dimensions consistently indicates a change in carpet appearance. Hence, a fractal dimension can be used as an effective descriptor of carpet roughness.