Texture characterization of digital images which have a periodicity or a quasi-periodicity

In this paper we analyse digitally generated fractal images added to periodic patterns using the variance of grey levels with four parameters. The variogram shows a linear fit at low scale and a multiple periodic behaviour at high scale. The image texture is characterized by the fractal dimension D at low scale and two textural parameters at high scale: d(min) and d(per). The intersection of the straight line that fits the fractal region and the tangent line at the maximum of the periodic region determines the d(min) parameter; it accounts for the smallest cell size with enough statistical weight to produce periods. The dper parameter approaches the average distance between the nearest cells with enough statistical weight to produce periods. The characterization is completed with the study of the image anisotropies through changes under rotation in fractal dimension D and topothesy Lambda. This analysis is applied to SEM images of CSi emery paper particles of different grades and origin. The results of d(min) compare satisfactorily with dimensional characteristics of particle sizes, according to Federation of European Producers of Abrasives and ISO 6344/1 and 6344/3 standards. The d(per) values are congruent with the average distance between particles for different grades of paper, thus making possible the evaluation of different qualities.