Characterizing Anisotropy of the Deterministic Features in Paper Structure with Wavelet Transforms

A novel method for evaluating the anisotropy of the deterministic features in stochastic 2D data is introduced. The ability of the wavelet transform to identify abrupt discontinuities or edges could be used to char- acterize the boundary of the deterministic area in 2D stochastic data, such as flocs in paper structure. The one-di- mensional wavelet transform with a small-scale range in MD and CD could quantify the amounts of edges in both directions, depending on the intensity of each floc. The flocs that are aligned in the MD direction result in a higher value of local wavelet energy in the CD direction. Therefore, the ratio of the total wavelet energy in the CD and MD directions can be used as a new anisotropy index. This index is a measure of the floc-orientation and can provide an excellent tool to obtain the orientation distribution and the major oriented angle of the flocs. Various simulated images and real stochastic data, such as the formation image in a pilot machine sample, have been tested; the results show that this analysis method is a very reliable technique for measuring the anisotropy of deterministic features.