Nonlinear image filtering for materials classification

The core of image spectrum enhancement (ση) is spatial differentiation of a suitable order, including a fractional one, followed by non linear transformations. When the control parameters are optimized, enhanced spectra seem to adequately describe the morphology of the image by separating structure from texture, which in turn are (statistical) properties of the image, or of the image set, as a whole. Image classification based on spectrum enhancement follows accordingly. If one is interested in structure and texture, then classification most likely succeeds. Indeed, the algorithm has been shown to perform in a satisfactory way on a variety of image sets, originated from as many different processes (nanodispersion, growth of tubulin microfilaments, formation of cell colonies, light scattering by material particles). Instead, spectrum enhancement, as any frequency domain method, is inappropriate to exactly locate isolated features or details. The applications to materials science described in this article differ by complexity of the algorithm and by the degree of "assimilation" to other experimental data. The morphology of TrBP has been described in a very simple way by means of the surface roughness index, ρ (Def. 5). Graphs of enhanced spectra of the investigated materials (Figure 4) have been related to surface structure and texture (Table I). Finally, ρ has been related to elemental microanalytical data from EDX spectroscopy (Figure 5). Possible developments include: the analysis of other types of TWP and studies of fracture dynamics. Images of other TWP materials by the ση algorithm is possible, provided the particle surfaces are visible. Namely, coarse particles from treadwear tests are clad by minerals (from anti-smear agents or from road pavement), as shown by the right panel of Figure 1. Micrometer sized particles are more easily imaged and analysed. Quantitative morphology of wear debris is relevant to the characterisation of rate dependent fracture mechanisms and therefore to assess the reliability of a given product. The application to nanodispersions has included the development of an automated classifier, capable of discriminating materials to some extent (Figure 8). Enhanced spectra of single tiles have been interpreted in relation to particle dispersion and the formation of aggregates (Figure 9). Correlation between the automated classifier and visual scoring has been obtained (Figure 10). Knowledge of the mixer parameters might have deepened the understanding of automated morphological analysis. Developments are needed at least in two directions. In the first place a relation shall be found between the Q of Eq. 19 and enhanced spectra. Namely, Q describes dispersion if evaluated locally (i.e., estimated from a single image), whereas its statistical properties describe distribution, and shall be estimated from an image set. Another issue of interest is the estimation of the representative elementary domain, U, from ση and other experimental techniques.