A new methodology for quantifying the multi-scale similarity of images

Metrology of devices becoming more and more sophisticated, the collected information is subsequently still increasing. The characteristics of an engineering surface can often be recorded as an image. To compare the characteristics of two different engineering surfaces X and Y tailored with different process parameters, to determine process parameters that have to be controlled to produce a surface with desired properties or to quantify the relevance of a post image treatment for characterising a particular surface property, a practical problem of major interest is therefore to answer the question “are images related to surfaces X and Y similar at all the length scales?”. An original method, based on recent information theory assumptions and on the multi-fractal formalism, is proposed to quantify the degree of similarity of a set of images at all the length scales. The relevance of this method for characterising the morphological textures of surfaces was developed on simulated images generated by means of a 3D fractal function simulating an abrasion process.