Linear and robust Gaussian regression filters

This paper presents a brief overview about Gaussian regression filters to extract surface roughness. The mathematical background in the spatial as well as in the frequency domain is discussed. It is shown that Gaussian regression filters work without any running in and running out sections and can approximate form up to pth degree. In the industrial world it is well known that linear filters are non robust, which means that any protruding peak or valley (also called `outlier') leads to a distorted roughness topography and effects the calculation of surface parameters directly. In particular plateau like surfaces are good candidates for such critical datasets. In the paper it is shown that such a distortion can be avoided by choosing an appropriate Ψ function. This proceeding leads to the so called robust Gaussian regression filter with all the advanced properties of the linear one.