The spline filter: A regularization approach for the Gaussian filter

The Gaussian filter described in the ISO 11562 standard has become the most widely used filtering technique in surface metrology. However, this filter is always plagued by the large distortions called end effects at the boundaries of the filtered result. In order to alleviate the end effects, the spline filter based on natural cubic splines is incorporated into ISO standard as a substitute. So there exist two kinds of linear profile filters with different transmission characteristics which also lead to different mean lines for the assessment of the same surface. A new spline algorithm for determining the Gaussian filtered mean line is deduced using the central limit theorem. The filter uses the cascade method of the approximating spline filter, and therefore can approximate the transmission characteristic of the Gaussian filter with high accuracy. It is proved that the transmission characteristic relative deviation of the cascade approximating spline filter from the Gaussian filter is only 0.3% when the cascade order approaches infinity. With this theorem, it is easy to achieve the unification of the international standard ISO 16610-21 and ISO 16610-22.