Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

A simple and fast spline filtering algorithm for surface metrology



Hao H. Zhang, Daniel B. Ott, Jun-Feng Song, D Ott, Wei Chu


The spline filters and the corresponding robust filters are commonly used filters recommended in ISO standards for surface evaluation. Generally, these linear and non-linear spline filters, composed of symmetric, positive-definite matrices, are always solved in an iterative fashion based on Cholesky decomposition. They have been demonstrated to be relatively efficient, but complicated and inconvenient to implement. A new algorithm for the spline filter is proposed by means of the discrete cosine transform or the discrete Fourier transform. The algorithm is conceptually simple and very convenient to implement.
Journal of Research (NIST JRES) -


Surface metrology, Spline filter, Discrete cosine transform, Discrete Fourier transform


Zhang, H. , Ott, D. , Song, J. , Ott, D. and Chu, W. (2015), A simple and fast spline filtering algorithm for surface metrology, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD, [online],, (Accessed February 22, 2024)
Created July 13, 2015, Updated November 14, 2018