An Overview of the Relationship Between Approximation Theory and Filtration
Abstract
This paper gives an overview of the similarities and differences between the requirements and techniques used in mathematical approximation theory and filtration in surface metrology. Although the two fields tend to use the same or similar mathematical objects to produce functions that simplify a function in a controlled manner, it is the way that this simplification is achieved which is the main difference between the two. Approximation theory uses norms to judge the closeness of the approximation while filtration uses the concept of wavelength to control the "smoothness" of the result of filtration. The new ISO definition of a filter is stated, together with a generalisation of the concept of wavelength through "brickwall" filters. This new ISO definition of a filter illustrates the closeness of approximation theory and filtration. The paper then proceeds to survey some recent developments in filtration in the hope that there can be some cross-fertilisation between approximation theory and filtration. These include wavelets, robust filters and non-linear filters such as the family of morphological filters, which includes envelope filters and alternating sequence filters (non-linear multiresolution). Examples from surface texture are used throughout the paper.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 2001
- Accession Number
- ADP013729
Entities
People
- Liam A. Blunt
- Paul J. Scott
- Xiang Q. Jiang
Organizations
- University of Huddersfield