Pattern analysis and metrology: the extraction of stable features from observable measurements

To extract patterns from observable measurements we need to be able to define and identify stable features in observable measurements that persist in the presence of small artificial features such as noise, measurement errors, etc. The representational theory of measurement is used to define the stability of a measurement procedure. A technique, 'motif analysis', is defined to identify and remove 'insignificant' features while leaving 'significant' features. This technique is formalized and three properties identified that ensure stability. The connection of motif analysis with morphological closing filters is established and used to prove the stability of motif analysis. Finally, a practical metrology example is given of motif analysis in surface texture. Here motif analysis is used to segment a surface into its significant features.