Novel similarity and distance measures with applications in machine learning, image and signal processing

• Bernhard Moser

This work relies on pure mathematical as well as on application-oriented research related to imposing additional compliance properties on (dis)similarity measures in various application contexts. The non-standard properties under consideration are a) t-transitivity w.r.t. triangular norms in the context of kernel-based methods, b) monotonicity and Lipschitz property w.r.t. autocorrelation and auto-misalignment function in the context of matching signal and image patterns and c) stability criteria at the level of (dis)similarity measures for event-based image and signal processing. This approach has brought about new theoretical findings in such various fields as a) determination of the texel size of nearly regular textures, b) self-adaptive template matching-based quality surface inspection algorithms, c) robust matching of event sequences that result from levelcrossing sampling, and pure mathematical findings such as a) the characterization of Hermann Weyl’s discrepancy norm in terms of a zonotope, b) a combinatorial approach for determining the distribution of the range of a simple random walk, and c) novel Pascal triangle identities which are related to Fibonacci numbers.