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On Stability of Distance Measures for Event Sequences Induced by Level-Crossing Sampling

While Shannon's paradigm of sampling is based on equidistant points in time, triggered by a clock, level-crossing sampling schemes are based on the evaluation of the input signal's amplitude. Three types of level-crossing concepts are considered: a) absolute level-crossings, b) absolute level-crossings with hysteretic quantization, that ignores repeated crossings, and c) thresholding changes. The latter is also referred to as send-on-delta. Such event-driven sampling principles are encountered in asynchronous event-based data acquisition of wireless sensor networks in order to reduce the amount of data transfer and energy consumption, in event-based imaging in order to realize high-dynamic range image acquisition or in biology in terms of neuronal spike trains. The paper addresses the similarity between the event sequences which encode the quantized signals resulting from such event-based sampling concepts. It is shown that such event-driven sampling principles induce instability effects when using dissimilarity measures which are state-of-the-art in this context. As an alternative metric, Hermann Weyl's discrepancy norm is introduced, by which such instability effects can be avoided.