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Dynamic Smoothing Meets Gravity

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STSW02 - Statistics of geometric features and new data types

authors: Jim Ramsay, Michelle Carey and Juan Li institutions: McGill University, University College Dublin, and McGill University Systems of differential equations are often used to model buffering processes that modulate a non-smooth high-energy input so as to produce an output that is smooth and that distributes the energy load over time and space. Handwriting is buffered in this way. We show that the smooth complex script that spells `”statistics” in Chinese can be represented as buffered version of a series of 46 equal-interval step inputs. The buffer consists of three undamped oscillating springs, one for each orthogonal coordinate. The periods of oscillation vary slightly over the three coordinate in a way that reflects the masses that are moved by muscle activations. Our analyses of data on juggling three balls and on lip motion during speech confirm that this model works for a wide variety of human motions. We use the term “dynamic smoothing” for the estimation of a structured input functional object along with the buffer characteristics.

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