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2020 | OriginalPaper | Chapter

3. Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series

Author : Sylvain Calinon

Published in: Mixture Models and Applications

Publisher: Springer International Publishing

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Abstract

This chapter presents an overview of techniques used for the analysis, edition, and synthesis of continuous time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition of basis functions. It provides a compact representation that aims at keeping the essential characteristics of the signals. Various types of basis functions have been proposed, with developments originating from different fields of research, including computer graphics, human motion science, robotics, control, and neuroscience. Examples of applications with radial, Bernstein, and Fourier basis functions are presented, with associated source codes to get familiar with these techniques.

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previous chapter Interactive Generation of Calligraphic Trajectories from Gaussian Mixtures

next chapter Multivariate Bounded Asymmetric Gaussian Mixture Model

We will see later that the rescaled form is required for some techniques, but for locally weighted regression, it can be omitted to enforce the independence of the local function approximators.

In [21], cosine basis functions are employed but the approach can be extended to other basis functions.

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, where \(\boldsymbol {H}_{2^D-D+1:2^D,m}\) is a vector composed of the last D elements in the column m of the Hadamard matrix H of size 2^D. Alternatively,

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can be constructed with the array ℓ _m, with m indexing the first dimension of the array

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with

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. In 2D, we have

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and

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, see Fig. 3.5d.

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Title: Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series
Author: Sylvain Calinon
Publisher: Springer International Publishing
Book: Mixture Models and Applications
Print ISBN: 978-3-030-23875-9

Electronic ISBN: 978-3-030-23876-6

Copyright Year: 2020
DOI: https://doi.org/10.1007/978-3-030-23876-6_3

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