Mixture Models for the Analysis, Edition, and Synthesis of Continuous Time Series
This is an incremental overview for researchers in fields like computer graphics and robotics, summarizing existing techniques without introducing new methods.
The chapter tackles the problem of analyzing, editing, and synthesizing continuous time series, particularly motion data, by using mixture models to decompose signals into basis functions for compact representation, with examples including radial, Bernstein, and Fourier basis functions.
This chapter presents an overview of techniques used for the analysis, edition, and synthesis of 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 will be presented, with associated source codes to get familiar with these techniques.