Lie Group Harmonic and Statistical Analysis of Human Movement

Statistical and harmonic analysis of 3-dimensional motions of objects or humans are instrumental to establish how
these motions differ, depending on various influences. When such motions involve no tearing, they may be described
by elements of the Euclidean Group. Algorithms developed in the author’s Ph.D. dissertation exploit the unique properties of Conformal Geometric Algebra to carry out such analyses efficiently by computer, despite complications resulting from the basic properties of the group; for example, the arithmetic average of two rotations is not a rotation. This project combines these methods with harmonic analysis, also formulated using Conformal Geometric Algebra, to permit statistical estimation of the rotational axes and frequencies of the periodic components of 3-dimensional motions. This will considerably enrich the analytical tools already developed by the author. The end goal is to make the extended package available to a wide variety of researchers, clinicians and commercial users.

Faculty Supervisor:

Peter F. Driessen

Student:

Partner:

GeoVerse Inc

Discipline:

Mathematics

Sector:

Professional, scientific and technical services

University:

University of Victoria

Program: