Abstract
Approximation is one of the most useful methods for understanding data distribution. However, most conventional approximation methods using Gausian distribution or uniform distribution do not pay sufficient attention to the geometric properties of data. This study focuses on Geometric Algebra (GA), which is a generalization of complex numbers and quaternions able to describe spatial objects and the relations between them. This paper uses conformal GA (CGA), which is a part of GA, to transform a vector in a real vector space into that in a CGA space and proposes a new approximation method using conformal vectors. In particular, the proposed approximation was able to express various data distributions, such as those based on hyper-spheres (-planes), circles (lines) and arcs. Using combination with particle filter, this paper shows that it was able to extract the joint positions of an object in 3 dimensional space from one camera, which could not be detected by conventional methods.
