Geometric Computing in Shape Space

In geometric computing, a shape is typically viewed as a set of points and then represented accordingly, depending on the available data and the application. However, it has been known for a long time that simple shapes may be treated more elegantly by viewing them as points in a higher-dimensional space. Examples include line and sphere geometries, kinematical geometry and Lie groups. Recently, fundamental mathematical properties of spaces of more complicated objects have been studied and applied to certain problems in image processing.