Directional statistics and shape analysis

This paper highlights distributional connections between directional statistics and shape analysis. In particular, we provide a test of uniformity for highly dispersed shapes, using the standard techniques of directional statistics. We exploit the isometric transformation from triangular shapes to a sphere in three dimensions, to provide a rich class of shape distributions. A link between the Fisher distribution and the complex Bingham distribution is re-examined. Some extensions to higher-dimensional shapes are outlined.