Statistics and category systems for the shape index descriptor of local 2nd order natural image structure

The shape index offers a natural and invariant description of pure 2nd order image structure. We discuss its properties and report novel natural image statistics for the shape index and the additional two parameters of curvedness and principal direction that form a complete and decoupled re-parameterisation of 2nd order structure. In a second main theme, we address three separate avenues to a categorisation of the shape index for natural images and suggest five feature categories as a natural 2nd order image structure ‘alphabet’.