Planar closed contour representation by invariant under a general affine transformation

This paper presents a new multiscale and zero-crossing, curvature-based shape representation technique for planar curves with general affine transformation. The method consists of the concept of describing a curve at varying levels of detail using features that are invariant with respect to transformations that do not change the shape of the curve. The process of describing a curve at increasing levels of abstraction is referred to as the affine evolution of that curve. This affine evolution does not change the physical interpretation of planar curves and characterize the behaviors of inflexion points of the curves during its evolution.