Shape characterization in natural scales by using the multiscale bending energy

This work presents a new approach to shape characterization and analysis based on multiscale bending energy. Shapes are represented by their outlines and their respective multiscale curvatures, i.e. the curvegram, are estimated by using a scheme based on Fourier descriptors. The shrinkage problem is circumvented through perimeter normalization, which is crucial for allowing the quantitative analysis of the curvegram. Local and global multiscale bending energies are calculated from the curvegram, and the latter (i.e. global energy) is used in order to define the natural scales of the shape under analysis. Several issues concerning multiscale curvature quantitative analysis are discussed. The results regarding the application of the proposed technique to neuromorphometry are presented and discussed