Statistically valid graph representations of scale-space geometry

Abstract

This paper presents a statistical scale-selection criterion for graph representations derived from differential geometric features of a greyscale image in a Gaussian scale space. The image gradient in scale space derives hierarchical and topological relationships among the bright and dark components in the image. These relationships can be represented as a tree and a skeleton-like graph, respectively. Since the image at small scales contains invalid geometric features due to noise and numerical errors, a validation scheme is required for the detected features. The presented scale-selection criterion allows us to identify the valid features used for the graph representations with statistical confidence. © 2008 Springer-Verlag.