Euclidean and Geodesic Distance Profiles

This paper presents a boundary-based, topological shape descriptor: the distance profile. It is inspired by the LBP (= local binary pattern) scale space – a topological shape descriptor computed by a filtration with concentric circles around a reference point. For rigid objects, the distance profile is computed by the Euclidean distance of each boundary pixel to a reference point. A geodesic distance profile is proposed for articulated or deformable shapes: the distance is measured by a combination of the Euclidean distance of each boundary pixel to the nearest pixel of the shape’s medial axis and the geodesic distance along the shape’s medial axis to the reference point. In contrast to the LBP scale space, it is invariant to deformations and articulations and the persistence of the extrema in the profiles allows pruning of spurious branches (i.e. robustness against noise on the boundary). The distance profiles are applicable to any shape, but the geodesic distance profile is especially well-suited for articulated or deformable objects (e.g.applications in biology).