Differential invariants of curves and surfaces such as curvatures and their derivatives play a central role in Geometry Processing. They are, however, sensitive to noise and minor perturbations and do not exhibit the desired multi-scale behaviour. Recently, the relationships between differential invariants and certain integrals over small neighborhoods have been used to define efficiently computable integral invariants which have both a geometric meaning and useful stability properties. This paper considers integral invariants defined via distance functions, and the stability analysis of integral invariants in general. Such invariants proved useful for many tasks where the computation of shape characteristics is important. A prominent and recent example is the automatic reassembling of broken objects based on correspondences between fracture surfaces.
author = "Helmut Pottmann and Johannes Wallner and Qixing Huang
and Yong-Liang Yang",
title = "Integral Invariants for Robust Geometry Processing",
journal = "Comput. Aided Geom. Design",
year = 2009,
url = "http://www.geometrie.tugraz.at/wallner/iirgp.pdf",
doi = "http://dx.doi.org/10.1016/j.cagd.2008.01.002",