Geometric soft hash functions for 2D and 3D objects

Hash functions play a fundamental role in cryptography, data integrity and digital signatures. They are a valuable tool for implementing authentication protocols for electronic and multimedia content. In this paper we define and study soft hash functions used to obtain digital fingerprints of 2D and 3D geometrical objects, based on the Radon Integral Geometric Transform. These geometric one-way functions satisfy the classical compression, ease of computation and collision resistant properties. The digests are invariant to certain geometric transformations such as rotation and translation, and present a soft property: they are sensible to the global geometrical shape but not to small and local perturbations of the geometry. The main applications are: classical pattern recognition and watermarking detection (or watermarking removal detection). Digital fingerprints of virtual CAD-based 3D models can be used for testing geometric integrity and origin authentication. and can also be used to implement anti-counterfeiting techniques for real manufactured 3D pieces. The soft property guaranties the robustness of the digest to the 3D scanning process, which introduces only small local errors.