Robust 2D Engineering CAD Graphics Hashing for Joint Topology and Geometry Authentication via Covariance-Based Descriptors

This paper investigates the joint authentication of topology and geometry information of 2D engineering computer-aided design graphics, which focus more on topological modeling than geometric modeling of objects. A robust hashing scheme is proposed for joint topology and geometry authentication. The covariance matrices of descriptors are explored to fuse and encode both topology and geometry features of different types into a compact representation. First, a normalized binary shape texture is rendered for each geometric object through the render-to-texture technique. Then, for each geometric object, geometry features are computed based on statistical features that are extracted from image rings. Additionally, topology features are generated according to the topological relations among joint objects. To generate hash codes of the graphic, all geometric objects are first grouped according to their geometry features. Then, for each group, the covariance matrices of descriptors are applied to fuse both the topology and geometry features of all objects, and the intermediate hash codes of each group are computed based on the covariance matrices. The final hash sequence is formed by concatenating the intermediate hash codes that correspond to each group. Secret keys are introduced into both feature extraction and hash construction. The hashes are robust against topology-preserving graphic manipulations and sensitive to malicious attacks. By decomposing the hashes, the locations of tampered objects can be determined. Experimental results are presented to evaluate the performance and show the effectiveness of the method.