Topology authentication for CAPD models based on Laplacian coordinates

Abstract

Topology authentication for computer-aided plant design (CAPD) models features intrinsically complex topological relations. This study investigates a semi-fragile watermarking scheme for CAPD models represented by parametric solids, which offers a solution to the problem of topology authentication. We first analyze the geometrical and topological structures of CAPD models. Then, we propose an effective semi-fragile watermarking method for topology authentication, which is based on Laplacian coordinates and quantization index modulation (QIM), against several attacks. We compute the custom Laplacian coordinate vector for each marked connection point according to the topological relation among joint plant components. The topology-based watermark for each marked connection point is generated from selected attributes of its joint plant component. Watermarks are inserted into the coordinates of marked connection points by adjusting the lengths of their Laplacian coordinate vectors. Both experimental results and theoretical analysis demonstrate that our approach can not only detect and locate malicious topology attacks, such as component modification and joint ends modification, but is also robust against various non-malicious attacks, such as similarity transformations and level-of-detail (LOD).