Prediction Error Expansion (PEE) based Reversible polygon mesh watermarking scheme for regional tamper localization

This paper proposes a block based semi-fragile reversible authentication scheme that achieves regional localization for different classes of geometry and topology based mesh attacks. First of all, the model bounding volume is spatially partitioned into sub-volumes using Octree data structure and for each sub-volume, the embeddable units are computed. Each embeddable unit is comprises of three vertices and one bit can be embedded to an embeddable unit using a Prediction Error Histogram (PEH) shifting strategy. In PEH shifting, few of the embeddable units are expandable and few are shiftable. To compute PEH, Vertex Normal Value Ordering (VNVO) is performed and the maximum prediction error value is expanded. During PEH generation, to achieve sharper histograms and to get minimum numbers of shiftable units, adaptive bin-width selection step is also added. Verification of each block is performed by computing CRC-8 using vertex information from the block and embedding to the expandable units of the corresponding block itself. The proposed method could generate a sharper histogram than the state of the art methods and the proposed embedding function incurred very low distortion to mesh surface. It also outperforms the prior arts by achieving regional taper localization for both geometrical as well as topological attacks. The results analysis justifies the superiority of the proposed work than state of the art methods.