Research On Reversible Watermarking Based On Three-Dimensional Meshes

Reversible data embedding embeds invisible data into a digital image in a reversible fashion, which can be used in such particularly sophisticated domains as military and medical image processing. With the development of Internet and3D modeling techniques, mesh watermarking technology has been a general concern, and reversible watermarking for three-dimensional meshes came up at the same time.This thesis proposes two different algorithms for reversible data hiding. One is based on general difference expansion in which the mesh model needs dividing into disjoint area comprised of one vertex and its1-ring neighboring vertices. The other is based on prediction-error expansion. In the first method, differences among the vertices’coordinates are calculated and expanded to embed the watermark bits To further reduce the distortion a threshold is chosen so that the difference with too large magnitude will not be expanded. In the second method, we predict a vertex position by calculate the centroid of its1-ring neighbors. Then the prediction error, that is, the difference between the predicted and real positions, is expanded for data embedding. We detect the curvature for selective embedding without referring to the location map, which is more practical. Both algorithms are actually difference expansion method and execute more efficiently without embedding the extra location information. However, these two different algorithms have their own value in practical applications. Reversible watermarking based on general difference expansion has rich capacity due to embedding multiple watermark bits in one embedding unit, which results in high payload density. Once the model is damaged or somehow changed, the embedding information will be difficult to extract. Therefore, this kind of algorithm is mainly used for fragile watermarking. On the contrary, reversible watermarking based on prediction-error expansion is sparse in density because there is only one watermark bit in each embedding unit. Therefore, this kind of algorithm can be explored for robust watermarking. We also explore and study the robustness of the three-dimensional reversible watermarking. Based on difference expansion, we choose center distance as the embedded watermark carrier to enhance the robustness against such unintentional attack as translation, rotation, noise, etc. In addition, we also discuss the synchronization of watermark in meshes and try to acquire an algorithm which is able to withstand the attack of vertices reordering. Vertices reordering will not change the content and topology of the meshes, but will seriously affect watermark extraction because most of the watermarking algorithms depend on the order of vertices in the file. Therefore, how to determine a simple robust intrinsic ordering for mesh elements continue to be a big challenge for3D meshes. According to the geometric characteristics of center distance, we appoint a relatively stable ordering for the embedding primitives, making the algorithm able to resist the attack of vertices reordering.The main contribution of this paper is propose reversible watermarking methods for3D meshes based on the mature reversible watermarking algorithm for images, in which we explore the geometric characteristics of meshes to determine the embedding carrier and the synchronization of watermark bits. Our proposed methods prove better performances both in capacity and invisibility compared to other similar methods. Since the embedding methods and extracting methods are completely invertible, the original meshes can be recovered after the extraction of watermark.