The ease of digital media modification and dissemination necessitates content protection beyond encryption. Information hidden as digital watermarks in multimedia enables protection mechanism in decrypted contents. The aims of this research are three-fold: (i) to investigate the strength and limitations of current watermarking schemes, (ii) to design and develop new schemes to overcome the limitations, and (iii) to evaluate the new schemes using application scenarios of copyright protection, tamper detection and authentication. We focus on geometrically robust watermarking and semi-fragile watermarking for digital images. Additionally, hybrid schemes that combine the strength of both robust and semi-fragile watermarks are studied. Robust watermarks are well suited for copyright protection because they stay intact with the image under various manipulations. We investigated two major approaches of robust watermarking. In the synchronization approach, we employed motion estimation for watermark resynchronization. We also developed a novel watermark resynchronization method that has low computational cost using scale normalization and flowline curvature. In another approach, we firstly analyzed and improved a blind watermark detection method. The new method reduces significantly the computational cost of its watermark embedding. Secondly, we created a geometric invariant domain using a combination of transforms, and adapted the blind watermark detection method that we improved. It totally eliminates the need of resynchronization in watermark detection, which is a very desirable achievement that can hardly be found in existing schemes. On the other hand, semi-fragile watermarks are good at content authentication because they can differentiate minor image enhancements from major manipulations. New capabilities of semi-fragile watermarks are identified. Then, we developed a semi-fragile watermarking method in wavelet domain that offers content authentication and tamper localization. Unlike others, our scheme overcomes a major challenge called cropping attack and provides approximate content recovery without resorting to an original image. Hybrid schemes combine robust and semi-fragile watermarks to offer deductive information in digital media forensics. We firstly carried out a pilot study by combining robust and fragile watermarks. Then, we performed a comparative analysis on two implementation methods of a hybrid watermarking scheme. The first method has the robust watermark and the fragile watermark overlapped while the second method uses non-overlapping robust and fragile watermarks. Based on the results of the comparative analysis, we merge our geometric invariant domain with our semi-fragile watermark to produce a hybrid scheme. This hybrid scheme fulfilled the copyright protection, tamper detection, and content authentication objectives when evaluated in an investigation scenario.

On étudie la conjecture des graphes jumeaux dénombrables, cas spécifique d’une conjecture de Thomassé, qui dit que le nombre de jumeaux d’un graphe dénombrable ( ses sous-graphes propres desquels il est aussi un sous-graphe propre) est soit nul, soit infini. On commence par étudier les graphes auto-abrités, que nous définissons, et en utilisant notre classification de ces graphes nous prouvons la conjecture dans certains cas, en précisant la cardinalité exacte du nombre de jumeaux. Nous donnons également des contre-exemples à l’article de l’arXiv «Self-contained graphs». / We make progress on the Graph Alternative Conjecture, a special case of a conjecture of Thomassé which says that the number of twins of a countable graph (i.e. its proper subgraphs of which that graph is also a proper subgraph) is either null or infinite. We begin by studying self-embedded graphs, which we define, and using our classification of these graphs, we prove the conjecture in some cases while specifying the exact number of twins. We also give counter-examples to a paper on arXiv called "Self-contained graphs".