We present a new optimal watermarking scheme based on discrete wavelet transform (DWT) and singular value decomposition (SVD) using multiobjective ant colony optimization (MOACO). A binary watermark is decomposed using a singular value decomposition. Then, the singular values are embedded in a detailed subband of host image. The trade-off between watermark transparency and robustness is controlled by multiple scaling factors (MSFs) instead of a single scaling factor (SSF). Determining the optimal values of the multiple scaling factors (MSFs) is a difficult problem. However, a multiobjective ant colony optimization is used to determine these values. Experimental results show much improved performances of the proposed scheme in terms of transparency and robustness compared to other watermarking schemes. Furthermore, it does not suffer from the problem of high probability of false positive detection of the watermarks. 1. Introduction With the advent of numeric era at the end of 20th century, the exchange of digital documents became a very easy task. This extraordinary technical revolution from analog to numerical technology was not achieved without generating anxiety in terms of the protection of the authors rights since multimedia documents can be quite easily duplicated, modified, and illegally attacked without deterioration. Affected by significant revenue losses multimedia documents author’s are motivated more than ever to secure their documents. In this context digital watermarking was introduced: it consists of inscribing invisible (or visible) data into the multimedia documents. This is done in two stages: embedding and extracting process. Digital watermarking schemes for images can be classified into different classes according to embedding domain, embedding rule, imperceptibility, and permanency. In terms of robustness, the watermarking algorithm can be classified into three categories: fragile, semifragile, and robust. Fragile watermarking is designed to detect any modification in such a way that slight modifications or tampering on the watermarked image will destroy the watermark. This type is employed to ensure the integrity and image authenticity. Conversely, robust watermarking is designed to be resistant against attacks that attempt to remove or destroy the watermark without degrading the visual quality of the watermarked image significantly. Robust watermarking is typically employed for copyright protection and ownership verification. Semifragile watermarking combines the properties of fragile and robust watermarking in order to detect
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