This paper proposes a new approach for assessing the presence of a digital watermark in images and videos. This approach relies on a Bayesian formulation that allows to compute the probability that a watermark was generated using a given key. The watermarking itself relies on the discrete Fourier transform (DFT) of the image, of video frames or of three dimensional chunks of video scene. Two kinds of information are hidden in the digital data: a watermark and a template. Both are encoded using an owner key to ensure the system security and are embedded in the 2D or 3D DFT magnitude of the image or video. The watermark is encoded in the form of a spread spectrum signal. The template is a key based grid and is used to detect and invert the effect of an affine geometric transformation (rotations, scaling and/or aspect ratio change) or in the case of the video frame-rate changes, aspect-ratio modification and rescaling of frames. It is shown that, for the spread spectrum signal described in the paper, it is possible to positively detect the presence of a watermark without necessarily decoding it, given only the key used to generate it. To do that, the Bayesian approach allows the deduction of the relative log-probability of the presence of a watermark in an image given only the key. All that is required for positive watermark verification is the key. This approach also allows to infer the number of bits contained in the watermark. The performance of the presented techniques and the usefulness of the relative log-probability are shown through various applications and experimental results.