## 5 Considerations on the Proposed Scheme  
The proposed watermarking algorithm performs a block-wise SVD transform on the original image. Naturally, the first question that we encounter is: which is the optimal size of the blocks used throughout the watermarking process? We noticed that the embedding block size is an important parameter which affects the requirements, properties and behaviour of the watermarking scheme. It is important to note that the application of a block-wise transform on the original image produces more robust features against signal processing operations and common attacks, than features provided by a whole transform. Moreover, the features obtained from the SVD transform (i.e., singular values and vectors) have a different behaviour: the _stability_ (and, implicitly, the _robustness_) of the singular values and vectors is inversely proportional to the size of the segmentation block. Indeed, the SVD transform produces highly stable features when performed on large images (blocks). In general, the attacks which are very sensitive to the segmentation size are JPEG compression and noise addition (e.g., white Gaussian noise or salt and pepper noise) [20]. On the other hand, by splitting the cover image into small blocks, the watermark sequence can be embedded redundantly, i.e., each bit of the watermark is inserted in more image blocks. This ability confers to the watermarking scheme a high robustness against geometric attacks (e.g., translation, cropping and scaling). Unfortunately, to achieve robustness against the geometric attacks it is required to embed the watermark redundantly which causes a sharp reduction of the watermark payload, i.e., number of bits which can be embedded into the cover image [36]. Thus it is necessary to realize a trade-off between the robustness against geometric attacks and the payload of the watermark sequence. Besides these requirements of the watermarking scheme (robustness and payload) it is important to take into consideration the quality of the watermarked image [57] which is related to:  
* _Imperceptibility_: A perfectly imperceptible bit sample of the watermark is present if the watermarked media and the original cannot be distinguished. * _Undetectability_: The digital content due to the carried watermark information is not detectable if it is _consistent_ with the original data. Non-detectability cannot be directly linked to non-perceptibility that is based on the concepts of human perceptions. Non-detectability is related to the data source and its components. It describes the consistency with the original data. It is important to mention that segmenting the original image into small blocks satisfies the undetectability and imperceptibility features. Another important property that we need to consider when devising watermarking schemes is _security_. All existing watermarking algorithms which are not _secure_ cannot be used for copyright protection, for data authentication or to trace the illegal distribution of the digital content. Thus, a robust watermarking algorithm is _secure_ if an attacker, exploiting the knowledge of the applied watermark procedure and without knowing the secret keys used to watermark the digital content, cannot damage or destroy the hidden information of the watermark [36]. Moreover, complexity of the watermarking procedure may be related to security, since an attacker will be discouraged to search the embedding locations in a large embedding space and for a long secret key. Therefore, to increase the security of the algorithm, we can enlarge the embedding space and increase the size of the secret key by splitting the cover image into small blocks. In our scheme, the secret key \(K\) consists of two parts:  
* The seed used to generate the watermark sequence \(W\), i.e., the Gaussian distribution with zero mean and unitary variance. * The singular vectors chosen in the watermarking process and their components from which we construct the feature set.