A new approach to transparent embedding of data into digital images is proposed. It provides a high rate of the embedded data and is robust to common and some intentional distortions. The developed technique employs properties of the singular value decomposition (SVD) of a digital image. According to these properties each singular value (SV) specifies the luminance of the SVD image layer, whereas the respective pair of singular vectors specifies image geometry. Therefore slight variations of SVs cannot affect the visual perception of the cover image. The proposed approach is based on embedding a bit of data through slight modifications of SVs of a small block of the segmented covers. The approach is robust because it supposes to embed extra data into low bands of covers in a distributed way. The size of small blocks is used as an attribute to achieve a tradeoff between the embedded data rate and robustness. An advantage of the approach is that it is blind. Simulation has proved its robustness to JPEG up to 40%. The approach can be used both for hidden communication and watermarking.