Compression and rotation resistant watermark using a circular chirp structure

Digital watermarks for images can be made relatively robust to luminance and chrominance changes. More challenging problems are geometric or combined intensity/geometric attacks. In this work we use an additive watermarking model, commonly used in spread spectrum, using a new spreading function. The spreading function is a 2D circular chirp that can simultaneously resist JPG compression and image rotation. Circular chirp is derived from a block chirp by polar mapping. The resistance to compression is achieved by the available tuning parameters of a block chirp. Tuning parameters are chirp’s initial frequency and chirp rate. These two parameters can be used to perform spectral shaping to avoid JPEG compression effects. Rotational invariance is achieved by mapping the block chirp to a ring whose inner and outer diameters are selectable. Watermark is added in spatial domain but detection is performed in polar domain where rotation translates to translation.