Continuous Phase Modulated Halftones and Their Application to Halftone Data Embedding

We propose a generalization of periodic clustered-dot halftones, wherein the phase of the halftones is modulated using a secondary signal. The process is accomplished using an analytic halftone threshold function and allows halftones to be generated with different phase variation in different regions of the printed page. We demonstrate that ensuring continuity of the phase assures that the resulting halftone images are free from visible artifacts despite the modulation in phase. We present, applications of the proposed method to halftone data embedding, wherein the changes in phase or in frequency encode the embedded information. For the frequency embedding, using continuous phase modulation, we also consider the limitations on signals that are embedded within our framework. For both applications, we demonstrate how the embedded signals may be recovered from the printed halftones either using the image as a self-reference which reveals the watermark when it is shifted and overlaid with itself or by employing a separate transparency mask