This work presents an approximate global optimization method for image halftone by fusing multi-scale information of the tree model. We employ Gaussian mixture model and hidden Markov tree to characterized the intra-scale clustering and inter-scale persistence properties of the detailed coefficients, respectively. The model of multiscale perceived error metric and the theory of scale-related perceived error metric are used to fuse the statistical distribution of the error metric of the scale of clustering and cross-scale persistence. An Energy function is then generated. Through energy minimization via graph cuts, we gain the halftone image. In the related experiment, we demonstrate the superior performance of this new algorithm when compared with several algorithms and quantitative evaluation.

We present a new framework for embedding holographic halftone watermarking data into images by fusion of scale-related wavelet coefficients. The halftone watermarking image is obtained by using error-diffusion method and converted into Fresnel hologram, which is considered to be the initial password. After encryption, a scrambled watermarking image through Arnold transform is embedded into the host image during the halftoning process. We characterize the multi-scale representation of the original image using the discrete wavelet transform. The boundary information of the target image is fused by correlation of wavelet coefficients across wavelet transform layers to increase the pixel resolution scale. We apply the inter-scale fusion method to gain fusion coefficient of the fine-scale, which takes into account both the detail of the image and approximate information. Using the proposed method, the watermarking information can be embedded into the host image with recovery against the halftoning operation. The experimental results show that the proposed approach provides security and robustness against JPEG compression and different attacks compared to previous alternatives.