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\documentclass[12pt,journal,compsoc]{IEEEtran}\usepackage{alltt}\usepackage{amssymb}\usepackage{amsfonts}\usepackage{mathtools}\usepackage{array}\usepackage{amsmath}\usepackage{graphicx}\usepackage{float}\usepackage{lipsum}\begin{document}\subsection{Related Work}Fractal encoding can be done in spatial domain[10][11] and frequency domain[12]. Paul Darvin[13] suggested a fractal method that uses the information of range and domain region as key. Joan Paute and Fred Jordan[14] used key to generate coordinates of range blocks. Patrick Bas and Jean-Marc Chassery[15][16] used fractal scheme for watermarking. They find the transformation such that for each block D and R, a new range block $\hat R$ is calculated as\\$\hat R = \frac{\delta*S*D}{max(D)}+\bar R$\\where S determines the magnitude of the watermark, $\bar R$ is the mean of R and\[ \delta = \left\{\begin{array}{l l}& \quad \text{+1 if the embedded bit=1}\\& \quad \text{ -1 if the embedded bit=0}\end{array} \right.\]\subsection{Implementation}Implementation of the algorithm is based on the following assumptions:\begin{table}[ht]\centering % used for centering table\begin{tabular}{l} % centered columns (1 columns)\hline % inserts single horizontal line\\\noindent$\bullet$ Append data with the label END OF DATA.\\$\bullet$ XOR data with key.\\$\bullet$ Subsample domain blocks D so that they have same number of pixels \\