Unified framework for multi‐scale decomposition and applications

Since real‐world digital images differ in thousands ways, an adaptive multi‐scale decomposition scheme adapting to images is increasingly urgently required for image analysis and applications. In this paper, a unified framework for multi‐scale decomposition is developed. Instead of full using the extrema in bi‐dimensional empirical mode decomposition (BEMD), edges are fully taken into account because edges play an important role in images. First, effective edges are extracted using spatial scale, intensity difference and other parameters through their coarse‐to‐fine edge detection approach. Given Gaussian noise series with the same variance are added to these edges repeatedly to produce extrema. Then the produced extrema on edges are employed to interpolate to calculate the mean and further the different detail components from multiple noised signals on average. Through manipulating the parameters of this framework, multiple decomposition patterns: the alternative edge‐preserving multi‐scale decomposition and non‐edge‐preserving multi‐scale decomposition along with in‐between transitional multi‐scale decomposition can be obtained, respectively. It shows that the existing multi‐scale decomposition methods of BEMD can be taken as special cases of this decomposition framework. Finally, comparisons with other methods are performed and numerous applications of this decomposition approach are explored to show its efficiency.