Fast EMD For Multi-channel Images Based On Morphological Filtering And Its Application

EMD(Empirical Mode Decomposition)is suitable for processing nonlinear and non-stationary signals and is completely data-driven.Its proposal is regarded as an important innovation in the field of signal analysis and processing.EMD can overcome the limitation of the selection of basis in Fourier analysis and Wavelet analysis,and is widely used in the analysis and processing of the signals from Meteorology,Geology,Electric power system,etc.Although two-dimensional EMD has been widely used in image processing and analysis,the existing EMD methods for multi-channel images still have some improvement room in terms of computational efficiency,decomposition quality,etc.To ameliorate,this paper proposes a simple and efficient multi-channel image EMD method,and applies it to image fusion and color image watermarking,which can be described briefly as follows:1.A fast multi-channel image EMD method based on morphological filtering is proposed.It uses the morphological expansion and erosion filter to calculate the upper and lower envelopes of the input image,which can be used to realize the fast calculation of the multi-channel image EMD.The size of the morphological filter window is determined by the average extreme distance of each channel image.The proposed EMD method can decompose a multi-channel image adaptively into several intrinsic modal images(IMFs)with scales from fine to course,and a residue representing the overall change trend of the image.The comparison of a large number of color image decomposition experiments shows that this method can not only obtain better decomposition results,but also can significantly improve the decomposition efficiency of multi-channel images.2.An image fusion method based on the proposed fast multi-channel image EMD method using morphological filtering is presented.It first uses the fast multi-channel image EMD method based on morphological filtering to decompose the input images into several intrinsic modal images with different scales and a residual image,and then devises two different criteria to fuse the intrinsic modal images and the residual images.The quality of the fused image can be improved according to a reconstruction way with image enhancement.A large number of comparative experiments on image fusion show that the presented fusion method can quickly and effectively perform image fusion.3.A color image watermarking method based on the proposed fast multi-channel image EMD method using morphological filtering is presented.It first transforms the watermark image into a one-dimensional watermark signal through Arnold transformation and Hilbert curve,and then uses the fast multi-channel image EMD method based on morphological filtering proposed in this paper to conduct the multi-scale decomposition of the color host image,and finally embeds the one-dimensional watermark signal into the first intrinsic modal image.The extraction of the watermark image is the inverse process of the above watermarking embedding algorithm.The comparison with some classic watermarking algorithms shows that the presented watermarking method has achieved better results.