Improved bi-dimensional EMD and Hilbert spectrum for the analysis of textures

An improved bi-dimensional empirical mode decomposition (IBEMD) is proposed. Structure of image extremas represents the important feature of images, and is useful for the information extraction and analysis. The image extrema are classified into the five different sets, which are called as the structural extrema. The structural extrema are used instead of the classical extrema, and the BEMD (bi-dimensional empirical mode decomposition) algorithms based on the structural extrema are more accurate through interpolating the up and down envelopes. Specially, the IBEMD has the least NMSE (normalised mean square error) and the biggest SNR (signal-to-noise ratio) for the mode decomposition, and greatly improves the robustness of the BEMD. Moreover, quaternion Hilbert transform based space–spatial-frequency tool is improved, and applied to the texture analysis. The experiments of texture analysis show that the new approach is efficient for the application in texture analysis.