Edge detection, color quantization, segmentation, texture removal, and noise reduction of color image using quaternion iterative filtering

Abstract. Empirical mode decomposition (EMD) is a simple, local, adaptive, and efficient method for nonlinear and nonstationary signal analysis. However, for dealing with multidimensional signals, EMD and its variants such as bidimensional EMD (BEMD) and multidimensional EMD (MEMD) are very slow due to the needs of a large amount of envelope interpolations. Recently, a method called iterative filtering has been proposed. This filtering-based method is not as precise as EMD but its processing speed is very fast and can achieve comparable results as EMD does in many image and signal processing applications. We combine quaternion algebra and iterative filtering to achieve the edge detection, color quantization, segmentation, texture removal, and noise reduction task of color images. We can obtain similar results by using quaternion combined with EMD; however, as mentioned before, EMD is slow and cumbersome. Therefore, we propose to use quaternion iterative filtering as an alternative method for quaternion EMD (QEMD). The edge of color images can be detected by using intrinsic mode functions (IMFs) and the color quantization results can be obtained from residual image. The noise reduction algorithm of our method can be used to deal with Gaussian, salt-and-pepper, speckle noise, etc. The peak signal-to-noise ratio results are satisfactory and the processing speed is also very fast. Since textures in a color image are high-frequency components, we also can use quaternion iterative filtering to decompose a color image into many high- and low-frequency IMFs and remove textures by eliminating high-frequency IMFs.