Quaternion–Clifford Fourier and Wavelet Transforms

Abstract

This chapter presents the theory and use of the Clifford Fourier transforms and Clifford wavelet transforms. We will show that using the mathematical system of the geometric algebra, it is possible to develop different kinds of Clifford Fourier and wavelet transforms which are very useful for image filtering, pattern recognition, feature detection, image segmentation, texture analysis, and image analysis in frequency and wavelet domains. These techniques are fundamental for automated visual inspection, robot guidance, medical image processing, analysis of image sequences, as well as for satellite and aerial photogrammetry.