Signal Processing Using Frequency Domain Methods in Cliiord Algebra Master Thesis

The aim of this Master Thesis is to extend the classical concepts of the Fourier transform and the cross correlation in order to create an intrinsic multi{dimensional signal analysis which is more exible with regard to distortions. Frequency domain methods and pattern matching are two signal{theoretic approaches which are frequently applied in computer vision. By comparing one{dimensional signal processing with multi{dimensional signal theory new problems and requirements arise. Therefore, Lie groups and Cliiord algebras are introduced in order to obtain new representations of signals in the frequency domain and more eecient possibilities for comparing signals. Special consideration was given to the aspects of invariance and parameter estimation. This thesis nally raises issues for future research in the eld of local approaches and new spectral representations.