Algebra of dual quaternions in image analysis

Abstract

This work has two goals. Firstly it is to acquaint the reader with the classical use of quaternions and dual quaternions in geometry. Secondly the generalization of the Fourier transform into the set of dual quaternions. At first it goes into algebraic properties and structure of quaternions and ways of their inscriptions. Later dual numbers are introduced and consecutively with their help dual quaternions. Then the work deals with description of rotations and translations using quaternions and dual quaternions, that enable their easy description. Finally the discreet dual quaternion Fourier transform is defined, and for its effective calculation the algorithm is derived, which is then brought into effect as a code in program environment MATLAB