Panoramic Image Processing using Non-Commutative Harmonic Analysis Part I: Investigation

Automated surveillance, navigation and other applications in computational vision have prompted the need for omnidirectional imaging devices and processing. Omnidirectional vision involves capturing and interpreting full 360° panoramic images using rotating cameras, multiple cameras or cameras coupled with mirrors. Due to the enlarged field of view and the type of sensors required, typical techniques in image analysis generally fail to provide sufficient results for feature extraction and identification. A non-commutative harmonic analysis approach takes advantage of the Fourier transform properties of certain groups. Past work in representation theory already provides the theoretical background to analyze 2-D images though extensive numerical work for applications is limited. We will investigate the implementation and computation of the Fourier transform over groups, such as the motion group. The Euclidean motion group SE(2) is a solvable Lie group that requires a 2-D polar FFT and has symmetry properties that could be used as a tool in processing panoramic images.