Harmonic analysis for the affine group of visual motion

For the task of 3D visuomotor tracking, local image-based transformations of moving object surfaces can be modeled by a six-parameter affine group on the 2D intensity function. The six degrees of freedom of the Euclidean rigid-body motion group project perspectively to a unique six-dimensional vector field group. This allows convolution kernels, to be specified by the invariants of the subgroups of 2D visual motion in terms of conjugate harmonic functions providing infinitesimal measures of the one-parameter groups comprising the local affine transformations in the moving scenes. The subgroups form a canonical basis for estimating 3D relative motion and surface orientation, as specified by the state of a quarternion. Using these convolution kernels as measures of the rigid-motion tangent space, it is possible to integrate the global trajectory on a 6D manifold by means of a standard recursive estimator