Nonlinear Motion Detection

Abstract

This work presents new ideas in multidimensional signal theory: an isotropic quadrature filter approach for extracting local features of arbitrary curved signals without the use of any steering techniques. We unify scale space, local amplitude, orientation, phase and curvature in one framework. The main idea is to lift up signals by a conformal mapping to the higher dimensional conformal space where the local signal features can be analyzed with more degrees of freedom compared to the flat space of the original signal domain. The philosophy is based on the idea to make use of the relation of the conformal signal to geometric entities such as hyper-planes and hyper-spheres. Furthermore, the conformal signal can not only be applied to 2D and 3D signals but also to signals of any dimension. The main advantages in practical applications are the rotational invariance, the low computational time complexity, the easy implementation into existing Computer Vision software packages, and the numerical robustness of calculating exact local curvature of signals without the need of any derivatives. Applications can be optical flow and object tracking not only limited to constant velocities but detecting also arbitrary accelerations which correspond to the local curvature.

We acknowledge funding by the German Research Foundation (DFG) under the project SO 320/4-2.