Optimale Operatoren in der Digitalen Bildverarbeitung

A novel method for optimal choice of filter operators is presented. Single filters as well as filter families with linear or nonlinear optimal criteria can be addressed by different weighted norms in wave number domain. Coefficients of filters with arbitrary support can be optimized in floating point or fixed point accuracy. Numerous examples are presented to illustrate optimization of filters e.g by isotropy, rotation invariance or accuracy of absolute value, and each is followed by discussions of results. Errors are decreased by up to 3 orders of magnitude compared to standard parameter choices. In an investigation of displacements calculated by the well known structure tensor approach with optimal filters the results are improved in two respects. Firstly, estimation errors are decreased by approximately two orders of magnitude and secondly, they are more robust with respect to noise. The greatly improved performance is demonstrated by a tracking application. A novel explicit discretization for anisotropic diffusion filtering using optimal filters is introduced. Numerical errors of this scheme obtained by comparison with a novel analytical solution are about 1.5 to 2.5 orders of magnitude smaller than the errors introduced by the best comparable standard method. The new method clearly outperforms the latter in a reconstruction test. Due to the higher stability with respect to larger time steps, the new method is 3 to 4 times faster than other explicit schemes.