Direct representation and detecting of multi-scale, multi-orientation fields using local differentiation filters

A computational framework is provided for representing and detecting multiple orientation fields from a set of local differentiation filters such as multiscale Gaussian derivatives. The representation is direct and closed-form, i.e., it is not necessary to steer the filters in order to detect multiple orientations. They can be estimated in a single-shot manner by solving algebraic equations. The filter does not need to be strongly tuned to orientations, since the derived algorithm does not suffer from the problem of interference between signal components of the multiple orientations. The capability of extracting the characteristic image structures of different scales is demonstrated by simulation. These advantages are accomplished by using the principle of superposition