Orientation Estimation Based on Weighted Projection onto Quadratic Polynomials

Essentially all Computer Vision strategies require initial computation of orientation structure or motion estimation. Although much work has been invested in this subfield, methods have so far been very computationally demanding and/or not very robust. In this paper we present a novel method for computation of orientation tensors for signals of any dimensionality. The method is based on local weighted least squares approximations of the signal by second degree polynomials. It is shown how this can be implemented very efficiently by means of separable convolutions and that the method gives very accurate orientation estimates. We also introduce the new concept of orientation functionals, of which orientation tensors is a subclass. Finally we demonstrate the critical importance of using a proper weighting function in the local projection of the signal onto polynomials.