A framework for estimation of orientation and velocity

The paper makes a short presentation of three existing methods for estimation of orientation tensors, the so-called structure tensor, quadrature filter based techniques, and techniques based on approximating a local polynomial model. All three methods can be used for estimating an orientation tensor, which in the 3D case can be used for motion estimation. The methods are based on rather different approaches in terms of the underlying signal models. However, they produce more or less similar results, which indicates that there should be a common framework for estimation of the tensors. Such a framework is proposed, in terms of a second order mapping from signal to tensor with additional conditions on the mapping. It is also shown that the three methods in principle fall into this framework.