Estimation of Multiple Orientations in Multi-Dimensional Signals

We present a solution to the general problem of estimating multiple orientations in multi-dimensional signals. The solution is divided in a linear part that provides the mixed-orientation space (MOS), and a non-linear part that gives the actual orientation spaces. We show that the angle between two overlaid orientations is an invariant that can be derived from the MOS without solving the non-linear part, and that all other invariants are generated by this angle. Results obtained for synthetic images illustrate that the above invariant is a useful image feature for various applications such as pattern recognition and texture segmentation.