Towards multiple-orientation based tensor invariants for object tracking

We derive a new scale- and rotation-invariant feature for characterizing local neighbourhoods in images, which is applicable in tasks such as tracking. Our approach is motivated by the estimation of optical flow. Its least-squares estimate requires the inversion of a symmetric and positive semi-definite 2×2-tensor, which is computed from spatial image derivatives. Only if one eigenvalue of the tensor vanishes, this tensor describes the local neighbourhood in terms of orientation. Estimating optical flow, however, requires that this tensor be regular, i.e., that both its eigenvalues do not vanish. This indicates that the local region contains more than one orientation. Double-orientation neighbourhoods (like X junctions or corners) are especially suited for tracking or optical flow estimation, but the two underlying orientations cannot be extracted from the standard structure tensor. Therefore, we extend this tensor such that it can characterize double-orientation neighbourhoods. From this extended tensor, we derive a rotation- and scale-invariant feature which describes the orientation structure of the local regions, and analyze its performance.