Improved curvature and anisotropy estimation for curved line bundles

The gradient-square tensor describes the orientation dependence of the squared directional derivative in images. The ratio of eigenvalues is a measure of local anisotropy. For an area showing shift invariance along some orientation (think of a piece of straight rail track) one of the tensor eigenvalues is zero. In practical situations (think of a piece of curved rail track) rotation invariance (perhaps around a remote center) occurs more often than shift invariance. Then curvature contributes to the smallest eigenvalue. In order to avoid this we deform a local area in such a way that the rotational symmetry becomes a translational one. Next the gradient square tensor defined on the transformed area, is expressed in derivatives of the original area. A curvature corrected anisotropy measure is defined. The correction turns out to be simple and straightforward. An average-curvature estimate for the area results as a valuable by product.