In this article, we consider techniques that provide edge strength at each pixel using two orthogonal directions and question their invariance with respect to a rotation.
Lacroix, V. (1990). Edge-detection - What About Rotation Invariance. Pattern Recognition Letters, 11(12), 797-802. https://doi.org/10.1016/0167-8655(90)90033-X (Original work published 1990)