DARTS-PD: Differentiable Architecture Search With Path-Wise Weight Sharing Derivation

Catadioptric images are produced in omnidirectional vision systems and can be expressed on Riemannian manifolds. The existing edge detectors are operated either in Euclidean space, or on Riemannian manifolds with isotropic image filtering. in this paper, a new type of edge detection is proposed?it is operated on Riemannian manifolds with anisotropic image filtering. For that, an anisotropic image filtering kernel on Riemannian manifolds is derived by solving the anisotropic heat equation embedded with Riemannian metric. With this kernel, a novel anisotropic edge detector is then developed. Compared to an edge detector operated in Euclidean space, our edge detector is more suitable for catadioptric images, since their geometric structure information will be taken into account in the detection process. Compared to existing edge detectors customized for catadioptric images, the new edge detector has a higher efficiency in preserving image edges and thus can produce more true positives.