Discrete Weierstrass-Type Representations

Domain Adaptive Video Semantic Segmentation via Cross-Domain Moving Object Mixing

“…Thus to see the parallelism between the two spaces, we need to understand both geometries without any dependence on metrics. We propose Laguerre geometry [20] as the commonground for understanding the geometry of both Euclidean and isotropic 3-spaces without any use of inner products (see also [23,Example 3.3]).…”

“…The corresponding Laguerre geometry of isotropic geometry was given in [10,24,26]; our primary motivation for using Laguerre geometry is to unify the approaches to Euclidean geometry and isotropic geometry. Thus in Section 2, we show that the Laguerre geometric description of Euclidean space carries over to isotropic space by viewing both space forms as hyperplanes in the Minkowski 4-space (see also [22,23]). In particular, we carefully review the notions of Laguerre geometry in Euclidean space in Section 2.1, where the Euclidean notions will provide valuable intuition for the definitions of points, spheres, planes, and normals in isotropic space, which we introduce in Section 2.2.…”