We propose a geodesic distance based scattering power decomposition for compact polarimetric (CP) synthetic aperture radar (SAR) data acquired over agricultural landscapes. The proposed technique decomposes the polarized portion of total backscattered in proportion to normalized target similarity measures. measures are derived from distances, which computed between Kennaugh matrices observed an...

In this paper, two new geodesic distance transforms for gray-scale images are presented. The first transform, the Distance Transform on Curved Space (DTOCS), performs the calculation with integer numbers. The second transform, the Weighted Distance Transform on Curved Space (WDTOCS), gives a weighted distance map with real numbers for an arbitrary gray-value image. Both transforms give a distan...

We provide evidence that the KPZ exponents in two-dimensional quantum gravity can be interpreted as scaling exponents of correlation functions which are functions of the invariant geodesic distance between the fields.

We prove the convergence of geodesic distance during the quantization of the space of Kähler potentials. As applications, this provides alternative proofs of certain inequalities about the K-energy functional in the projective case.

1. Introduction Let M be a compact manifold Riemannian manifold of dimension n ≥ 2, with a metric of sectional curvature bounded above by χ ≤ 0 (non-positive curvature). In this paper we prove that in the case of negative curvature (χ < 0) on such manifolds there exist pairs of points connected by at least 2n + 1 geometrically distinct geodesic segments (i.e. length minimizing). A class of poin...