a projective parameter of a geodesic as solution of certain ode is defined to be a parameter which is invariant under projective change of metric. using projective parameter and poincaré metric, an intrinsic projectively invariant pseudo-distance can be constructed. in the present work, solutions of the above ode are characterized with respect to the sign of parallel ricci tensor on a finsler s...

We define a geodesic distance associated with the polarization space of non-singular coherency matrices. Its introduction on HPD(2) (the manifold of Hermitian positive definite matrices of dimension 2) can be directly related to the Jones calculus. The expression of distance and related notion of mean value in this particular metric space are also presented. We investigate the properties of thi...

The L-metric or Fubini-Study metric on the non-linear Grassmannian of all submanifolds of type M in a Riemannian manifold (N, g) induces geodesic distance 0. We discuss another metric which involves the mean curvature and shows that its geodesic distance is a good topological metric. The vanishing phenomenon for the geodesic distance holds also for all diffeomorphism groups for the L-metric.

In this paper, a novel Patch Geodesic Derivative Pattern (PGDP) describing the texture map of a face through its shape data is proposed. Geodesic adjusted textures are encoded into derivative patterns for similarity measurement between two 3D images with different pose and expression variations. An extensive experimental investigation is conducted using the publicly available Bosphorus and BU-3...

We propose a new class of distances for the purpose of data clustering, called the geodesic distance, and introduce a geodesic extension of K-medoids algorithm. We analyze the theoretical properties of the geodesic distance within a clustering framework and prove that the geodesic K-medoids algorithm converges to the correct clustering assignment in the asymptotic regime, even in the presence o...

The FastGeodis package provides an efficient implementation for computing Geodesic and Euclidean distance transforms (or a mixture of both), targeting utilisation CPU GPU hardware. In particular, it implements the paralellisable raster scan method from Criminisi et al. (2009), where elements in row (2D) or plane (3D) can be computed with parallel threads. This is able to handle 2D as well 3D da...

Recent papers have clearly shown the advantage of using the geodesic distance instead of the Euclidean one in methods performing non-linear dimensionality reduction by means of distance preservation. This new metric greatly improves the performances of existing algorithms, especially when strongly crumpled manifolds have to be unfolded. Nevertheless, neither the Euclidean nor the geodesic dista...

We propose an extension of the algorithm for nonlinear dimensional reduction locally linear embedding (LLE) based on the usage of the geodesic distance (ISOLLE). In LLE, each data point is reconstructed from a linear combination of its n nearest neighbors, which are typically found using the Euclidean distance. We show that the search for the neighbors performed with respect to the geodesic dis...