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...

introduction: appropriate definition of the distance measure between diffusion tensors has a deep impact on diffusion tensor image (dti) segmentation results. the geodesic metric is the best distance measure since it yields high-quality segmentation results. however, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. the main goal of this ...

Introduction: Appropriate definition of the distance measure between diffusion tensors has a deep impact on Diffusion Tensor Image (DTI) segmentation results. The geodesic metric is the best distance measure since it yields high-quality segmentation results. However, the important problem with the geodesic metric is a high computational cost of the algorithms based on it. The main goal of this ...

Shape analysis is a fundamental and difficult problem in computer vision. It is crucial for recognition, video tracking, image retrieval and other applications. This paper proposes 2D shape analysis by using geodesic distance. It focuses on how to apply geodesic distance for shape matching and shape decomposition. Geodesic Fourier Descriptors is developed as a kind of shape representation for s...

We propose a new approach to compute geodesic distance transformations in arbitrary 2D and 3D domains. The distance transformation proposed here is robust and has proved to have a computational complexity linear in the domain size. Our scheme is based on a new technique which we call occlusion points propagation, and with a higher accuracy than other geodesic distance transformations proposed b...

We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.

Billera, Holmes, and Vogtmann introduced an intriguing new phylogenetic tree metric for weighted trees with useful properties related to statistical analysis. However, the best known algorithm for calculating this distance is exponential in the number of leaves of the trees compared. We point out that lower and upper bounds for this distance, which can be calculated in linear time, can differ b...

In this paper, we present two feature extraction methods for two-dimensional face recognition. Our approaches are based on facial feature points detection then compute the Euclidean Distance between all pairs of this points for a first method (ED-FFP) and Geodesic Distance in the second approach (GD-FFP). These measures are employed as inputs to a commonly used classification techniques such as...

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.