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...

the present study modeled how future terrestrial net primary productivity (npp) changes spatiotemporally for the eastern mediterranean biomes of turkey using carnegie ames stanford approach (casa) model, moderate resolution imaging spectroradiometer (modis) data, the four regional climate change scenarios (rcp 2.6, rcp 4.5, rcp 6.0 and rcp 8.5), and such ancillary data as percent tree cover, la...

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...

With a dependency grammar, this study provides a unified method for calculating the syntactic complexity in linear and hierarchical dimensions. Two metrics, mean dependency distance (MDD) and mean hierarchical distance (MHD), one for each dimension, are adopted. Some results from the Czech-English dependency treebank are revealed: (1) Positive asymmetries in the distributions of the two metrics...

This paper describes the Subgradient Marching algorithm to compute the derivative of the geodesic distance with respect to the metric. The geodesic distance being a concave function of the metric, this algorithm computes an element of the subgradient in O(N log(N)) operations on a discrete grid ofN points. It performs a front propagation that computes the subgradient of a discrete geodesic dist...

Here, we intend to introduce an invariant bipolar representation for curved surfaces based on the superposition of the two geodesic potentials defined from two given reference points on the surface. By considering a levels set of such geodesic potentials, a finite set of invariant points under 3D motion group is obtained. We propose to compare two different numerical algorithms which compute th...

Tropical rain forest expansion and savanna woody vegetation thickening appear to be a global trend, but there remains uncertainty about whether there is a common set of global drivers. Using geographic information techniques, we analyzed aerial photography of five areas in the humid tropics of northeastern Queensland, Australia, taken in the 1950s and 2008, to determine if changes in rain fores...