In this article, a novel image de-noising method is proposed. This method is based on spherical coordinates system. First, spherical transform is re-defined in wavelet domain, and the properties of the spherical transform in wavelet domain are listed. Then, a new adaptive threshold in spherical coordinate system is presented. It has been proved based on Besov space norm theory. After that, a no...

Perfectly matched layers (PML’s) are derived for cylindrical and spherical finite-difference time-domain (FDTD) grids. The formulation relies on the complex coordinate stretching approach. Two-dimensional (2-D) cylindrical and three-dimensional (3-D) spherical staggered-grid FDTD codes are written based on the time-domain versions of the equations. Numerical simulations validate the formulation...

We introduce an alternative coordinate system based on derivative polar and spherical coordinate functions and construct a root-to-canopy analytic formulation for tree fractals. We develop smooth tree fractals and demonstrate the equivalence of their canopies with iterative straight lined tree fractals. We then consider implementation and application of the analytic formulation from a computati...

We present discretization schemes for the Poisson equation, the isothermal drift-diffusion equations, and a generalized higher-order moment equation of the Boltzmann transport equation for general orthogonal coordinate systems like cylindrical and spherical systems. The use of orthogonal coordinate systems allows to reduce the dimension of the problem from three to two. We give an approximation...

Since the domain of crystallographic orientations is three-dimensional and spherical, their insightful rendering or rendering of related probability density functions requires (i) to exploit the effect of a given orientation on crystallographic axes, (ii) to consider spherical means of the orientation probability density function with respect to lower–dimensional manifolds, and (iii) to apply p...

2 Vector Analysis 6 2.1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Scalar Products . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The Gradient . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 The Divergence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.5 The Curl . . . . . . . . . . . . . . . . . . . . . . . . . . . ...

For the present discussion, we define a “coordinate system” as a system for describing positions in space. Any physical law should be expressible in a form that is invariant with respect to our choice of coordinate systems; we certainly do not expect that the laws of physics change when we switch from spherical coordinates to cartesian coordinates! It follows that we should be able to express p...

The problem of feature transformation arises in many fields of information processing, including machine learning, data compression, computer vision and geosciences applications. Here we discuss an approach that seeks a hyperspherical coordinate system preserving geodesic distances in the high dimensional hyperspectral data space. A lower dimensional hyperspherical manifold is computed using a ...

Parallel coordinates is one of the most popular and widely used visualization techniques for large, high dimensional data. Often, data attributes are visualized on individual axes with polylines joining them. However, some data attributes are more naturally represented with a spherical coordinate system. We present a novel coupling of parallel coordinates with spherical coordinates, enabling th...

Objectives: We used a 3-compartment boundary element method (BEM) model from an averaged magnetic resonance image (MRI) data set (Montreal Neurological Institute) in order to provide simple access to realistically shaped volume conductor models for source reconstruction, as compared to individually derived models. The electrode positions were transformed into the model’s coordinate system, and ...