Analytical Tensor Voting in ND Space and its Properties.

This article aims to propose a novel Analytical Tensor Voting (ATV) mechanism, which enables robust perceptual grouping and salient information extraction for noisy N-dimensional (ND) data. Firstly, the approximation of the decaying function is investigated and adopted based on the idea of penalizing the 1-tensor votes by distance and curvature, respectively, followed by the derivation of analytical solution to the 1-tensor voting in ND space from the geometric view. Secondly, a novel spherical representation mechanism is proposed to facilitate the representation of the elementary tensors in various dimensional spaces, where the high dimensional spherical coordinate system is utilized to construct the controllable unit vectors and corresponding 1-tensors. Accordingly, any elementary K-tensor is represented by the surface integration of the constructed 1-tensors over the unit K-sphere. Thirdly, the ATV mechanism is constructed using the adopted decaying function and proposed spherical representation mechanism, where the analytical solution to tensor voting in ND space is derived, which enables the robust and accurate salient information extraction from noisy ND data. Finally, several interesting properties of the proposed ATV mechanism are investigated. Experimental results on synthetic and real data validate the effectiveness, efficiency and robustness of the proposed method in perceptual grouping tasks in 3D,10D or higher dimensional spaces.

Mie scattering by a uniaxial anisotropic sphere.

The field solution to the electromagnetic scattering of a plane wave by a uniaxial anisotropic sphere is obtained in terms of a spherical vector wave function expansion form. Using the source-free Maxwell's equations for uniaxial anisotropic media and making the Fourier transform of the field quantities, the electromagnetic fields in the spectral domain in uniaxial anisotropic media are assumed to have a form similar to the plane wave expanded also in terms of the spherical vector wave functions. Applying the continuous boundary conditions of electromagnetic fields on the surface between the air region and uniaxial anisotropic sphere, the coefficients of transmitted fields and the scattered fields in uniaxial anisotropic media can be obtained analytically in the expansion form of vector wave eigenfunctions. Numerical results for some special cases are obtained and compared with those of the classical Lorenz-Mie theory and the method of moments accelerated with the conjugate-gradient fast-Fourier-transform approach. We also present some new numerical results for the more general uniaxial dielectric material media.