In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each glob...In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial date. we give an explicit expression of all the curvatures for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.展开更多
A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new ...A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.展开更多
文摘In this paper, the existence of a global tangent frame on every oriented and connected smooth 3-manifold will be used to develop a global frame method in 3-dimensional geometry and topology. Corresponding to each global tangent frame, we define a Poisson matrix on the 3-manifold. And using it as an initial date. we give an explicit expression of all the curvatures for some Riemannian metric. The method is well applied to 3-manifolds with constant Poisson matrix. Such 3-manifolds are essentially the homogeneous spaces of 3-dimensional Lie groups.
文摘A global dual frame （GDF） representation for the digital ridgelet reconstruction algorithm is discussed and a novel concept of local dual frame （LDF） is presented. Based on the properties of LDF, we propose a new digital ridgelet reconstruction algorithm. The method reduces the redundancy in the digital ridgelet reconstruction while keeping the characteristics of low computation cost. When applying it to the image compression and denoising, good results are obtained.
