We propose a watermarking scheme based on the multi-channel watermarking framework, which is mainly used to resist geometric attacks. This watermarking scheme generates watermarking templates from one image transform domain which is obtained after DWT (Discrete wavelet transform) and DFT (Discrete Fourier transform) transformation to one of image channels and then embeds these watermarking temp...

The Kustaanheimo–Stiefel (KS) transformation maps the non-linear and singular equations of motion of the three-dimensional Kepler problem to the linear and regular equations of a four-dimensional harmonic oscillator. It is used extensively in studies of the perturbed Kepler problem in celestial mechanics and atomic physics. In contrast to the conventional matrixbased approach, the formulation o...

We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an ...

Curvelet transformation proposed in 1999, on the basis of wavelet transformation, is a new multi-scale geometric analysis method. Besides scale parameter and location parameter, it adds an azimuth parameter in structure elements compared with wavelet transformation, which makes the Curvelet transformation express anisotropic singular boundary of lines or curves. So, Curvelet transformation is b...

In dealing with transformation group, topological approach is very natural. But, it is not sufficient to investigate geometric properties of transformation group and we need geometric method. Frankel-McDuff Conjecture is very interesting in the point that it shows struggling between topological method and geometric method. In this paper, the author suggest generalized FrankelMcDuff conjecture a...

Since 1915, statisticians have been applying Fisher’s Z-transformation to Pearson product-moment correlation coefficients. We offer new geometric interpretations of this transformation.