Optimized logarithmic phase masks used to generate defocus invariant modulation transfer function for wavefront coding system

In a previous Letter [Opt. Lett. 33, 1171 (2008)], we proposed an improved logarithmic phase mask by making modifications to the original one designed by Sherif. However, further studies in another paper [Appl. Opt. 49, 229 (2010)] show that even when the Sherif mask and the improved one are optimized, their corresponding defocused modulation transfer functions (MTFs) are still not stable with respect to focus errors. So, by further modifying their phase profiles, we design another two logarithmic phase masks that exhibit more stable defocused MTF. However, with the defocus-induced phase effect considered, we find that the performance of the two masks proposed in this Letter is better than the Sherif mask, but worse than our previously proposed phase mask, according to the Hilbert space angle. (C) 2010 Optical Society of America

Knotted wave dislocation with the hopf invariant

We study the wave dislocations with an induced gauge potential. The topological current characterized the wave dislocations is constructed with the dual of Abelian gauge field. And the topological charges and locations of the wave dislocations are determined by the phi-mapping topological current theory. Furthermore, it is shown that the knotted wave dislocations can be described with a Hopf invariant in the wave field. At last we discussed the evolution of the knotted wave dislocations.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Local histogram based geometric invariant image watermarking

Compared with other existing methods, the feature point-based image watermarking schemes can resist to global geometric attacks and local geometric attacks, especially cropping and random bending attacks (RBAs), by binding watermark synchronization with salient image characteristics. However, the watermark detection rate remains low in the current feature point-based watermarking schemes. The main reason is that both of feature point extraction and watermark embedding are more or less related to the pixel position, which is seriously distorted by the interpolation error and the shift problem during geometric attacks. In view of these facts, this paper proposes a geometrically robust image watermarking scheme based on local histogram. Our scheme mainly consists of three components: (1) feature points extraction and local circular regions (LCRs) construction are conducted by using Harris-Laplace detector; (2) a mechanism of grapy theoretical clustering-based feature selection is used to choose a set of non-overlapped LCRs, then geometrically invariant LCRs are completely formed through dominant orientation normalization; and (3) the histogram and mean statistically independent of the pixel position are calculated over the selected LCRs and utilized to embed watermarks. Experimental results demonstrate that the proposed scheme can provide sufficient robustness against geometric attacks as well as common image processing operations. (C) 2010 Elsevier B.V. All rights reserved.

A novel invariant and sequence comparison for DNA

We consider numerical characterization of DNA primary sequence based on the positions of bases (a, t, c, g) and the pairs of bases X, Y in DNA (X, Y=a, t, c, g). This leads to a representation of DNA by a numerical sequence. Then, we extract a novel invariant (molecular connectivity index) from the derived numerical sequences. The suitable invariant can offer a characterization of DNA primary sequence. Finally, we provide an illustration of its utility by making a comparison between ten DNA sequences belonging to beta-globin gene in different species. The evolutionary relationships of ten species we have revealed in this contribution accord with phylogenetic tree properly.