The symplectic geometry characterization of second order singular J- symmetric differential operators was investigated. By constructing different quotient spaces, self-adjoint extensions of second order J- symmetric differential operators were studied using the method of symplectic geometry. Then classification and description of complete J-Lagrangian submanifold corresponding with self-adjoint domains of second order differential operators were obtained.

The conventional fuzzy C means clustering algorithm couldn't consider any spatial information, and it is no good to noise image segmentation. In order to overcome this shortcoming, a fuzzy C-means clustering algorithm using spatial information for image segmentation was proposed. The new algorithm could make full use of pixels neighborhood feature by improving the membership function, furthermore local information and non local information were introduced in dissimilarity of data and clustering center. Experimental results show that this method is effective in image segmentation, and has better performance of resisting noise.

 

A spatial color image retrieval method without any segmentation step was proposed. Thumbnail of query image was extracted in CIELab color space considering the human visual characteristic.Thumbnails of images were matched using EMD.An unsupervised matching criterion was presented based on a contrario approach. The experimental results show that our image retrieval is more simple and robust, and has better performance than image retrieval based on regions segmentation.