小学数学奥林匹克试题解题思路种种

解某些图形试题时，通常需要先将其中的某部分图形移动，或者采用分割的方法，将图形分割成若干份，然后再逐一进行计算，这种解题方法叫做“移割法”。

Segmentation of High Spatial Resolution Remote Sensing Images of Mountainous Areas Based on the Improved Mean Shift Algorithm

Using conventional Mean Shift Algorithm to segment high spatial resolution Remote sensing images of mountainous areas usually leads to an unsatisfactory result, due to its rich texture information. In this paper, we propose an improved Mean Shift Algorithm in consideration of the characteristics of these images. First, images were classified into several homogeneous color regions and texture regions by conducting variance detection on the color space. Next, each homogeneous color region was directly segmented to generate the preliminary results by applying the Mean Shift Algorithm. For each texture region, we conduct a high-dimensional feature space by extracting information such as color, texture and shape comprehensively, and work out a proper bandwidth according to the normalized distribution density. Then the bandwidth variable Mean Shift Algorithm was applied to obtain segmentation results by conducting the pattern classification in feature space. Last, the final results were obtained by merging these regions by means of the constructed cost functions and removing the oversegmented regions from the merged regions. It has been experimentally segmented on the high spatial resolution remote sensing images collected by Quickbird and Unmanned Aerial Vehicle(UAV). We put forward an approach to evaluate the segmentation results by using the segmentation matching index(SMI). This takes into consideration both the area and the spectrum. The experimental results suggest that the improved Mean Shift Algorithm outperforms the conventional one in terms of accuracy of segmentation.

An algorithm for segmentation of lung ROI by mean-shift clustering combined with multi-scale HESSIAN matrix dot filtering

A new algorithm for segmentation of suspected lung ROI(regions of interest)by mean-shift clustering and multi-scale HESSIAN matrix dot filtering was proposed.Original image was firstly filtered by multi-scale HESSIAN matrix dot filters,round suspected nodular lesions in the image were enhanced,and linear shape regions of the trachea and vascular were suppressed.Then,three types of information,such as,shape filtering value of HESSIAN matrix,gray value,and spatial location,were introduced to feature space.The kernel function of mean-shift clustering was divided into product form of three kinds of kernel functions corresponding to the three feature information.Finally,bandwidths were calculated adaptively to determine the bandwidth of each suspected area,and they were used in mean-shift clustering segmentation.Experimental results show that by the introduction of HESSIAN matrix of dot filtering information to mean-shift clustering,nodular regions can be segmented from blood vessels,trachea,or cross regions connected to the nodule,non-nodular areas can be removed from ROIs properly,and ground glass object(GGO)nodular areas can also be segmented.For the experimental data set of 127 different forms of nodules,the average accuracy of the proposed algorithm is more than 90%.

Symmetry and nonexistence of positive solutions to an integral system with weighted functions

Consider the system of integral equations with weighted functions in Rn,{u(x) =∫Rn|x-y|α-nQ(y)v(y)qdy1,v(x)=∫Rn|x-y|α-nK(y)u(y)pdy,where 0 < α < n,1/(p+1) + 1/(q+1)≥(n-α)/n1,α/(n-α) < p1q < ∞1,Q(x) and K(x) satisfy some suitable conditions.It is shown that every positive regular solution(u(x)1,v(x)) is symmetric about some plane by developing the moving plane method in an integral form.Moreover,regularity of the solution is studied.Finally,the nonexistence of positive solutions to the system in the case 0 < p1q <(n+α)/(n-α) is also discussed.