点格局分析中边缘校正的一种新算法及其应用

A new algorithm of the edge correction in the point pattern analysis and its application

在点格局分析中,通常选取一个矩形作为研究区域,而K(d)函数估计值的方差倾向于随着距离尺度的增加而增加。作为一种粗略的指导,距离尺度的最大值一般为矩形最小边长度的一半。在这种情况下,边缘校正的权重最小值为0.25。通过在校正圆上等弧长取点,用校正圆上落在研究区域之内的点数除以整个校正圆上的点数,作为边缘校正权重的近似值。点数越多,这种近似算法越接近传统的精确算法。这种近似算法不仅适用于计算研究区域为矩形的边缘校正权重,而且适用于计算研究区域为任意多边形的边缘校正权重。此外,当矩形研究区域中点事件的信息不足时,这种算法可以允许计算接近到距离尺度的上限(即矩形对角线长度的一半)对应的K(d)函数。

In the point pattern analysis, the study region is generally chosen as a rectangle. Because the variance of the estimation of the K（d） function tends to increase with the distance scale, its maximum is usually less than one-half the length of the shorter side of the rectangle at estimating the K（d） function. In this case, the minimum of edge-corrected weight is proved to be 0.25. Then a new algorithm of edge-corrected weight is proposed in this paper. A number of points are drawn every an identical segment of the edged-corrected circle. The proportion of the number of points in the study region to the number of points in the whole edge-corrected circle, is approximately equal to the edge-corrected weight. Obviously, the larger the number of points is, the more accurate K（d） function calculated with the algorithm is. With respect to the advantage of the algorithm, it can be applicable to estimating the K（d） function when the study region is a rectangle or an arbitrary polygon. Furthermore, as the information of the point events in a rectangle is not enough, the algorithm can permit us to estimate the K（d） function corresponding to the upper limit of the distance scale （ i. e. one-half the length of the diagonal of the rectangle）.