中文摘要：

利用距离变换和栅格叠加分析,提出一种实现任意距离定义的2-site Voronoi图生成方法。首先进行距离变换得到距离图,然后通过邻近关系对边界进行划分得到2-site Voronoi图,最后将生成的距离图和2-site Voronoi图叠加。实验表明,该文提出的2-site Voronoi图生成方法可以快速构建多种距离类型和不同邻近关系下的Voronoi图,共生成了21种距离函数下的最远、最邻近和次邻近Voronoi图,解决了Voronoi图的多样性问题。该方法并不局限于点状发生元,可以生成任意形态发生元Voronoi图,并可以扩展生成N-site Voronoi图,生成的广义距离图可用来模拟成组的发生元在诸多约束条件下的区域增长过程。

英文摘要：

In contrast with the regular（1-site）Voronoi Diagram,the 2-site VD has more variants due to the change of the distance function.Generating the 2-site VD with respect to arbitrary distance functions and constraints remains a challenge in the field.This paper proposes a flexible and general approach to generate 2-site VD by combining the distance transform and raster overlay into a unified framework.This framework is characterized by the two procedures of raster overlay：the first overlay procedure whose operator is used to control the distance function,and the second overlay procedure whose operator is specified by the neighbor relationship.By manipulating the two overlay operators,the nearest-（furthest-,etc.）neighbor 2-site VDs with respect to the various distance functions can be obtained.The proposed approach was implemented and tested with 21 kinds of distance functions.The results show improved flexibility and robustness over existing vector-based approaches and emphasize the convenience of extending to general sites and N-site VD.The proposed approach also produces N-pair-site distance map：a new type of distance map,providing an easy and convenient way to simulate the region-growing process of the sites previously grouped into different pairs.