模糊类别制图的空间统计学方法

A GEOSTATISTICAL APPROACH TO FUZZY CATEGORICAL MAPPING *

类别地图是地理信息系统（ＧＩＳ）应用中所利用的重要数据类型。这类数据可以从摄影测量和遥感技术得到。用摄影测量方法（影像判读）制作的类别地图常以点、线和多边形的离散目标形式描述，而遥感图像分类方法输出的类别地图以连通光栅块形式表达。不论哪一种情况，在每一个多边形或者光栅块（即制图单元）中仅允许单一类别，边界内部非均匀性和模糊形已经被“过滤”了。这样的类别地图沿用了古典脆集合论（Ｃｒｉｓｐｓｅｔｔｈｅｏｒｙ），因为每个制图单元只允许完全（１．０）或者零（０．０）隶属度。然而，更客观合理的方法应建立在模糊集合论（Ｆｕｚｚｙｓｅｔｔｈｅｏｒｙ）的基础之上，即每一位置属于各个候选类别的隶属度介于０．０和１．０之间，而且这些隶属度的总和为１．０。模糊方法对于以多光谱数据为基础的遥感分类工作相对地说比较常见。

This paper documents principles of geostatistics, in particular, Indicator Kriging for deriving fuzzy categorical maps. This is followed by an empirical test, in which fuzzy maps of land cover were created by identifying well defined locations from polygonal land cover data plotted from aerial photographs and then applying indicator Kriging to estimate the probability vectors of finding all candidate classes at individual grid cells. As reference, proportion data of component land cover types in each grid cell were also calculated. Results confirm the theoretical strength and practical efficiency of indicator kriging method for deriving fuzzy categorical maps.