Kappa系数
Kappa在遥感里主要应该是使用在accuracy assessment上。比如我们就
计算
标准
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Kappa值来更好的检验分类结果的正确程度。
The Kappa Index of Agreement (K): this is an important index that the cross classification outputs. It measures the association between the two input images and helps to evaluate the output image. Its values range from -1 to +1 after adjustment for chance agreement. If the two input images are in perfect agreement (no change has occurred), K equals 1. If the two images are completely different, K takes a value of -1. If the change between the two dates occurred by chance, then Kappa equals 0. Kappa is an index of agreement between the two input images as a whole. However, it also evaluates a per-category agreement by indicating the degree to which a particular category agrees between two dates. The per-category K can be calculated using the following formula (Rosenfield and
Fitzpatrick-Lins,1986):
K = (Pii - (Pi.*P.i )/ (Pi. - Pi.*P.i )
where:
P = Proportion of entire image in which category i agrees for both dates ii
P. = Proportion of entire image in class i in reference image i
P. = Proportion of entire image in class i non-reference image i
As a per-category agreement index, it indicates how much a category have changed between the two dates. In the evaluation, each of the two images can be used as reference and the other as non-reference.
Kappa 系数是在综合了用户精度和制图精度两个参数上提出的一个最终指标，他的含义就是用来评价分类图像的精度问题，在遥感里主要应该使用在精确性评价(Accuracy Assessment)和图像的一致性判断。如果两幅图像差异很大，则其Kappa系数小。也可以通过计算标准Kappa值来更好的检验分类结果的正确程度。如简单Kappa系数、加权Kappa系数以及总Kappa系数等等。
Kappa系数仅适用于行数和列数相等的方表。由Cohen在1960年提出，公式如下:
Kappa=(P0-Pc)/(Pp-Pc)
式中，P0 是两期图件上类型一致部分的百分比，即观测值;Pc=Rn*Sn,期望值;Pp= P1+Pn,即真实值。
简单Kappa系数的计算式:
K=(P0-Pc)/(1-Pc)
式中，P0为观测一致率，Pc为期望一致率。
当两个诊断完全一致时，Kappa值为1。当观测一致率时，Kappa值为正数，且Kappa值越大，说明一致性越好。当观测一致率小于期望一致率时，Kappa值为负数，这种情况一般来说比较少见。根据边缘概率的计算，Kappa值的范围应在-1~1之间;Kappa>=0.75时，两者一致性较好，0.4<=Kappa<0.75时，两者一致性一般;Kappa<0.4时，两者一致性差.
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