The Effect of Prior Probabilities in the Maximum Likelihood Classification on Individual Classes: A Theoretical Reasoning and Empirical Testing

The effect of prior probabilities in the maximum likelihood classification on individual classes receives little attention, and this is addressed in this paper. Prior probabilities are designed only for overlapping spectral signatures. Accordingly, their effect on an individual class is independent of the classes that are spectrally separable from this class. The theoretical reasoning reveals that an increased prior probability, which shifts the decision boundary away from the class mean, will increase the assignment and boost the producer’s accuracy as compared to the use of equal priors; though the change of the user’s accuracy is not constant, it is expected to decrease in most cases. The tendency is just the opposite when a lower prior probability is used. A case study was conducted using Landsat TM data provided along with ERDAS Imagine® software. Two other pieces of evidence derived from the published literature are also presented. Introduction The maximum likelihood classification (MLC) is the most widely used method of classifying remotely sensed data (Maselli et al., 1992). In standard digital image processing, MLC has been considered to be the most advanced classification strategy for a long time (Maselli et al., 1992). One of the superior properties of the MLC algorithm is that it can make use of the prior probabilities derived from ancillary information concerning the area to be classified, so that remotely sensed data can be integrated with data collected conventionally (Maselli et al., 1990). By helping to resolve confusion among classes that are poorly separable (McIver and Friedl, 2002), prior probabilities can be a powerful and effective aid to improve classification accuracy (Strahler, 1980). It is desirable to obtain a reliable prior probability for each class and use it to at least classify the pixels likely to be PHOTOGRAMMETRIC ENGINEER ING & REMOTE SENS ING Sep t embe r 2009 1109 Zheng Mingguo and Cai Qianguo are with the Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences & Natural Resources Research, Chinese Academic of Sciences, Beijing 100101, China ([email protected]). Qin Mingzhou is with the College of Environment and Planning, Henan University, Kaifeng 475001, China. Photogrammetric Engineering & Remote Sensing Vol. 75, No. 9, September 2009, pp. 1109–1117. 0099-1112/09/7509–1109/$3.00/0 © 2009 American Society for Photogrammetry and Remote Sensing The Effect of Prior Probabilities in the Maximum Likelihood Classification on Individual Classes: A Theoretical Reasoning and Empirical Testing Zheng Mingguo, Cai Qianguo, and Qin Mingzhou misclassified (Ediriwickrema and Khorram, 1997). However, it is a common practice to perform the MLC with equal prior probabilities, as reliable prior probabilities are not always available. Up until now, a large number of studies have been carried out on the incorporation of prior probabilities into MLC (e.g., Maselli et al., 1990; Maselli et al., 1992; Strahler, 1980; Gorte and Stein, 1998; Pedroni, 2003). These studies are generally dedicated to an improvement in the general performance of the classifier over the entire image under examination and frequently culminate in reporting an improved overall accuracy or Kappa coefficient. However, overall accuracy or Kappa coefficient represents an average accuracy for all classes, and provides little information about individual classes. As compared to the use of equal priors, a higher overall classification accuracy is expected if prior probabilities are properly estimated. However, this does not mean a synchronous improvement in the classification accuracy for all individual classes. In many cases, though an increased Kappa coefficient or overall accuracy can be achieved by inserting prior probabilities into MLC, producer’s accuracy or user’s accuracy for individual classes decrease for some classes while they increase for others. Obviously, not all classes in a case are of interest; sometimes the purpose of a classification is simply to obtain information about one or several individual classes. Therefore, the effect of prior probabilities on individual classes deserves some attention. The objective of this paper is to understand how prior probabilities affect the MLC discrimination process and particularly to investigate the effect of prior probabilities on individual classes. One section of the present paper is dedicated to the discussion of the effect of prior probabilities on the MLC discrimination process. Further, a mathematical reasoning is carried out and some general rules are established on the variation in the classification accuracy of individual classes after the incorporation of prior probabilities into MLC. Finally, a case study is conducted to test these rules using Landsat TM data provided along with ERDAS Imagine® software.