Keywords: multi-temporal remote sensing images, supervised fuzzy classification
Abstract This paper presents a supervised approach for classifying multi-temporal remote sensing images. One major disadvantage to use the supervised classification of multi-temporal data is that each image is required to select its training data, even the images cover the same area. An attempt to use the fuzzy training method to avoid repeated selection of training data in each image is proposed here. Theoretically, the fuzzy training method is able to deal with the problem of mixture of training classes, therefore, the classification map generated from first-period image can be automatically becoming the fuzzy training sites for second-period image. The proposed approach is tested by a series of simulated multi-temporal images. The results indicate that the method presented here has great potential to extend to the practical applications.
1. Introduction
In processing of multi-temporal remote sensing images, accurate and convenient classification is among one of difficult tasks in practical applications (Baber, 1985). This study aims to use supervised algorithm to classify multi-temporal images. One major procedure of using supervised algorithm is the collection of training data that is relatively time-consuming and labor-intensive (Lillesand, 2000). Furthermore, the image responses may change due to variability in time and space within the multi-temporal images (Richards, 1993). Therefore, the problem that faces the supervised classification of multi-temporal images is that the training data has to be repeatedly selected for each image within the multi-temporal remote sensing data (Schowengerdt,1997). For this reason, a concept is proposed: choosing training set and finishing classification in first-period image, then the training data of the following period images would be automatically generated from the first-period classification image. The most difficult part of the study is that the class positions, numbers, and contents may change in the following-period images. Thus it would generate the complicated mixture of the training classes when it attempts to automatically select the training data for second-period image. This study uses the fuzzy training method (Wang, 1990) to overcome the mixing problem of training classes. Basically, the fuzzy approach allows the heterogeneity to exist within the training sites and may contain mixing classes in the training data. Consequently, the change of class positions and contents in second-period images can be tackled by the characteristics of the fuzzy training data, while the detection of change of class numbers leave a key problem in the process of automated selection of training data. This problem is studied and the solutions are obtained from a series of analysis of fuzzy means and covariance matrix of the training data. A series of simulated data are tested, and the results indicate that the proposed fuzzy training method has the potential to automatically classify multi-temporal remote sensing images.
2. Method
The following section 2.1 discusses the fuzzy training method and the section 2.2 present the multi-temporal supervised classification.
2.1 Fuzzy training
Basically, the fuzzy training method is the training procedure of supervised fuzzy classification. In this procedure, the conventional mean and covariance parameters of training data are represented as a fuzzy set. The following two equations (Equ.1 and Equ.2) describe the fuzzy parameters of the training data:
where µ
c* is the fuzzy mean of training class c,
åc* is the fuzzy covariance of training class c,
x
i is the vector value of pixel i, f
c(x
i) is the membership of pixel
x
i to training class c, n is the total number of pixels of the training data. In order to find the fuzzy mean (Equ.1) and fuzzy covariance (Equ.2) of every training class, it must know the membership of pixel xi to training class c first. In this study, the membership function is defined based on the conventional maximum likelihood classification algorithm with fuzzy mean and fuzzy covariance.
where
f
c(x
i) is the membership of pixel
x
i to class c, P
c*(x
i) is the maximum likelihood probability of pixel xi to class c, m is the number of classes, n is the number of the bands. These equations would ultimately produce the fuzzy mean and fuzzy covariance for each training class. Consequently, the membership values would be used to describe the mixing classes in every training site.
