2.2. The supervised fuzzy classification of multi-temporal images
As long as the necessary fuzzy mean and fuzzy covariance of each training class are calculated from the procedures described at the previous section 2.1, a fuzzy supervised classification can be implemented at first-period image of multi-temporal data. Accordingly, the membership values of each pixel calculated from Equ.3 can be used to generate a classification map. Then the classification map is overlaid with second-period image, and the positions of the classes can be used as the reference to collect the training data. However, the problem always arises when second-period image has some variations in the class positions, contents, and numbers. The fuzzy training method with the capability to mix the training classes, in fact, would successfully manage the variation of the class positions and contents as long as the class numbers stays the same. It appears that the class numbers of second-period image has to be decided before the fuzzy supervised classification can be applied to second-period image. The values of fuzzy covariance and fuzzy mean of training data actually provide some answers to the problem of the class numbers. Accordingly, the threshold techniques are used to obtain the change of the class numbers. A high fuzzy covariance threshold will suggest an increase of the class numbers, while a high distance threshold between different fuzzy means will indicate a decrease of the class numbers. Therefore, with the class numbers known, the fuzzy training and classification will bring back to train and classify second-period image.
3. Test Data and the Results
The class variation of second-period image basically can be grouped into class positions, contents, and numbers. Their possible combination would be summarized to five cases, which is described as follows.
| class variation |
Class numbers |
Class contents |
Class positions |
| Case 1 |
no-change |
no-change |
change |
| Case 2 |
no-change |
change |
no-change |
| Case 3 |
no-change |
change |
change |
| Case 4 |
increase |
change |
change |
| Case 5 |
decrease |
change |
change |
A series of images to simulate above five cases is generated for testing the proposed method. The following is the testing results and their discussions.
Case 1:
 |
| (a) |
(b) |
(c) |
Fig.1 (a) simulated 1st-period image; (b) 2nd-period image (case 1); (c) classification image
Case 1 represents the situation with 'no-change' in both class numbers and class contents, but 'change' in class positions. The testing results are showing in Figure 1. The visual inspection (Fig.1(b) and (c)) and 96% overall accuracy indicate a successful classification.
Case 2
 |
| (a) |
(b) |
(c) |
Fig.2 (a) simulated 1st-period image; (b) 2nd-period image (case 2); (c) classification image
Case 2 represents the situation with 'no-change' in both class numbers and class positions, but 'change' in class contents. The testing results are showing in Figure 2. The visual inspection (Fig.2(b) and (c)) and 98% overall accuracy indicate a successful classification.
Case 3
 |
| (a) |
(b) |
(c) |
Fig.3 (a) simulated 1st-period image; (b) 2nd-period image (case 3); (c) classification image
Case 2 represents the situation with 'no-change' in class numbers, but 'change' in both class contents and class positions. The testing results are showing in Figure 3. The visual inspection (Fig.3(b) and (c)) and 99% overall accuracy indicate a successful classification.
