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Fig. 1. Decision tree regression approach for soft classification of remote sensing data. ‘D’ denotes the training data from the image, and ‘R’ denotes the known class proportions (referred here as soft reference data) as the target data. where / is the number of classes.

Figure 1 Decision tree regression approach for soft classification of remote sensing data. ‘D’ denotes the training data from the image, and ‘R’ denotes the known class proportions (referred here as soft reference data) as the target data. where / is the number of classes.

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Fig. 2. Assumed actual class proportions of pixels of the synthetic image.
Fig. 2. Assumed actual class proportions of pixels of the synthetic image.
discarded due to its different spatial resolution than the other bands. Four images were created through a random number generator based on Gaussian distribution using the extracted In this experiment, two datasets called the pure pixel dataset and the mixed pixel dataset were generated. Similar to other studies (e.g., Congalton, 1991), the training and testing sample sizes have been selected arbitrarily. From the pure pixel dataset, 250 randomly sampled pure pixels per class were used as training data, and 250 pure pixels per Fig. 3. Actual class proportion images (soft reference data).
discarded due to its different spatial resolution than the other bands. Four images were created through a random number generator based on Gaussian distribution using the extracted In this experiment, two datasets called the pure pixel dataset and the mixed pixel dataset were generated. Similar to other studies (e.g., Congalton, 1991), the training and testing sample sizes have been selected arbitrarily. From the pure pixel dataset, 250 randomly sampled pure pixels per class were used as training data, and 250 pure pixels per Fig. 3. Actual class proportion images (soft reference data).
Importance scores for various classes (synthetic data) Table 1
Importance scores for various classes (synthetic data) Table 1
Fig. 4. Decision tree regression model for class 1 (synthetic data).
Fig. 4. Decision tree regression model for class 1 (synthetic data).
Comparisons of soft classifications produced from DTR, MLC and FCM
Comparisons of soft classifications produced from DTR, MLC and FCM
Kurtosis values for training data extracted from the synthetic data
Kurtosis values for training data extracted from the synthetic data
Skewness values for training data extracted from the synthetic data
Skewness values for training data extracted from the synthetic data
on the fuzzy error matrix, as detailed in Binaghi et al. (1999) has also been employed to estimate the overall accuracy of soft classification. A fuzzy “min” operator is used to generate the elements of the fuzzy error matrix for each pixel by finding out the minimum of the predicted class proportions (i.e. soft classification) and the actual class proportions for that pixel (i.e. soft reference data). The elements of the fuzzy error matrix of each pixel are summed over all the pixels to generate the fuzzy error matrix for the whole classification process. The accuracy is determined in the conventional way as in the traditional error matrix for hard classification. For comparison purposes, two other well known classi- fiers—a probabilistic one, the most widely used MLC applied in the soft mode and a fuzzy set based one FCM, applied in the supervised mode—were also used, and their accuracy assessed. The soft classifications were produced using training datasets that contained both pure pixels and mixed pixels. Table 2 shows the classification results of DTR, MLC and FCM in terms of traditional and fuzzy error matrix based overall accuracy, and RMSE. In the case of mixed-pixel training data, a considerable difference between the traditional error matrix based overall accuracy and fuzzy error matrix based overall accuracy is observed. This shows Fig. 5. Class proportion images of class 1 obtained from MLC, FCM and DTR.
on the fuzzy error matrix, as detailed in Binaghi et al. (1999) has also been employed to estimate the overall accuracy of soft classification. A fuzzy “min” operator is used to generate the elements of the fuzzy error matrix for each pixel by finding out the minimum of the predicted class proportions (i.e. soft classification) and the actual class proportions for that pixel (i.e. soft reference data). The elements of the fuzzy error matrix of each pixel are summed over all the pixels to generate the fuzzy error matrix for the whole classification process. The accuracy is determined in the conventional way as in the traditional error matrix for hard classification. For comparison purposes, two other well known classi- fiers—a probabilistic one, the most widely used MLC applied in the soft mode and a fuzzy set based one FCM, applied in the supervised mode—were also used, and their accuracy assessed. The soft classifications were produced using training datasets that contained both pure pixels and mixed pixels. Table 2 shows the classification results of DTR, MLC and FCM in terms of traditional and fuzzy error matrix based overall accuracy, and RMSE. In the case of mixed-pixel training data, a considerable difference between the traditional error matrix based overall accuracy and fuzzy error matrix based overall accuracy is observed. This shows Fig. 5. Class proportion images of class 1 obtained from MLC, FCM and DTR.
Fig. 6. Class proportion images of class 2 obtained from MLC, FCM and DTR. kurtosis value of 0. According to the skewness and kurtosis values of synthetic data, shown in Tables 3 and 4, the distribution of the training data consisting of pure pixels is a Gaussian distribution. However, the distribution of training data consisting of mixed pixels has the skewness and kurtosis values that deviate significantly from 0, and therefore is non-Gaussian. As a result, the accuracy of MLC designed based on the Gaussian assumption deterio- rates. Although, the overall accuracy of MLC is higher than that of DTR and FCM, hardening is not an acceptable means to evaluate the accuracy of soft classification, as demon- strated earlier. Looking at the values of RMSE and the As expected, the MLC trained by the data containing pure pixels produces higher classification accuracy in comparison to that produced from DTR and FCM. This is due to the fact that the MLC is designed here under the assumption of Gaussian distribution and this assumption is valid for the training data consisting of pure pixels. DTR ranks the second whereas FCM yields the worst accuracy. The Gaussian distribution has a skewness value of 0 and a
Fig. 6. Class proportion images of class 2 obtained from MLC, FCM and DTR. kurtosis value of 0. According to the skewness and kurtosis values of synthetic data, shown in Tables 3 and 4, the distribution of the training data consisting of pure pixels is a Gaussian distribution. However, the distribution of training data consisting of mixed pixels has the skewness and kurtosis values that deviate significantly from 0, and therefore is non-Gaussian. As a result, the accuracy of MLC designed based on the Gaussian assumption deterio- rates. Although, the overall accuracy of MLC is higher than that of DTR and FCM, hardening is not an acceptable means to evaluate the accuracy of soft classification, as demon- strated earlier. Looking at the values of RMSE and the As expected, the MLC trained by the data containing pure pixels produces higher classification accuracy in comparison to that produced from DTR and FCM. This is due to the fact that the MLC is designed here under the assumption of Gaussian distribution and this assumption is valid for the training data consisting of pure pixels. DTR ranks the second whereas FCM yields the worst accuracy. The Gaussian distribution has a skewness value of 0 and a
Fig. 7. Class proportion images of class 3 obtained from MLC, FCM and DTR. overall accuracy derived from the fuzzy error matrix, it can be clearly seen that the DTR produced considerab y higher accuracies than MLC and FCM. Fig. 3 shows the class proportion images of soft reference data. Figs. 5—8 respectively show the class proportion images produced from MLC, FCM and DTR trained with both pure- and mixed-pixel training datasets. These figures also depict that when the training data contain pure pixels, MLC the highest accuracy. On the other hand, in case o data comprising of mixed pixels, MLC is not generate class proportions as accurately as FCM produces f training able to or DTR. Moreover, the DTR produces the highest accuracy when the A multispectral remote sensing image acquired by Landsat ETM+ sensor (spatial resolution: 30 m) in 1999 has been used to produce a land cover classification. A portion consisting of 221 x 327 pixels covering a part of Syracuse area has been selected. The area encompasses a
Fig. 7. Class proportion images of class 3 obtained from MLC, FCM and DTR. overall accuracy derived from the fuzzy error matrix, it can be clearly seen that the DTR produced considerab y higher accuracies than MLC and FCM. Fig. 3 shows the class proportion images of soft reference data. Figs. 5—8 respectively show the class proportion images produced from MLC, FCM and DTR trained with both pure- and mixed-pixel training datasets. These figures also depict that when the training data contain pure pixels, MLC the highest accuracy. On the other hand, in case o data comprising of mixed pixels, MLC is not generate class proportions as accurately as FCM produces f training able to or DTR. Moreover, the DTR produces the highest accuracy when the A multispectral remote sensing image acquired by Landsat ETM+ sensor (spatial resolution: 30 m) in 1999 has been used to produce a land cover classification. A portion consisting of 221 x 327 pixels covering a part of Syracuse area has been selected. The area encompasses a
Importance scores for various classes (remote sensing image)
Importance scores for various classes (remote sensing image)
Fig. 8. Class proportion images of class 4 obtained from MLC, FCM and DTR.
Fig. 8. Class proportion images of class 4 obtained from MLC, FCM and DTR.
Comparison of classifications obtained from DTC and DTR
Comparison of classifications obtained from DTC and DTR
From the outputs of the DTR, we get the prediction of class proportions for the five classes being mapped. We also generate the hard classification, for which a decision tree classifier (DTC) has been used instead of decision tree regression. Fig. 9a shows the reference data for assessing the accuracy of hard classification. In Fig. 9b, hard classification as obtained by hardening the soft outputs from the five regression trees is shown whereas in Fig. 9c, the hard classification as obtained from a DTC is The results of soft classification using DTR have also been compared with the soft outputs from MLC and FCM. Classification accuracies obtained from the three soft classification methods are shown in Table 7. Among the three soft classification methods, DTR has clearly achieved considerably higher accuracy (~20% improvement based on the traditional error matrix and ~15% improvement based on the fuzzy error matrix) than MLC and FCM.
From the outputs of the DTR, we get the prediction of class proportions for the five classes being mapped. We also generate the hard classification, for which a decision tree classifier (DTC) has been used instead of decision tree regression. Fig. 9a shows the reference data for assessing the accuracy of hard classification. In Fig. 9b, hard classification as obtained by hardening the soft outputs from the five regression trees is shown whereas in Fig. 9c, the hard classification as obtained from a DTC is The results of soft classification using DTR have also been compared with the soft outputs from MLC and FCM. Classification accuracies obtained from the three soft classification methods are shown in Table 7. Among the three soft classification methods, DTR has clearly achieved considerably higher accuracy (~20% improvement based on the traditional error matrix and ~15% improvement based on the fuzzy error matrix) than MLC and FCM.
Comparison of DTR, MLC and FCM Table 7 For all the classes, DTR general y produces the smallest value of RMSE among the three classifiers. However for class water, the value of RMSE corresponding to DTR is slightly higher than MLC and FCM. Only 95 pixels belonging to class water were present in the randomly selected 2000 pixels of training data. An increase in the number of training samples of this c in a more accurate mapping of this ass would have resulted class also. FCM produce more misclassifications than DTR. For class water, we see that DTR can detect all the lakes more clearly than the MLC and FCM. Thus, the visual depiction of the results also demonstrates that the DTR achieves more meaningful soft classification than obtained from MLC and FCM classifiers.
Comparison of DTR, MLC and FCM Table 7 For all the classes, DTR general y produces the smallest value of RMSE among the three classifiers. However for class water, the value of RMSE corresponding to DTR is slightly higher than MLC and FCM. Only 95 pixels belonging to class water were present in the randomly selected 2000 pixels of training data. An increase in the number of training samples of this c in a more accurate mapping of this ass would have resulted class also. FCM produce more misclassifications than DTR. For class water, we see that DTR can detect all the lakes more clearly than the MLC and FCM. Thus, the visual depiction of the results also demonstrates that the DTR achieves more meaningful soft classification than obtained from MLC and FCM classifiers.
Fig. 10. Comparison of class proportions of tree from different classifiers with reference image. Referring to Figs. 10—14, (a) shows the soft reference images for the 5 classes, (b) shows the corresponding images generated by DTR, (c) shows the corresponding images generated by MLC and (d) shows the corresponding images generated by FCM. For classes tree, grass and impervious area, it can be seen that the results obtained by DTR are smoother than MLC and FCM. The smoothness may be the result of information loss due to the pruning process adopted in DTR. MLC results in more misclassi- fications and also the boundaries of classes are not smooth. FCM although sharpens the class proportion images but loses some edges. For example, for the class soil, MLC and Decision tree learning is a promising approach for classification and regression problems. In this paper, we have applied this approach for soft classification of remotely sensed data. In particular, we used decision tree regression to predict the class proportion of all pixels. The results show that DTR can explore the complex relationships between bands and classes and can identify the most useful combination of bands that increases the class separability between any two classes. The DTR approach is simple and flexible and does not depend on the implicit assumption
Fig. 10. Comparison of class proportions of tree from different classifiers with reference image. Referring to Figs. 10—14, (a) shows the soft reference images for the 5 classes, (b) shows the corresponding images generated by DTR, (c) shows the corresponding images generated by MLC and (d) shows the corresponding images generated by FCM. For classes tree, grass and impervious area, it can be seen that the results obtained by DTR are smoother than MLC and FCM. The smoothness may be the result of information loss due to the pruning process adopted in DTR. MLC results in more misclassi- fications and also the boundaries of classes are not smooth. FCM although sharpens the class proportion images but loses some edges. For example, for the class soil, MLC and Decision tree learning is a promising approach for classification and regression problems. In this paper, we have applied this approach for soft classification of remotely sensed data. In particular, we used decision tree regression to predict the class proportion of all pixels. The results show that DTR can explore the complex relationships between bands and classes and can identify the most useful combination of bands that increases the class separability between any two classes. The DTR approach is simple and flexible and does not depend on the implicit assumption
Fig. 11. Comparison of class proportions of grass from different classifiers with reference image.
Fig. 11. Comparison of class proportions of grass from different classifiers with reference image.
Fig. 12. Comparison of class proportions of soil from different classifiers with reference image.
Fig. 12. Comparison of class proportions of soil from different classifiers with reference image.
Related topics:
Remote SensingGeomatic EngineeringLand cover classificationTHERMAL INFRARED REMOTE SENSING DATAAccuracy AssessmentFuzzy C-mean
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