*4.1. MLM Classifier Results*

Creating a test multichannel image, we have taken into account the following typical properties of classes that might take place in real-life RS images:

**Property 1.** *Features rarely have distributions close to Gaussian; since in our case, color component values (see the test color image and its components in Figure 2a–d, respectively) are the used features, then this property relates to them;*

**Figure 2.** *Cont*.

**Figure 2.** Three-channel test image: original (**a**), its three components (**b**–**d**), compressed with providing PSNR-HVS-M = 36 dB (**e**), compressed with providing PSNR-HVS-M = 30 dB (**f**).

**Property 2.** *Objects that relate to a certain class are rarely absolutely homogeneous (even water surface usually cannot be considered as absolutely homogeneous); many factors lead to diversity (variations) of pixel values as variations of physical and chemical characteristics of reflecting or irradiating surface, noise, etc.*

**Property 3.** *Features overlap (intersect) in the feature space; just this property usually leads to misclassifications especially if such overlapping takes place for many features;*

**Property 4.** *The numbers of pixels belonging to di*ff*erent classes in each RS image can di*ff*er a lot, it might be so that a percentage of pixels belonging to one class is less than 1% whilst for another class, there can be tens of percent of the corresponding pixels.*

**Property 5.** *There can be objects of two or even more classes in one pixel [54,55] that requires the application of unmixing methods but we do not consider such, more complex, situations in our further studies (usually more than three components of multichannel RS data are needed to carry out e*ffi*cient unmixing).*

Let us show that we have, in a more or less extent, incorporated these properties in our test image. Table 1 contains data about seven classes, histograms for them, and approximations using Johnson SB-distribution. Class 1 can be conditionally treated as "Roads", Class 2—as agricultural fields (Field-Y), Class 3—as agricultural fields of another color (Field-R), Class 4—as "Water", Class 5—as "Grass", Class 6—as "Trees", Class 7—as some very textural or heterogeneous class like urban area or vineyard ("Texture").

**Table 1.** Information about classes.

As one can see, Property 1 (non-Gaussian distribution) holds for practically all particular distributions. Property 2 (internal heterogeneity) takes place for all classes, especially for Classes 2 and 7. Property 3 (intersection of features) takes place for many classes—all three features for Classes 1 and 2, all three features for Classes 5 and 6; features of Class 7 overlap practically with all other classes (intersection of features can be also seen from a comparison of component images where some classes can be hardly distinguished, e.g., Classes 2 and 4 in Green component, Figure 2c). Property 4 is also observed—there is a small percentage of pixels belonging to Class 1 whilst quite many pixels belong to Classes 4, 5, and 7.

Figure 3a presents the true map of classes where Class 1 is shown by light brown, Class 2—by yellow; Class 3—by red, Class 4—by blue; Class 5—by light green, Class 6—by dark green, Class 7—by white.

**Figure 3.** Classification results: true map (**a**); classification map for original image (**b**); classification map for image compressed with PSNR-HVS-M = 36 dB (**c**); classification map for image compressed with PSNR-HVS-M = 30 dB (**d**).

MLM classifier applied to original image pixel-wise (Figure 3a) produces a classification map given in Figure 3b. As one can see, there are quite many misclassifications. Classes 4 and 6 are classified in the best way (probabilities of correct classification P44 and P66 are equal to 0.85 and 0.82, respectively) whilst Class 5 is recognized in the worst manner (P55 = 0.19). Classes 1 and 7 are not recognized well (P11 and P77 are equal to 0.48 and 0.42, respectively). Classes 2 and 3 are characterized with P22 = 0.67 and P33 = 0.77, respectively.

Quite low probabilities of classification can be explained by several factors. Some of them have been already mentioned above—intersections in feature space are sufficient. One more possible reason is that the MLM classifier is based on distribution approximations and these approximations can be not perfect (see histograms and their approximations in Table 1).

Quite many pixels are erroneously related to Class 7 ("Texture") for which distributions are very wide and they intersect with distributions for other classes.

Figure 2e,f presents images compressed providing PSNR-HVS-M ≈ 36 dB and PSNR-HVS-M ≈ 30 dB. In these cases, CR values are about 4.5 and 8.9, respectively (for component-wise lossy compression). For the case of PSNR-HVS-M≈36 dB, introduced distortions are visible [45]. They mostly appear themselves as smoothing of variations in quasi-homogeneous regions (consider the fragments for Class 6 (dark blue) for images in Figure 2a,e). The effects of such suppression of noise or high-frequency variations due to lossy compression are known for lossy compression [36,37] and they might have even a positive effect for classification (under certain conditions). For the case of PSNR-HVS-M ≈ 30 dB, the distortions due to lossy compression (see the compressed image in Figure 2f) appear themselves in variations' smoothing and edge/object smearing (this can be seen well for Class 1). Clearly, such effects might have an impact on classification.

Probabilities of correct classification for classes are given in Table 2. Note that the MLM classifier has been "trained" using distribution approximations obtained for the original (uncompressed) three-channel image. As one can see, probabilities for particular classes depend on compressed image quality and compression ratio in a different manner. P11 steadily decreases and becomes close to zero. This happens because of two reasons. First, features for Class 1 sufficiently intersect with features for Class 2. Second, due to lossy compression, feature distribution after compression differs from feature distribution for the original image (for which the MLM classifier has been trained) where this difference increases with the reduction of PSNR-HVS-M and CR increase. This is illustrated by distributions presented in Table 3 for Class 1 and, partly, in Table 4 for Class 2.


**Table 2.** Probabilities of correct classifications for particular classes depending on image quality.


**Table 3.** Illustration of distribution changes due to lossy compression for Class 1.

**Table 3.** *Cont*.

**Table 4.** Illustration of distribution changes due to lossy compression for Class 2.

Analysis of data in Table 2 also shows the following. There are some classes (Classes 3–6) for which a larger CR and smaller PSNR-HVS-M (that correspond to more sufficient lossy compression) results in a reduction of probabilities of correct classification (analyze data in columns for P33, P44, P55, and P66). Meanwhile, there are classes, for which probabilities of correct classification increase—see data for P77. This is because of the decrease in misclassifications in the texture area (see the maps in Figure 3c,d). There is also one class (Class 2) for which P22 is the largest for PSNR-HVS-M about 40 dB (due to noise filtering effect) but it reduces for smaller PSNR-HVS-M (larger CR).

One probable reason why the MLM classifier trained for original images and applied to compressed ones loses efficiency is that feature distributions observed for compressed data differ from those ones observed for original RS data and used for classifier training.

Then, one can expect that the MLM classifier has to be trained for compressed images. We have carried out the corresponding study and the results are presented in Table 5. The conclusion that follows from the analysis of data in Table 5 might seem trivial—it is needed to train the MLM classifier for compressed images with the same characteristics of compression. Following this rule leads to a considerable improvement in classification accuracy. For example, if original data are used in training and then the MLM classifier is applied to data compressed providing PSNR-HVS-M = 42 dB, then Pcc = 0.501. At the same time, if the image compressed providing PSNR-HVS-M = 42 dB was used in training, Pcc radically increases and becomes equal to 0.579. Even more surprising results are observed for cases of images compressed producing PSNR-HVS-M equal to 36 and 30 dB. Pcc for the corresponding training reaches 0.597 and 0.527, respectively. Note that Pcc = 0.627 for original image classified using training for the original image. Then, it occurs that for images compressed with PSNR-HVS-M about 40 dB almost the same Pcc is observed if they are trained for the corresponding compressed images.


**Table 5.** Total probabilities of correct classification Pcc for different images depending upon "training" data.

Classification maps obtained for this methodology of training are presented in Figure 4a,b. They can be compared to the maps in Figure 3c,d, respectively. This comparison clearly demonstrates that training for the corresponding compressed data is preferable. Many classes are recognized sufficiently better. One interesting point is that many classifications might appear in the neighborhoods of sharp edges in multichannel images (near edges of Class 4). This is because such edges are smeared by lossy compression and pixels with "intermediate values" that can be referred to as "wrong classes" appear.

**Figure 4.** Classification maps for the compressed image with providing PSNR-HVS-M = 36 dB using maximum likelihood method (MLM) classifier trained for the same compressed image (**a**); compressed image with providing PSNR-HVS-M = 30 dB using MLM classifier trained for the same compressed image (**b**).

### *4.2. NN-Based Classification*

Let us start by analyzing data for classifying the original three-channel image using NN training for this image. The obtained confusion matrix is presented in Table 6. The corresponding map is given in Figure 5a. As one can see, several classes are recognized well: Field-R (Class 3), Water (class 4), Trees (Class 6). There are many misclassifications for Classes "Roads" (with Class Field-Y that has practically the same colors) and "Texture" (its pixels can be erroneously related to classes "Water", "Trees", "Grass", and, more rarely, Field-Y). The results are relatively bad for Class 2 and Class 5. Thus, even for this almost ideal case (classified image is the same as that one used for training, the NN-based classifier able to work with non-Gaussian distributions of features is applied), the classification results are far from being perfect.

**Table 6.** Confusion matrix for the original image classified by neural networks (NN) trained for this image.


**Figure 5.** Classification results: for compressed image (PSNR-HVS-M = 42 dB) (**a**), for compressed image (PSNR-HVS-M = 36 dB) (**b**); for compressed (PSNR-HVS-M = 30 dB) (**c**).

Taking into account the results for the MLM classifier, we also considered the case when the NN classifier has been trained for the original image and then applied to compressed images. The data obtained for the cases of PSNR-HVS-M equal to 42 dB, 36 dB, and 30 dB are given in Tables 7–9, respectively. Analysis of data in Table 7 shows the following. As was expected, all probabilities have changed. Let us consider the diagonal elements marked by Bold that correspond to probabilities of correct classification of particular classes. In this sense, there are interesting observations (compare the corresponding data in Tables 6 and 7): some probabilities have decreased sufficiently (see P11), some decreased slightly (P33, P44, P66, P77). Meanwhile, some probabilities have slightly increased (P22 and P55).


**Table 7.** Confusion matrix for compressed image classified by NN trained for the original image and applied for the compressed image (PSNR-HVS-M = 42 dB).

**Table 8.** Confusion matrix for compressed image classified by NN trained for original image and applied for the compressed image (PSNR-HVS-M = 36 dB).


**Table 9.** Confusion matrix for compressed image classified by NN trained for the original image and applied for the compressed image (PSNR-HVS-M = 30 dB).


Analysis of data in Tables 8 and 9 shows that lossy compression negatively influences P11, i.e., Probability of correct classification for the Class "Road". Recall that the same effect has been observed for the MLM. With a larger CR (smaller provided PSNR-HVS-M), probabilities P33 and P77 continue to decrease. P22 slowly increases. P44 remains practically the same and very high. P66 also remains practically the same. Finally, P55 decreases. Thus, we can state that being trained for the original image, the NN classifier continues working well for PSNR-HVS-M about 40 dB and then its performance starts making worse faster (with further increase of CR).

Figure 5 shows classification results for the test image compressed providing three different values of PSNR-HVS-M. The results are quite similar. However, some differences can be noticed:


to be classified contains a class like "Texture". The problems occur for the class "Texture" itself and the classes for which there is an intersection of features with features of the class "Texture".

Let us now check what happens if compressed images are used for training. Table 10 presents the confusion matrix obtained for the case of NN training using image compressed providing PSNR-HVS-M = 42 dB. These data can be compared to the corresponding data in Table 7. If compressed image is employed for training, probabilities P11, P55, and P77 are sufficiently better, probability P22 is sufficiently worse, other probabilities are slightly worse. Thus, the quality of classification, in general, slightly improves. The classification map is presented in Figure 6b.


**Table 10.** Confusion matrix for compressed image classified by NN trained for this image (PSNR-HVS-M = 42 dB).

(**c**) (**d**)

**Figure 6.** Results of image classification by NN trained for the same image: original (**a**), compressed with PSNR-HVS-M = 42 dB (**b**), compressed with PSNR-HVS-M = 36 dB (**c**), compressed with PSNR-HVS-M = 30 dB (**d**).

The next considered case is the classification of the image compressed producing PSNR-HVS-M = 36 dB. The obtained probabilities are given in Table 11, the classification map is presented in Figure 6c. The probabilities of correct classification in Table 11 are almost the same as the corresponding values in Table 10. Comparing the data in Tables 8 and 11, it is possible to state that it is worth using a compressed image for training (most probabilities of correct classification for classes are better in this case). The classification map is given in Figure 6c and it is quite similar to those in Figure 6a,b. This means that there is no considerable degradation of classification accuracy compared to the previous two cases.

**Table 11.** Confusion matrix for compressed image classified by NN trained for this image (PSNR-HVS-M = 36 dB).


Finally, the last case is the classification of the image compressed providing PSNR-HVS-M = 30 dB, i.e., with considerable distortions. The confusion matrix is given in Table 12, the classification map is represented in Figure 6d. Compared to the corresponding data in Table 9, a sufficient increase of P11, P55, P66, and P77 is observed, P22, P33, and P44 have increased a little too. This means that it is worth using the compressed image for training, especially if compression is carried out with a large CR.

**Table 12.** Confusion matrix for compressed image classified by NN trained for this image (PSNR-HVS-M = 30 dB).


Attentive analysis of the classification map in Figure 6d allows noticing quite many misclassifications near the edge between classes "Water" and "Trees" where these misclassified pixels are related to "Texture". We associate this effect with edge smearing and other effects that happen near high contrast edges if the compression ratio is quite high.
