In this section, the proposed structure label matrix completion method is evaluated with several experiments. First, the effectiveness of the proposed method on a PolSAR image is investigated with different down-sampling rates. Next, the effectiveness of the structure priority distribution for the entire label matrix is validated. Finally, the effectiveness of the proposed label matrix completion with a structure prior for two different PolSAR datasets is evaluated to establish the superiority of our proposed framework. All experiments are conducted on a desktop PC equipped with an i5
[email protected] GHz and 16 GB of memory in the TensorFlow environment. In the following, the total accuracy is the number of well-classified pixels divided by the number of all pixels. Meanwhile, the classification accuracy and kappa coefficient are given in Tables 3 and 5 on two different PolSAR datasets, respectively. The overall accuracy and kappa coefficient are calculated by the following equation [
21,
26]:
where
denotes the number of pixels with the correct label compared with the “Total” number of the pixels
N.
is the diagonal element of the confusion matrices and
,
are the
k-th row and
k-th column of the confusion matrices, respectively. They denote the number of classes
k divided into the
k-th class and
k-th class separated into others, respectively.
4.1. Parameter Analysis
Information for the PolSAR database tested and detailed here is shown in
Figure 4.
Figure 4a is the Pauli RGB image of Flevoland from NASA/JPL AIRSAR in 1989, which is an L-band four-look PolSAR database of size 750 × 1024 and a resolution of 12 × 6 m.
Figure 4b,c show the ground-truth image and all terrains in this dataset, respectively, which includes 15 different classes. Here, the
under-sampled image is used for semi-supervised classification with a light network and completing the label matrix for the entire image.
Parameters play an important role in the classification performance, which is usually chosen within a range. The parameters to be tested are the coefficients
and
before the MRF term and Laplace term, the aims of which are to retain smoothness in one region and the edge between two regions, respectively. In our experience, we vary the parameter from
to 10 for
and
to
with the interval of
for
. Classification accuracy versus different parameter setting values is shown in
Figure 5. On the one hand, the classification-accuracy values are almost unchanged as the change of parameter
, which reveals that the Laplace term is robust in the proposed method. On the other hand, classification accuracy increases as parameter
varies from
to 1, while decreasing from 1 to 10 and thus reaching the highest value when
is 1. As a whole, it can be seen that the classification-accuracy values exhibit little difference for various
. Thus, in the following experiments, the chosen parameter values are 1 and
for
and
, respectively.
4.2. Classification Performance with Different Down-Sampling Rates
To validate the robustness of the label matrix completion method, the down-sampled PolSAR images with different down-sampling rates were tested on dataset Flevoland, as shown in
Figure 4. In
Table 1, the number of pixels in the down-sampled images are given to illustrate the computational cost compared with the entire image. First, the classification results are shown in
Figure 6a–d with down-sampling rates of
,
,
, and
, respectively. Then, a priority matrix for the entire image is obtained by adding the labels into the corresponding locations in the large PolSAR image, as shown in
Figure 6e–h. Finally, the final label matrix completion results are shown in
Figure 6i–l.
In
Table 1, it can be seen that many fewer samples are to be classified with the down-sampling operation, which results in low computational and storage costs. In this way, a fast classification process will be realized. The computation times used by different down-sampled images and the entire image are given in
Table 2, which shows that less time is needed for down-sampled images than that for the entire image. From the classification accuracies in
Table 2, it can be concluded that satisfactory values are obtained when the sampling rate is
,
, and
. The accuracy values of these label matrix completion results are 99%, 97%, and 96%, respectively. Even though the accuracy of the training pixels used is 0.6%, the classification accuracy value is high enough. More importantly, the classification accuracy values are good enough for almost all categories when the down-sampling rate is
. The classification accuracy is poor because the down-sampled image would significantly destroy the structure information of the entire image. It is relatively obvious that pixels in the minor class Building could not be classified correctly. It also results in low accuracy values for down-sampled images with
and
sampling rates. However, the reduction of accuracy value is relatively low compared with the computation time, as shown in
Table 1.
The runtimes in
Table 1 were tested on the down-sampled images and the entire images with the same light classification network setting as in [
50]. The classification results correspond to
Figure 6 and
Table 2. It can be concluded that the computation times of different down-sampled images are proportional to the sampling rates. The time for the
down-sampling-rate image is only 13.765 s, which is less than the 344 s the whole image needs. It costs only
time for the whole image compared to that for the
down-sampling data. Similar results are obtained with the other down-sampled PolSAR images. Therefore, with a suitable light network, a huge PolSAR image can reach a satisfactory classification result with much lower computation time and storage. This situation makes the proposed method able to be widely applied in all the excellent classification methods of the light network to process the down-sampled PolSAR images.
Regarding the visual classification results with the proposed label matrix completion method, experiments were conducted on images with different down-sampling rates. It is obvious that the visual results of the down-sampled images are satisfactory, as shown in
Figure 6a–d, which have the correct structure and smooth regions. Almost every terrain can be classified correctly in these images. In the completed label prior map images in
Figure 6e–h, the structure of regions are retained for the special down-sampling strategy with an adaptive prior learning method. With different sampling rates, the completed label prior image varies greatly when more information is obtained with a high sampling rate, as in
Figure 6e. Thus, the final completed label matrix of the image with high sampling rate is better than that with low sampling rate.
Figure 6i illustrates better performance in keeping the structure of regions, while the label matrix in
Figure 6l with a
sampling rate exhibits obvious over-fitting where regions in the unconnected part are continuous, such as the terrain Grass. The results of images with
and
sampling rates are satisfactory in keeping region structure and smoothness. In general, the performance of label matrix completion is excellent for PolSAR image terrain classification on accuracy values, visual results, and computation time.
To show the robustness of the proposed method with different labeled data and sampling rates, the box plots of different sampling rates are given in
Figure 7. From the plot results, it can be seen that the classification-accuracy value increases with decreasing sampling rate, because the higher classification-accuracy value is obtained with more labeled data. With the same sampling rate, the classification-accuracy value is stable. The variance of the classification-accuracy value decreases with different sampling rates from
to
. The classification-accuracy result of the down-sampled image is the lowest with a
sampling rate. Furthermore, the completion results will vary greatly for fewer known labels in the inversion of the matrix completion problem.
4.3. Structure Prior for Label Matrix Completion
The effectiveness of structure prior information for label matrix completion was validated. All of the experiments were carried out on the PolSAR image Flevoland database from NASA/JPL AIRSAR with a
down-sampling rate. The classification visual results and accuracy values are given in
Figure 8.
Figure 8a is the result of the down-sampled image, where the accuracy value is 94.94%. Filling the down-sampled image into the entire image as shown in
Figure 8b, the overall accuracy value is 5%. In addition, the structure of regions can be retained by the uniform sampling method as in
Figure 8b. Thus, the classification result with the MRF prior is good in terms of both the visual result and accuracy value in
Figure 8c. However, the boundary between different regions is not smooth in the result without the Laplace priority, and the classification visual result in
Figure 8d is the best for every region being homogeneous and the boundary is smooth. This is obvious in the regions that are outlined by red boxes as shown in
Figure 8c,d.