3.1.

Classification algorithm

Dynland clustering algorithm includes the following main steps:

The algorithm is nonparametric; it is described in detail in the paper [1]. As a result, all pixels of the image are distributed into clusters of different size and shape in the 10-dimensional feature space related to 10 Sentinel-2 bands.

Classes (categories) are assigned to each cluster using the following algorithm taking the image, clusters and reference at the input.

Let n be the number of categories, R_i, i ∈ [1, n] reference of the category i within the image, m - number of clusters and C_j,j ∈ [1, m] set of pixels in cluster j. We will use notation ||S|| for number of pixels in set S.

Classification happens in 2 steps. For some cases where additional analysis is required (Section 3.3), only the first step is used. We will use terms initial classification (step 1) and full classification (step 2).

If a cluster overlaps with reference set of exactly one category, it is obvious choice to assign that category to all pixels in such cluster.

If a cluster overlaps more than one set of reference, the category it overlaps the most should be assigned: . If the reference set is untrustworthy (imprecise and/or outdated), this category is only assigned if at least a certain fraction of a cluster overlaps the reference of the category (initial classification threshold is used).

For the second step we are left with clusters that do not overlap any reference at all. We use pixels from already assigned clusters to assign temporary category labels to all unassigned pixels based on spectral similarity. Any supervised algorithm can be used for this step; we used KNN [5]. Afterwards we treat those temporary labels as reference set for clusters that didn’t overlap actual reference: , where L_j are temporary labels of category j.

3.2.

Clustering step analysis

The Dynland clustering algorithm starts with forming a cluster around each pixel and operates with the cluster-pixel matrix indicating which pixels are put in which cluster(s). Such approach requires huge memory resources limiting the number of pixels to be clustered. Although it is using sparse matrices to operate with such data (implementation in MATLAB [6]), memory limitations strongly affect the applicability of the algorithm. To deal with this problem, we propose to use a sampling procedure taking each n-th pixel from the image on both axes, perform clustering of these pixels and distribute other pixels within the formed clusters afterwards. The procedure used for distribution was KNN looking for one nearest neighbor using the Euclidian distance. It is understandable that the nonparametric nature of the Dynland clustering is compromised in this way and that results in lower accuracy of classification.

The approach described above was used to create 9 different clustering results – each obtained using a different clustering (overleap) step (using every pixel, using every 2^nd, 3^rd, …, 9^th). Each of these clustering results was then assigned categories using a classifier described in Section 3.1. Classification was performed using 80% of reference pixels from each category of the reference (remaining 20% were used for validation).

Classification results were compared to reference, evaluated visually and by calculating the Cohen’s kappa coefficient. Visual analysis shows that classification is degraded even with the clustering step value of 2 (see Figure 6). If n=4, one of the smallest categories (transition mires and quaking bogs) is completely lost in the label image.

Figure 6.

Clustering step analysis results- classified image for the Cena bog area (yellow: agriculture, green: forests; orange: active raised bogs; light green: degraded raised bogs; light blue: transition mires and quaking bogs; brown: licensed peat extraction sites; tan: abandoned peat extraction sites). Clustering step is indicated to the left of each image.

Kappa values for classification decrease with each increase of the clustering step (see Figure 7). The image of Dobele has the least decrease of kappa values for different clustering steps; for other 2 images, this decrease is more significant.

Figure 7.

Clustering step analysis results.

3.3.

Methods for compensation of missing reference

If the classification is performed for an image fragment where the reference data is missing for some category, the resulting label image will not include pixels of that category. If that happens, and the category is actually present within the fragment area, reclassification is needed to obtain the properly classified image.

Two reclassification methods are proposed and were analyzed. They are based on combined processing of two images: 1) the target image is the one which is classified now and for which some reference data are missing; 2) the supplementary image is the one which can be classified properly because the reference data are available in full (for all categories).

In the first approach, initial classification is performed for the target image. The result depends on the threshold value setting the minimum overlap of the cluster with reference for assigning a category to the cluster (we will call it “initial classification threshold”). After that, remaining clusters of the target image are assigned categories based on their similarity with classified pixels of the supplementary image.

The second approach uses initial classification of the supplementary image (again obtained using different thresholds), classified pixels of categories for which the reference data are missing in the target image are added to the target image to be classified along with their classification result to be used as the reference). Newly constructed image is then clustered and the full classification is obtained.

In order to effectively analyze reclassification performance, both images (with full reference) were tested by artificially removing one reference category from the target image and using the other as the supplementary image, repeating that for every category. After reclassification, its results were compared against the full reference of the image to calculate the kappa coefficient. The results are illustrated in Figures 8 and 9.

Figure 8.

Classification accuracy of the first method for west (left) and east (right) images.

Figure 9.

Classification accuracy of the second method for west (left) and east (right) images.

For the first method, increase of the initial classification threshold mostly affected reclassification due to missing reference data for the forest class. For most other class exclusions classification result is nearly constant (Figure 8). There is a significant variation between exclusion of different classes.

Classification results for the second method are virtually unaffected by the initial classification threshold and having very little variation between different class exclusions (Figure 9).

3.4.

Discussion

As expected for the clustering step analysis, best classification results were obtained if clustering of every pixel was used, gradually declining with every increase of the clustering step. The best kappa values and the least decrease for the image of Dobele are explained by only having 3 categories in the reference of that image (other images had 6 – 7 categories).

Accuracy increase with increasing initial classification threshold for the first reclassification method is explained by outdated reference available for this image. It mostly affects the forest class; it is assumed that clear cuts of the forest have occurred so that the reference data are outdated.