Pixel-Level Decision Fusion for Land Cover Classification Using PolSAR Data and Local Pattern Differences

Abstract

Combining various viewpoints to produce coherent and cohesive results requires decision fusion. These methodologies are essential for synthesizing data from multiple sensors in remote sensing classification in order to make conclusive decisions. Using fully polarimetric Synthetic Aperture Radar (PolSAR) imagery, our study combines the benefits of both approaches for detection by extracting Pauli’s and Krogager’s decomposition components. The Local Pattern Differences (LPD) method was employed on every decomposition component for pixel-level texture feature extraction. These extracted features were utilized to train three independent classifiers. Ultimately, these findings were handled as independent decisions for each land cover type and were fused together using a decision fusion rule to produce complete and enhanced classification results. As part of our approach, after a thorough examination, the most appropriate classifiers and decision rules were exploited, as well as the mathematical foundations required for effective decision fusion. Incorporating qualitative and quantitative information into the decision fusion process ensures robust and reliable classification results. The innovation of our approach lies in the dual use of decomposition methods and the application of a simple but effective decision fusion strategy.

1. Introduction

Remote sensing technologies have profoundly changed our ability to collect information about the Earth’s surface, allowing for the monitoring and classification of land cover and land use in a variety of scenarios. The combination of diverse datasets, including PolSAR, optical, etc. has considerably increased the possibility for urban land cover classification, ecological land mapping, and overall sea and land monitoring. Using remote sensing data for land cover classification is critical for addressing a variety of environmental and urban planning concerns. This introduction provides a detailed summary of recent research initiatives that investigate the use of many data sources and decision-level approaches to improve the precision and resilience of land cover classification.

Urban areas are dynamic environments, and monitoring land cover changes in these regions is essential for urban planning and development. An approach by González-Santiago et al. [1] explored deep self-supervised hyperspectral-LiDAR fusion, leveraging self-supervised learning to enhance land cover classification. Hyperspectral image classification also benefits from innovative fusion techniques. Tu et al. [2] proposed a superpixel-pixel-subpixel multilevel network, addressing the challenges of mixed spectral features and noise in hyperspectral images, resulting in superior classification performance. The use of machine learning algorithms in remote sensing was explored by Arpitha et al. [3], who employed various classifiers within Google Earth Engine for comprehensive land use and land cover mapping. Moreover, the fusion of optical and SAR data showed great potential in improving classification outcomes. Liu et al. [4] developed a dual-input model utilizing image-level fusion for SAR-optical cross-modal feature learning, significantly enhancing classification accuracy. Recent research has explored various advanced methods for improving PolSAR image classification. For instance, Hua et al. [5] proposed a Multi-Modal Contrastive Fully Convolutional Network (MCFCN) that integrates multi-modal features and contrastive learning, which effectively addresses the challenges of speckle noise and enhances classification accuracy with limited labeled data. Lv et al. [6] proposed a nonparametric sample augmentation approach for hyperspectral image classification, improving classification performance through iterative sample augmentation. Quan et al. [7] presented a multimodal fusion strategy that integrates SAR and optical data at the feature level, significantly improving land cover classification results. In another study, Chen et al. [8] investigated the complementary strengths of fully polarimetric SAR and optical imaging. Their method utilized polarimetric decomposition techniques and object-based decision tree classification, resulting in enhanced accuracy by combining data from these two sources.

A study conducted by Bui and Mucsi [9] compared two fusion methods, layer-stacking and Dempster–Shafer (D-S) theory-based approaches, using Sentinel-1 and Sentinel-2 data. They found that decision-level fusion with the D-S theory provided the best mapping accuracy for urban land cover mapping. Another study by Jin et al. [10] introduced a Bayesian decision-level fusion approach for multi-sensor data, significantly improving the classification accuracy by considering detailed spectral and phenomenology information. This probabilistic framework allowed for substantial improvements in classification accuracy, especially when combining multi-sensor data with distinct characteristics such as spectral and temporal features. However, a potential drawback of this method is its computational complexity and the need for extensive prior information. Bayesian inference can be demanding in terms of computational resources, especially when large datasets or numerous variables are involved. The integration of SAR and optical data has been a focal point in several studies. Maggiolo et al. [11] proposed a decision fusion technique combining optical and SAR data through Markov Random Fields (MRFs). The strength of this method lies in its ability to account for spatial dependencies between neighboring pixels, which is particularly advantageous in large-scale applications. By optimizing classification through spatial correlation, this approach helps mitigate noise and improve the consistency of the classification output over wide areas. However, the approach may be sensitive to noise in the spatial relationships, meaning that in areas with highly variable pixel values or complex textures, the model might not perform as well, leading to suboptimal classifications. Zhu et al. [12] developed a more advanced decision-level fusion method that integrates multi-band SAR images with the Dempster–Shafer (D-S) evidence theory and convolutional neural networks (CNNs). This hybrid approach merges the feature extraction capabilities of CNNs with the uncertainty-handling strength of the D-S theory, resulting in a highly robust classification system. The use of CNNs automates feature extraction, while the D-S theory ensures more reliable decision-making when dealing with conflicting or uncertain data from multiple sensors. For instance, the training of CNNs requires a large amount of labeled data, and the process can be time-consuming and computationally intensive. Papadopoulos et al. [13] introduced a correlated decision fusion method that integrates fully polarimetric SAR data and thermal infrared images. By focusing on the transmission of quality bits, this approach improves the classification accuracy by leveraging data quality. However, one potential disadvantage is that fully polarimetric SAR data can be challenging to acquire, as it often requires specialized equipment and expertise. Furthermore, the correlated decision fusion method might face limitations when the data sources (SAR and thermal) are not perfectly aligned or when the correlation between these modalities is weaker than expected, which could hinder the method’s effectiveness in certain environments. Chen et al. [14] presented a decision-level fusion method by integrating Landsat 8 and Sentinel-1 data through decision-level fusion (DLF). Their research highlighted that DLF significantly improved crop classification accuracy, illustrating the effectiveness of data fusion in agricultural applications.

Browsing through the bibliography, Local Binary Patterns (LBP) were broadly used not only to extract features for land cover classification but also for the identification of drunk people by extracting patterns on their forehead vessels using thermal infrared imagery, as discussed in papers [15,16]. Additionally, the specific feature extraction methodology was also used for the analysis of Ground Penetrating Radar (GPR) [17] data to highlight the hyperbolic peaks that represent buried objects or more generally various subsurface structures.

In this study, there are two objectives. First, we aim to learn how the implementation of a Local Pattern Differences (LPD) descriptor to the scattering components of Pauli and Krogager on PolSAR data will affect the accuracy of the three classifiers, and second, we aim to see how much we can improve the overall accuracy combining these three classifiers using the Bayesian decision fusion. To achieve this objective, the first step is to preprocess the acquired data. The specific procedure is composed of calibration, polarimetric decomposition, terrain correction, and finally registration. By accurately aligning the images, we establish a consistent spatial reference for subsequent analysis and classification. After preprocessing, we examine how we can overcome the speckle noise of the datasets by choosing suitable variables such as the optimal thresholds and the quantization window size for a more sufficient feature extraction. Furthermore, our objective is to find patterns between the scatterers that we can use as features and characterize the land cover types.

The novelty of our method lies in the implementation of two decomposition techniques as a base for feature extraction for the LPD descriptor, which has previously only been implemented in raw SAR data. Then, we fed with these features the three classifiers, such as a simple Neural Network (NN), a Decision Tree (DT) and a Random Forest (RF), whose outputs are local decisions for each land cover type. To address the possible vulnerability of each classifier, we fused them using a modified Bayesian decision fusion that uses their accuracies as a weight to highlight the more efficient model.

In the subsequent sections, we delve deeper into our study. Section 2 outlines the study area and materials utilized. Section 3 elaborates on the preprocessing of PolSAR data, and a reference is made to the decomposition methods we use. In Section 4, we analyze the LPD descriptor that we use for feature extraction. In Section 5, we refer to the classifiers we use and the results of each individual classifier, while in Section 6, we quote the mathematics behind our decision fusion method and the overall experimental results in the fusion center. In Section 7, the results of our study, the possible imperfections, the reasons behind them, and the thoughts of how to improve this work are discussed.

2. Study Area and Materials

The broader area of Vancouver was chosen as the study area, which is located in the polygon from the coordinates ${123}^{°}{16}^{\prime }27″\mathrm{W}$ to ${122}^{°}{57}^{\prime }29″\mathrm{W}$ Longitude and ${49}^{°}{21}^{\prime }10″\mathrm{N}$ to ${49}^{°}{08}^{\prime }48″\mathrm{N} \mathrm{L}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{u}\mathrm{d}\mathrm{e}$. The study area consists of five main types of land cover including Urban, Forest, Sea, Crops and Industrial. The location of the study area is depicted in Figure 1. Also, we used the data from satellite ALOS, which has an absolute orbit of 16,982 and an incidence angle (near-far) of ${22.73}^{°}$ and ${24.97}^{°}$ degrees, respectively. An ALOS PALSAR P1.1 Single Look Complex (SLC) product was acquired on 2 April 2009, with an L band as the center frequency, a PLR beam mode, and 30 m in spatial resolution. VV, VH, HV and HH polarizations were used in our study. Images of ALOS PALSAR were freely downloaded from the Alaska Satellite facility data search (https://search.asf.alaska.edu, accessed on 31 July 2023).

3. Preprocessing: Fully PolSAR

As it was mentioned previously, polarimetric SAR decomposition techniques were used in this work as a basis for our LPD feature extraction. In particular, it was Pauli’s and Krogager’s decompositions used together that gave us the opportunity for the high accuracy detection of both natural and man-made land cover types. Further along in this section, we will cover the presentation of the techniques we used so that the reader can easily understand the proposed approach as well as a brief presentation of the pre-processing steps.

3.1. Pauli’s Decomposition

The core concept of Pauli’s decomposition is to represent the scattering matrix [S] of a pixel into a sum of elementary scattering matrices, each expressing specific deterministic scattering mechanisms [18,19,20]. In the context of the conventional orthogonal linear $(h,v)$ basis, assuming $S_{hv}=S_{vh}$, the Pauli basis $\left[S_a\right], \left[S_b\right], \left[S_c\right]$ can be described using the following three 2 × 2 matrices:

$$\left[S_a\right]={\displaystyle \frac{1}{\sqrt{2}}}\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]$$

(1)

$$\left[S_b\right]={\displaystyle \frac{1}{\sqrt{2}}}\left[\begin{array}{cc}1& 0\\ 0& -1\end{array}\right]$$

(2)

$$\left[S_c\right]={\displaystyle \frac{1}{\sqrt{2}}}\left[\begin{array}{cc}0& 1\\ 1& 0\end{array}\right]$$

(3)

Consequently, given a measured scattering matrix $\left[S\right]$, it can be represented as follows:

$$\left[S\right]=\left[\begin{array}{cc}{S}_{hh}& S_{hv}\\ S_{hv}& S_{vv}\end{array}\right]=\alpha \left[S_a\right]+\beta \left[S_b\right]+\gamma \left[S_c\right]$$

(4)

where: $S_{hh}$ represents the horizontal-to-horizontal scattering polarization, $S_{hv}$ represents a transition or scattering from a horizontal to vertical polarization, which is equal to $S_{vh}$, and $S_{vv}$ represents the vertical to vertical polarization. Also, scattering coefficients are calculated as:

$$\alpha ={\displaystyle \frac{S_{hh}+S_{vv}}{\sqrt{2}}}$$

(5)

$$\beta ={\displaystyle \frac{S_{hh}-S_{vv}}{\sqrt{2}}}$$

(6)

$$\gamma =\sqrt{2}{S}_{hv}$$

(7)

The matrix $\left[S_a\right]$ corresponds to the scattering matrix of a sphere, a plate, or a trihedral reflector. In this context, the intensity of the coefficient $\alpha$ indicates the power scattered by targets characterized by single- or odd-bounce scattering. The second matrix, $\left[S_b\right]$, represents the scattering mechanism of a dihedral oriented at 0 degrees, with $\beta$ indicating the power scattered by such targets. Lastly, the third matrix, $\left[S_c\right]$, pertains to the scattering mechanism of a diplane oriented at 45 degrees, where the coefficient $\gamma$ is associated with scatterers capable of returning orthogonal polarization. Volume scattering is a prime example of this type of scattering. This correspondence is illustrated in

Table 1. Pauli bases and the corresponding meaning [21].

Pauli Basis	Meaning
$S_a$	Single- or odd-bounce scattering: this occurs when a radar signal interacts with a target and undergoes a single reflection or bounce before reaching the radar sensor.
$S_b$	Double- or even-bounce scattering: This can happen, for instance, when radar waves hit a surface, reflect off, and then reflect again off another surface before returning to the sensor.
$S_c$	Volume scattering: This type of scattering is more complex and involves multiple interactions within the target volume, leading to a scattering signal that does not follow a simple direct path (forest canopy).

.

3.2. Pauli Color-Coded Representation

The polarimetric information of the scattering matrix can be depicted by combining the intensities (${\left|S_{hh}\right|}^2,{\left|S_{\mathit{v}\mathit{v}}\right|}^2,2{\left|S_{hv}\right|}^2$) into a single RGB image. However, a significant limitation is the difficulty in physically interpreting the resulting image in terms of ${\left|S_{hh}\right|}^2,{\left|S_{\mathit{v}\mathit{v}}\right|}^2,2{\left|S_{hv}\right|}^2$. To address this, an RGB image can be created using the intensities ${\left|\alpha \right|}^2,{\left|\beta \right|}^2,{\left|\gamma \right|}^2$, which correspond to distinct physical scattering mechanisms, as outlined in Table 1. The most used coding scheme is:

$${\left|\beta \right|}^2\to red {\left|\gamma \right|}^2\to green {\left|\alpha \right|}^2\to blue$$

(8)

3.3. Krogager’s Decomposition

Interpreting a SAR image, especially a fully polarimetric SAR image, is highly challenging [22]. The goal of polarimetric decomposition is to represent the scattering matrix (coherent decomposition) or, when a second-order description is necessary, the covariance matrix (incoherent decomposition) as a mixture of canonical objects. These objects offer a more straightforward physical interpretation.

Let $S(x,y)$ denote a 2-by-2 scattering matrix. A coherent polarimetric decomposition can be expressed as:

$$S\left(x,y\right)=\sum _{m=1}^M{c}_m{S}_m\left(x,y\right)$$

(9)

In this context, $S_m\left(x,y\right)$ represents the response of the m-th canonical object, $c_m$ denotes the weight of $S_m\left(x,y\right)$ in the combination that results in $S\left(x,y\right)$, M is the number of components, and x and y are the spatial coordinates. The Krogager polarimetric decomposition is characterized using the circular polarization scattering matrix $S_{(R,L)}(x, y)$, where $R$ signifies the right-handed circular component and L represents the left-handed circular component. In monostatic radar systems, such as SAR, the scattering matrix is symmetric. Consequently, the $S_{\left(R,L\right)}\left(x, y\right)$ components can be described in terms of linear polarization components as follows [23].

$$S_{RR}\left(x, y\right)={\displaystyle \frac{S_{HH}\left(x, y\right)-S_{VV}\left(x, y\right)}{2}}+i{S}_{HV}\left(x, y\right),$$

(10)

$$S_{LL}\left(x, y\right)={\displaystyle \frac{S_{HH}\left(x, y\right)-S_{VV}\left(x, y\right)}{2}}-i{S}_{HV}\left(x, y\right),$$

(11)

$$S_{RL}\left(x, y\right)=S_{LR}\left(x, y\right)={\displaystyle \frac{S_{HH}\left(x, y\right)+S_{VV}\left(x, y\right)}{2}},$$

(12)

where $i$ denotes the imaginary unit. According to [24], and omitting the $\left(x, y\right)$ dependence for simplicity, the Krogager polarimetric decomposition is defined as follows:

$$S_{(R,L)}=\left[\begin{array}{cc}{S}_{RR}& S_{RL}\\ S_{LR}& S_{LL}\end{array}\right]=e^{i\varphi }\left\{k_s{e}^{i{\varphi }_s}\left[\begin{array}{cc}0& i\\ i& 0\end{array}\right]+k_d\left[\begin{array}{cc}{e}^{i{2}_{\eta }}& 0\\ 0& {-e}^{-i{2}_{\eta }}\end{array}\right]+k_h\left[\begin{array}{cc}{e}^{i{2}_{\eta }}& 0\\ 0& 0\end{array}\right]\right\}$$

(13)

where $k_s$, $k_d$, and $k_h$ are real-valued quantities representing the scattering coefficients from a sphere, a diplane, and a helix, respectively. Additionally, $\varphi$ is the absolute phase term that depends on the distance between the target and the sensor, ${\varphi }_s$ represents the displacement of the sphere relative to the diplane and helix components, and $\eta$ denotes their orientation angle. The scattering coefficients $k_s$, $k_d$, and $k_h$ can be derived from the circular polarization scattering components [25] as follows:

$$k_s=\left|S_{RL}\right|,$$

(14)

$$k_d=\mathrm{m}\mathrm{i}\mathrm{n}\left(\left|S_{RR}\right|,\left|S_{LL}\right|\right),$$

(15)

$$k_h=\mathrm{a}\mathrm{b}\mathrm{s}(\left|S_{RR}\right|,\left|S_{LL}\right|)$$

(16)

where the symbol $\left|·\right|$ denotes the modulus of a complex quantity and $abs(\cdot )$ represents the absolute value.

Previous studies demonstrated that the Krogager decomposition is particularly effective among various coherent polarimetric decompositions in discriminating man-made targets from natural targets [25,26]. However, it lacks the ability to distinguish between different types of man-made targets. On the other hand, Pauli’s decomposition can distinguish natural targets very well [27]. So, the combination of these two will give us complementary information for our study area, which has plenty of mixed land cover types.

The SLC PolSAR data, depicted in Figure 2a, requires thorough preprocessing to extract valuable information. Utilizing the Sentinel Application Platform (SNAP) version 9.0.8, we follow a systematic procedure that includes radiometric calibration [28], Pauli’s and Krogager’s decomposition, and Geometric Doppler terrain correction [29].

Radiometric calibration is essential for converting raw digital values into physically meaningful units. This process adjusts the SAR image so that pixel values accurately represent the radar backscatter of the reflecting surface, while still preserving geometric distortions, as shown in Figure 2b. Next, the two decomposition methods are applied to transform the complex polarimetric matrices into three distinct components for each method (see one of the components in Figure 2c,d). This transformation provides a visual intuitive representation of polarimetric information, making it easier to interpret scattering mechanisms within the radar data. Finally, the Geometric Doppler terrain correction is employed to address geometric distortions caused by a varying topography. Using a Digital Elevation Model (DEM) [30], this correction adjusts for uneven terrain, ensuring that radar reflections align with accurate geographic coordinates. The result is a georeferenced dataset (Figure 2e,f), which is crucial for precise spatial analysis and scientific interpretation.

4. Feature Extraction: LPD

Building on the theoretical framework discussed earlier, we utilized Pauli’s (Figure 3b) and Krogager’s (Figure 3a) scattering components, extracted from the SNAP software (Version 9.0.8). These components represented as $\alpha , \beta , \gamma$ and ${k_s,k}_d,k_h$ correspond to the intensities of the scattering coefficients and were measured in decibels. Since negative decibel values cannot be directly used in color mapping, we applied a normalization process to each component. This involved adjusting their histograms to scale the values between 0 and 255 to see the compatibility with color representation.

In SAR images, as reported in previous research [31], various land cover types exhibit distinct textures due to differences in surface roughness [32]. However, these textures comprise different local structures at certain quantization levels. Our approach focused on the patterns of textures that were created by the combination of scatterers in each land cover type in SAR image. Figure 3 illustrates the products that we were working on, i.e., three bands from each decomposition method depicted as RGB images.

Observing Figure 3, it is evident that the local structures vary between different classes in terms of contrast. To capture these local structures, we quantize each band of the two decomposition methods into five intervals using a contrast technique. Choosing this number of intervals gave us the opportunity to capture local structures as effectively as possible and at the same time maintain computational efficiency and mitigate the impact of speckle noise. This approximation sufficiently captures the essential variations in local structures without introducing excessive complexity or noise sensitivity that might arise from using a higher number of levels.

After quantizing the bands, we constructed the LPD for each pixel by extracting statistical features from the local structures. Finally, pixels were classified using three different classifiers with the proposed LPD.

To implement the image quantization, a widely used contrast technique derived from the recent local binary pattern method [33,34] was applied. First, all pixel intensities within a moving window were quantized into five levels based on the difference between the central pixel and the surrounding pixels within the window. Let $g_c$ represent the intensity of the central pixel. The quantization procedure is then formulated as follows:

$$s\left(i\right)=\left\{\begin{array}{c}\begin{array}{cc}\begin{array}{c} 2\\ 1\end{array}& \begin{array}{c}{g}_i>g_c+t+20\\ {g_c+t+20>g}_i>g_c+t\end{array}\end{array}\\ \begin{array}{c}\begin{array}{cc} 0 & \left|g_i-g_c\right|\end{array}\le t\\ \begin{array}{cc}\begin{array}{c}-1\\ -2\end{array}& \begin{array}{c}{g_c-t>g}_i>g_c-t-20\\ g_i<g_c-t-20\end{array}\end{array}\end{array}\end{array}\right. , i\in \left[1,\dots ,h^2\right]$$

(17)

where ${ g}_i$ is the intensity of pixel $i$ in the window, and $t$ is a threshold. An example of the quantization process with $t=5$ is shown in Figure 4. After quantization, connected components of the same quantization level, which correspond to local patterns, can represent local structures. For instance, pixels with the value “2” and “1” capture sharp edges in urban areas, those with the value “0” describe homogeneous regions, and those with the values “−2”and “−1” can capture dark primitives. During the quantization stage, a soft threshold was employed to mitigate the impact of speckle noise.

To obtain more detailed information and accurately characterize the texture, it is necessary to use multiple thresholds. Utilizing multiple thresholds allows for capturing global information while also resisting speckle noise. Given that speckle is multiplicative, we recommend increasing the thresholds by multiplying them by a constant. For example, we selected thresholds of t = [5, 10, 15] because with low values of $t$, we can use all the information given from this study, and we also succeeded in avoiding mixed land covered areas with the label of “0” i.e., the homogenous region.

For a single threshold, following the quantization stage, we can identify three types of local structures. To characterize these local structures, we then used local mean and variance:

$$P_{ave}={\displaystyle \frac{1}{N^2}}{\sum }_{j=1}^{N^2}{g}_j$$

(18)

$$P_{var}={\displaystyle \frac{1}{N^2}}{\sum }_{j=1}^{N^2}{\left(g_j-P_{ave}\right)}^2$$

(19)

The mean feature extracted from the local structures captures local intensity fluctuations, making noisy pixels less noticeable [35]. Variance is an excellent measure for detecting boundaries and edges [35]. It is important to note that other effective measures can also be used to characterize local structures. Two parameters need consideration: the size of the moving window (h) and the thresholds (t). According to the investigation in [36], the optimal h depends on the image resolution and the classification task. In this work, a window size of h = 5 was selected as a balanced choice. A smaller window could lead to over-localized feature extraction, which might help detect subtle changes in the data but could also introduce noise or lead to overfitting. On the other hand, a larger window might overlook important localized variations, reducing performance. Once the parameters are set, the LPD feature vector was constructed for each pixel, with the following form:

$$LPD=\left[P_{ave,1},P_{var,1},\dots ,P_{ave,n},P_{var,n}\right]$$

(20)

with n as the number of thresholds that are suitable for each problem.

5. Classification: Experimental Results

As discussed in the previous section, the LPD descriptor was applied across the entire study area to extract the appropriate features for each pixel. After the LPD descriptor, each pixel had a unique identity, which consists of 36 features. For computational efficiency, we selected four 20 × 20 pixel windows to represent the four land cover types in our study. Specifically, we used red for urban areas, blue for the sea, yellow for crop, and green for forests, as illustrated in Figure 5.

For classification, we used 80% of the pixels as a training dataset and 20% as a testing dataset. These datasets were then “fed” to a simple 2-layer NN [37], an RF classifier [38], and a DT classifier [39], as shown in

Table 2. Number of pixels used for each class for training and testing.

Class	Number Assigned	Training Pixels	Testing Pixels
Urban	0	320	80
Sea	1	320	80
Crop	2	320	80
Forest	3	320	80

.

In

Table 3. Confusion matrix of decision tree.

	Class	0	1	2	3	Total
True Class	0	71	2	1	6	80
	1	2	61	17	0	80
	2	0	16	46	18	80
	3	13	1	11	55	80
	Total	86	80	75	79
Predicted Class

,

Table 4. Confusion matrix of neural network.

	Class	0	1	2	3	Total
True Class	0	74	1	1	4	80
	1	5	62	11	2	80
	2	1	13	51	15	80
	3	5	1	8	66	80
	Total	85	77	71	87
Predicted Class

and

Table 5. Confusion matrix of random forest.

	Class	0	1	2	3	Total
True Class	0	69	1	1	9	80
	1	0	76	4	0	80
	2	0	8	65	7	80
	3	10	0	5	65	80
	Total	79	85	75	81
Predicted Class

, the confusion matrices of each classifier are presented to understand how many of the predicted classes of the testing pixels were correctly classified with the true class labels and how many were incorrectly classified as a different class.

The analysis of the confusion matrices reveals that while each classifier has its strengths, the random forest consistently provided the best overall performance as we observe in

Table 6. Local cover types accuracies of the classifiers for each class and the overall accuracies.

Classifier		Class				Overall Accuracy
		Urban	Sea	Crop	Forest
Decision Tree	Accuracy (%)	88.8	76.3	57.5	68.8	72.9
Neural Network		92.5	77.5	63.8	82.5	79.1
Random Forest		86.3	95	81.2	81.2	85.9

, particularly in distinguishing sea and urban classes with the accuracies of 95% and 86.3%, respectively. The decision tree showed weaknesses in separating similar vegetative classes, such as crop and forest, with notable misclassifications due to overlapping spectral features or boundary effects. The neural network improved classification for urban and forest classes but still faced challenges with distinguishing sea from crop. Misclassifications are primarily due to spectral similarities and mixed pixels in boundary areas.

6. Decision Fusion: Experimental Results

The outputs from the feature extraction stage are fed, as we discussed above, into three classifiers: a simple neural network (NN), a random forest (RF), and a decision tree (DT) classifier. Based on Duda’s [40] pattern classification framework, we employed a Bayesian model suitable for our problem.

We have equal prior probabilities for each class, denoted as $P\left(C_1\right)=P\left(C_1\right)=\dots =P\left(C_k\right),$ where $k$ ranges from 1 to 4. Each classifier provides $k$ conditional probabilities (likelihoods) $P_j(X=c\mid C_k)$ with $j=1, 2, 3,$ representing the probability of each class $C_k$ given the evidence X (predictions from the classifiers).

From [41], it can be observed that the class posterior probability from multiple classifiers is given by

$$P(C_k\mid X=c)={\displaystyle \frac{P\left(C_k\right) \prod _{j=1}^3{P}_j\left(X=c∣C_k\right)\times w_j}{\sum _{k\prime }^{3}P\left(C_{k\prime }\right) \prod _{j=1}^3{P}_j\left(X=c∣C_{k\prime }\right)\times w_j}}$$

(21)

where $P\left(C_k\right)$ is the prior probability of class $C_k$, $P_j\left(X=c∣C_k\right)$ is the likelihood of the evidence $X$ (predictions from the classifiers) given class $C_k$ for classifier $j$, and $w_j$ is the reliability weight (accuracy) of classifier $j$.

Equation (21) essentially shows that the class posterior is proportional to the product of the conditional probabilities of class $C_k$ across the classifiers, each weighted by the classifier’s reliability and adjusted by the prior probabilities, divided by the evidence.

To avoid instabilities and to create a more efficient model, we proceeded with the log-posterior probabilities. After calculations, the class posterior probability equation became:

$$P\left(C_k∣X=c\right)={\displaystyle \frac{\exp \left(\log P\left(C_k\right)+\sum _j\log P_j\left(X=c∣C_k\right)\times w_j \right)}{\sum _{k^{\prime }}\exp \left(\log P\left(C_{k^{\prime }}\right)+\sum _j\log P_j\left(X=c∣C_{k^{\prime }}\right)\times w_j \right)}},$$

(22)

As a next step, the log-posterior probabilities must be normalized. To avoid overflow when exponentiating, we computed the maximum log-posterior probability for each class, subtracted this maximum value from each log-posterior probability, and converted the adjusted log-posterior probabilities back to regular probabilities. This ensures numerical stability and accurate calculations.

The final class predictions were determined by selecting the class with the highest posterior probability i.e.,

$${max}_{k=1}^4\left\{P\left(C_k∣X=c\right)\right\}$$

(23)

Although the initial classification results were promising, with all classifiers achieving over 70% accuracy—specifically 72.9% for the decision tree (DT) classifier, 79.1% for the neural network (NN) classifier, and 85.9% for the random forest (RF) classifier—we were confident that implementing the Bayesian-based decision fusion model would lead to an even better performance. Our expectations were confirmed, as we achieved an impressive overall accuracy of 98.1% at the fusion center. This represents an improvement of almost 12.2% over the “strongest” individual classifier. After decision fusion, the accuracy of each land cover type was configured, as shown in

Table 7. Posterior probabilities for each class according to our method.

	Class
	Urban	Sea	Crop	Forest	Overall Accuracy
Accuracy (%)	99.7	99.2	94.9	98.5	98.1

. In the following,

Table 8. Comparison of our methodology with the proposed Bayesian fusion methodology of Jin et al.

Study/Author	Data Sources/Inputs	Methodology	Classifiers Used	Evaluation Metrics	Classification Results
Jin et al. [10]	Multi-source satellite images (high spatial and temporal resolution) MODIS, LANDSAT	Spatiotemporal information fusion using Bayesian Decision Theory to integrate spatial and temporal data. Preprocessing involved aligning multi-source images spatially and temporally.	Support Vector Machine (SVM) (for LANDSAT) ED-similarity (for MODIS) and PBF	Class-wise and Overall Accuracy (OA)	PBF Class-wise Accuracy: Construction Land: 96% Crop1: 96% Crop2: 64% Gobi: 86% Grassland: 43% Slope Field: 57% Wasteland: 42% Water: 96% OA: 75%
Our study	PolSAR data Local Pattern Descriptor (LPD) for local structure analysis of the decomposition components.	Quantization of image bands using contrast technique; Local structure capture with LPD; Bayesian Decision Fusion combining Decision Tree (DT), Neural Network (NN), and Random Forest (RF) classifiers	Decision Tree, Neural Network, Random Forest (with Bayesian fusion)	OA, Class-wise accuracies, Posterior probabilities (after Bayesian fusion)	Pre-fusion: DT: 72.9% NN: 79.1% RF: 85.9% After fusion: OA: 98.1%

is briefly compared to our study with similar research. Recognizing the difficulty of directly comparing two methodologies due to the different approaches used, we selected the research most closely aligned with ours.

7. Discussion: Conclusions

7.1. Discussion

In this article, we proposed a novel land cover classification approach based on features that were extracted from two decomposition methodologies using a Local Pattern Differences descriptor to exploit as much as possible the advantages of both decompositions in target detection. Then, we employed three individual classifiers to categorize four land cover types using these features for training and finally we created a more robust and accurate model by “feeding” the local decisions into a Bayesian decision fusion model.

Our study area is the broader area of Vancouver and consists of four main land cover types: urban, sea, crop, and forests. We employed data from the ALOS satellite. The preprocessing steps involved radiometric calibration, Pauli’s and Krogager’s decomposition, and geometric Doppler terrain correction for PolSAR data. Feature extraction included the revealing of patterns that were hiding into the scattering coefficients.

As we can observe above from the three classifiers (Table 3, Table 4 and Table 5), we had a relatively large percentage of pixel misclassification in pixels that represents crop. More specifically, the DT classifier categorized 18 and 16 crop pixels as sea and forest, respectively. Τhe same phenomenon, but to a lesser extent, is also observed in the other two classifiers. Also, a lower percentage of forest pixels were mistakenly labeled as urban or crop in all classifiers.

Using the Fisher Linear Discriminant [42], we can visualize the feature space, projected onto the subspace generated by the eigenvectors with the largest eigenvalues (Figure 6a,b). Both images in Figure 6a,b depict the cluster separability of four land cover types for training and testing datasets. These errors were expected since we have a huge area without a 100% clear land cover type, as we inspect in Figure 6a,b below. There are urban areas mixed with trees, crops planted with trees, and not low vegetation, or they are over-watered, which was the main reason for the pixel misclassifications. Generally, we observe in Figure 6 that the areas with the greatest overlap are those of the sea, the forest, and crop.

The results demonstrate that random forest outperforms other models, especially in accuracy-challenging classes such as sea and crop, due to its robust handling of complex and noisy data patterns. This knowledge is valuable to researchers and practitioners in urban planning, environmental monitoring, and agricultural management, as it guides the selection of appropriate classifiers for specific land cover types.

We prove that it is possible to address the limitations of individual classifiers and to take advantage of their strengths by employing a Bayesian decision fusion model to combine their local decisions and compute the posterior probabilities for each class. For the fusion to be considered successful, the overall accuracy at the fusion center is needed to surpass that of the best individual classifier. Our experimental results demonstrate this success, with an overall accuracy improvement of 12.1% over the random forest’s 85.9%. Specifically, we achieved 99.7% accuracy for urban pixels, 99.2% for sea, 94.4% for crop, and 98.5% for forest.

7.2. Conclusions

Through this classification and decision fusion process, we not only deepened our understanding but also identified areas for future exploration that could further enhance accuracy. As we believe, the limitations for one study are the cause for further innovations in the scientific world. We try to motivate researchers to possibly work not only with raw data but also with preprocessed datasets that can hide features that could be helpful for classification. Furthermore, identifying and incorporating additional pixel-level features would allow for a clearer distinction of mixed land cover types in datasets with speckle noise or other interferences. Optimization of the classifier’s parameters would be one more important subject for examination, as well as the use of some other classification techniques that would give better separability among the classes. Also, the usage of more land cover types can provide a more generalized approach to the classification.

Looking ahead, the field presents challenges and opportunities. Our goal is addressing the open challenges in this research domain, by using the correlation between the pixels of our study area and refining the integration of quality information for decision fusion. The nature of land cover that frequently changes necessitates the continuous improvement of methodologies.

On the other hand, these challenges also pave the way for innovative breakthroughs. Progress in machine learning techniques, sensor advancements, and increased computational power offers the potential for developing more advanced and precise classification approaches. Tapping into the intersections of new technologies such as remote sensing and artificial intelligence may reveal fresh opportunities to improve land cover analysis.

In conclusion, the future of this research area lies in overcoming obstacles while capitalizing on opportunities for progress. Ongoing investigation, innovation, and the adoption of the latest technologies will be crucial in steering our research forward, ultimately leading to a deeper and more complete understanding of land cover patterns and dynamics.