Unsupervised Gaussian-Noise-Robust Remote Sensing Change Detection via FRFCM-IRM Change Intensity Modeling and SEEDSAM-Constrained HCRF

1. Introduction

With the rapid development of remote sensing technology for Earth observation, the capability of acquiring remote sensing images has significantly improved, providing important data support for the dynamic monitoring of the Earth’s surface environment [1,2]. As one of the key research tasks in remote sensing image analysis, remote sensing change detection aims to identify areas where changes have occurred in different land-cover types, surface feature conditions, or spatial structures, and to extract the corresponding change information by analyzing differences between remote sensing images of the same area obtained at different times [3,4]. As change detection techniques can effectively reveal the spatiotemporal evolution of land surface features, they have important practical value in fields such as land-use analysis, urban expansion analysis, ecological and environmental assessment, and disaster emergency management [5,6,7,8].

However, during the actual imaging process, remote sensing images are often affected by noise due to factors such as sensor performance and the imaging environment, thereby reducing image quality and the reliability of detection results [9,10,11]. Among different noise types, Gaussian noise is one of the typical and common forms of noise in remote sensing images, usually appearing as random disturbances in pixel gray-level values or spectral characteristics [12,13]. For change detection tasks, Gaussian noise interferes with the difference distribution between bi-temporal images, producing abnormal differences in unchanged areas and leading to false detections in the detection results. Meanwhile, when the spectral differences in truly changed areas are weak or the boundaries are unclear, Gaussian noise can easily mask true change information, resulting in problems such as shifted change boundaries and missed detections [14,15]. Therefore, suppressing the interference of Gaussian noise with change detection results while maintaining the spatial continuity of truly changed areas is a key issue in improving the reliability of remote sensing change detection.

In response to these issues, existing remote sensing change detection methods can be broadly divided into supervised and unsupervised methods according to whether they rely on manually annotated training data [16,17]. Among them, unsupervised change detection methods can automatically identify change information in multi-temporal images, avoiding problems commonly faced by supervised methods, such as difficulty in obtaining training data, high annotation costs, and limited data representativeness. Therefore, unsupervised change detection algorithms have greater practical value in real-world applications [18,19,20]. According to the way change features are obtained, these algorithms can be further divided into traditional methods and deep learning-based methods [21,22].

Typical traditional unsupervised change detection methods include image differencing [23], ratio methods [24], principal component analysis (PCA) [25], and change vector analysis (CVA) [26]. These methods usually construct difference information or change features from bi-temporal images and then combine them with techniques such as threshold segmentation to obtain change detection results [27,28]. Zhang et al. [29] proposed a generalized extreme value (GEV)-based unsupervised SAR change detection method, which models superpixel regions with the GEV distribution and uses a GEV-based likelihood ratio test (LRT) statistic to measure intertemporal similarity. Lee and Kim [30] enhanced the detectability of small targets by utilizing Berger’s method to fuse logarithmic-ratio images with non-coherent change detection images, and further improved robustness through an adaptive fuzzy membership function. However, when Gaussian noise exists in bi-temporal remote sensing images, the difference information or change features are disturbed by noise, making false detections and missed detections more likely to appear in the detection results. To improve robustness against Gaussian noise, clustering methods and probabilistic graphical models have been introduced into unsupervised change detection [31,32,33]. Clustering methods usually identify changed areas by adaptively partitioning the distribution of difference features. Among them, Fuzzy C-Means (FCM) [34] uses membership degrees to describe the degree to which a pixel belongs to different signal classes, but it does not make effective use of spatial information [35]. To address this limitation, improved fuzzy clustering methods such as FCM_S [36], KFCM_S [37], and FLICM [38] incorporate spatial neighborhood information, kernel distance metrics, or fuzzy local factors to enhance clustering stability under noise interference. Unlike improved fuzzy clustering methods, which mainly improve noise resistance at the feature clustering stage, probabilistic graphical models usually impose constraints on change detection results at the level of change labels [39]. Typical models include the Markov random field (MRF) [40], Adaptive MRF [41], Level set-MRF[42], conditional random field (CRF) [43], Fully Connected CRF [44] and hybrid conditional random field (HCRF) [45]. These models usually integrate observed features, change labels, and spatial structural relationships to constrain detection results, thereby reducing isolated false detections caused by Gaussian noise and improving the spatial consistency of the detection results. However, most traditional unsupervised methods still rely on difference features and local spatial relationships. Under strong Gaussian noise or complex land-surface conditions, their detection results may still suffer from false detections, missed detections, and unstable boundaries.

In recent years, deep learning methods have gradually been introduced into unsupervised remote sensing change detection tasks, with their core advantage lying in the ability to automatically extract spectral change features from bi-temporal images through neural networks [46,47]. Shen et al. [48] proposed a Progressive Self-Optimization Network (PSONet), which leverages spectral, deep, and class signals to capture “weak-to-strong” change signals and progressively optimize a lightweight network. Tao et al. [49] developed a Cross-Domain Difference Representation Learning (CDRL) framework capable of effectively learning the semantics of changed and unchanged pixels, thereby accurately identifying land-cover changes. In addition, spatial relationships and contextual information have also been incorporated into deep learning methods [50,51]. Lv et al. [52] proposed the Graph Contrastive Learning Network (GCLN) for land-cover change detection in heterogeneous remote sensing images. This method constructs pairwise graph structures from the perspectives of spectral similarity and dissimilarity, and uses graph features to learn short- and long-range dependencies for change detection. Béchaz et al. [53] proposed the 2Player framework, in which a Geographical Correspondence Module (GCM) is introduced to provide structural information, while a filtering strategy is incorporated to reduce the influence of label noise. With the development of visual foundation models, models such as the Segment Anything Model (SAM) [54] have been introduced into remote sensing image analysis tasks, providing new pathways for unsupervised change detection. Zuo et al. [55] integrated the SAM with instance-level change generation, where SAM is adopted to extract object instances for generating pseudo bi-temporal change samples in single-temporal unsupervised change detection. However, unsupervised methods mainly rely on the difference information contained in bi-temporal images to identify changes, and their detection results are therefore often affected by image quality and noise intensity. When strong Gaussian noise exists in bi-temporal images, random noise disturbances reduce the distinguishability between changed and unchanged areas, making it difficult for the change detection model to stably identify real change information. Therefore, enhancing the resistance of unsupervised change detection methods to Gaussian noise remains an issue that requires further study in remote sensing change detection.

To address the above issues, we propose an unsupervised Gaussian-noise-robust change detection method for remote sensing images, termed FRIH-SEEDSAM. The method first uses Fast and Robust Fuzzy C-Means (FRFCM) [56] to perform morphological reconstruction on bi-temporal remote sensing images. It then clusters the gray-level histograms of the reconstructed images into signal classes and applies median-based membership filtering to the fuzzy membership degrees in the clustering results, so as to suppress the influence of local abnormal values caused by Gaussian noise on the signal classes and improve their stability. To establish reliable correspondences between the signal classes, the Integrated Region Matching (IRM) algorithm [57], a region-based similarity measurement method, is used to establish weighted matching relationships between the signal class centers of the bi-temporal images. During the matching process, IRM comprehensively considers the membership information of pixels with respect to multiple signal class centers and uses it to calculate the change intensity of spatially corresponding pixels. This weighted matching mechanism reduces the influence of local abnormal memberships caused by noise on the calculation of change intensity and works together with the noise-resistant clustering characteristics of FRFCM to generate a more stable change intensity map. Subsequently, the change intensity information is input into the HCRF model, where change labels are constrained by pixel features and neighborhood information. At the same time, the Energy-Driven Sampling (SEEDS) [58]-guided Segment Anything Model (SEEDSAM) uses the centroids of the superpixels generated by SEEDS segmentation as point prompts for SAM to perform object-level segmentation on the change intensity map, thereby segmenting spatially continuous regions with similar change intensities into objects. Based on these objects, an object potential function is constructed and introduced into the HCRF to constrain the change results. Through object-level constraints, the method can not only further suppress isolated false detections caused by Gaussian noise, but also use intra-object regional consistency to alleviate missed detections, making the final change detection results closer to real ground object changes in terms of boundaries and morphology. The main work of this study is summarized as follows:

• Construction of an unsupervised Gaussian-noise-robust change detection framework, FRIH-SEEDSAM.

By integrating FRFCM, IRM, HCRF, and SEEDSAM, an unsupervised Gaussian-noise-robust change detection framework is formed. This framework follows a progressive process from pixel-level change information extraction and neighborhood information incorporation to object-level constraints. It can obtain more stable change detection results from noisy bi-temporal images.

2.

Generation of the change intensity map based on FRFCM and IRM.

FRFCM is used to cluster bi-temporal remote sensing images. Within FRFCM, morphological reconstruction and membership filtering are performed to obtain more stable signal class centers and membership degrees. The IRM algorithm is then used to establish weighted matching relationships between the signal class centers and fuzzy membership degrees of the bi-temporal images, thereby calculating change intensity information and providing stable input for subsequent constrained optimization.

3.

Constraint optimization of change intensity information using HCRF and SEEDSAM.

The HCRF performs constrained optimization of the change detection results at the pixel, neighborhood, and object levels. Since SEEDS-generated superpixels better follow the boundary structures in the change intensity map, this paper also proposed an SEEDSAM to perform segmentation on the change intensity map using the centroids of SEEDS superpixels as point prompts for SAM, and the segmentation results are used to construct the object potential function. This allows pixels that are spatially distant but belong to the same object to be constrained by change-label consistency, thereby introducing object-level long-range spatial dependencies into the change detection process. This improves intra-object consistency and the integrity of change boundaries, strengthening the method’s resistance to Gaussian noise disturbances.

2. Principle of the Proposed Algorithm

We propose an FRFCM-IRM change detection model and combine it with HCRF. Meanwhile, SEEDSAM segmentation results are used to construct the object potential function of HCRF, thereby improving the robustness of the FRIH-SEEDSAM algorithm under Gaussian noise interference.

2.1. Algorithm Framework

As shown in Figure 1, the unsupervised FRFCM-IRM algorithm takes the signal class centers and fuzzy membership degrees of bi-temporal images as input data. The IRM algorithm is used to establish weighted matching relationships between the signal classes of the bi-temporal images, thereby calculating the pixelwise change intensity. In this study, the FRFCM-IRM method is used to generate a change intensity map, which is then combined with HCRF for spatially constrained optimization of the change intensity information.

In HCRF, the change intensity map is first clustered using FCM. The fuzzy membership degrees of pixels belonging to the changed and unchanged classes are used to define the unary potential function, and the eight-neighborhood information of the center pixel is incorporated to construct the pairwise potential function. Meanwhile, to further incorporate the spatial information of the image, superpixel segmentation – SEEDS - is performed on the change intensity map. The centroid positions of the superpixel are then used as prompts for SEEDSAM to obtain object-level segmentation results, which are further used to calculate the object potential function. Eventually, post-processing is performed based on the HCRF results to obtain the final change detection results.

2.2. FRFCM

The traditional FCM clustering algorithm can decompose pixels into multiple signal classes according to different fuzzy membership degrees, establishing a one-to-many relationship between pixels and signal classes. This provides an effective way to address mixed-pixel decomposition in remote sensing images. However, FCM is relatively sensitive to noise. When remote sensing images are affected by noise, the signal class centers and fuzzy membership degrees may deviate to some extent. To improve the robustness of FCM against noise interference, FCM_S incorporates local spatial information into the FCM clustering process. Although this method improves clustering performance under noise interference, it also significantly increases the computational complexity of FCM. For this reason, we use FRFCM, which is based on morphological reconstruction and membership filtering. Compared with traditional FCM clustering, FRFCM first converts the bi-temporal multispectral remote sensing images into gray-level representations and then performs clustering on their gray-level histograms, so that the clustering objects are shifted from pixels to gray levels, thereby improving clustering efficiency. After the clustering process is completed, the obtained cluster centers and fuzzy memberships are mapped back to the multispectral space. Meanwhile, through morphological reconstruction and membership filtering, FRFCM can improve noise robustness and enhance the stability of the clustering results. Its objective function is as follows:

$$Jm=\sum _{1\le l\le G}{\displaystyle \sum _{k=1}^n}{{\gamma }_l\left(u_{kl}\right)}^q{‖{\xi }_l-v_k‖}^2$$

(1)

where $G$ and $n$ represent the number of gray levels and the number of clusters in the image, respectively; ${\gamma }_l$ denotes the statistical count of gray level $l$ in the image; ${\xi }_l$ represents gray level $l$ in the reconstructed image; $u_{kl}$ denotes the fuzzy membership degree of gray level $l$ belonging to the $k$-th cluster; and $v_k$ denotes the cluster center of the $k$-th cluster.

2.2.1. Morphological Reconstruction

Improved FCM-based methods can partially suppress the influence of noise on images by incorporating local spatial information. However, this also increases computational complexity and may cause a certain loss of edge details. Preprocessing images through morphological reconstruction can remove isolated noise points in advance while preserving the main image regions. FRFCM performs morphological reconstruction on the original image through a closing operation. During reconstruction, the original image is used as a constraint to ensure that the gray-level range of the reconstructed image does not exceed that of the original image. Finally, the reconstructed image is fused with the original image using weighted fusion to smooth image details and textures.

2.2.2. Membership Filtering

Most improved FCM-based methods that introduce local spatial information need to repeatedly calculate the Euclidean distances between neighboring pixels and cluster centers during the clustering process, which increases computational complexity and reduces clustering efficiency. After clustering the gray-level histogram, FRFCM restores the gray-level fuzzy membership degrees and signal centers back into the multispectral space and then applies a median filter to the fuzzy membership degrees. Membership filtering uses the correlation between neighboring membership degrees to correct membership anomalies caused by noise, thereby correcting misclassified pixels. At the same time, this process avoids repeated calculation of the Euclidean distances between neighboring pixels and cluster centers during iteration, significantly improving clustering efficiency.

2.3. IRM

To establish reliable correspondences between the bi-temporal clustering results and reduce the influence of abnormal memberships on change intensity, the IRM algorithm is introduced to construct weighted matching relationships for the signal classes captured by the FRFCM. The IRM algorithm follows the “Most Similar Highest Priority” (MSHP) principle to match signal classes with close centers in multispectral. In this way, it can assess the overall similarity between coregistered pixels and shows strong robustness to inaccurate clustering results. On this basis, an FRFCM-IRM-based change detection framework is constructed by coupling FRFCM clustering with the IRM algorithm. Owing to the noise robustness of FRFCM, the signal class centers and fuzzy membership information obtained from the clustering process are relatively stable. Based on the captured signal classes, IRM establishes weighted matching relationships and calculates the change intensity of spatially corresponding pixels, thereby further reducing the influence of noise disturbances on change intensity information and generating a more stable change intensity map. When bi-temporal remote sensing images are processed using FRFCM, the pixel feature of pixel $p_i^1$ in the Time 1 image is defined as $f_i^1=\left\{\right(v_1,u_1\left(p_i^1\right))\dots \dots (v_k,u_k\left(p_i^1\right))\dots \dots (v_n,u_n\left(p_i^1\right)\left)\right\}$, and the pixel feature of pixel $p_j^2$ in the Time 2 image is defined as $f_j^2=\left\{\right(v_1^{\text{'}},u_1^{\text{'}}\left(p_j^2\right))\dots \dots (v_k^{\text{'}},u_k^{\text{'}}\left(p_j^2\right))\dots \dots (v_m^{\text{'}},u_m^{\text{'}}\left(p_j^2\right)\left)\right\}$, where $v_k$ and $v_k^{\text{'}}$ are the centers of signal classes $c_k$ and $c_k^{\text{'}}$, respectively; $u_k\left(p_i^1\right)$ and $u_k^{\text{'}}\left(p_j^2\right)$ are the fuzzy membership degrees of pixel $p_i^1$ with respect to signal class $c_k$ and pixel $p_j^2$ with respect to signal class $c_k^{\text{'}}$, respectively; and $n$ and $m$ denote the numbers of signal classes in the Time 1 and Time 2 images, respectively.

The IRM distance is calculated by matching the feature $f_i^1$ of pixel $p_i^1$ in the Time 1 image with the feature $f_j^2$ of pixel $p_j^2$ in the Time 2 image, thereby obtaining the change intensity between pixels in the two temporal images. As shown in Figure 2, during the signal class matching process, the IRM algorithm quantifies the fuzzy membership degrees as edge weights of the signal classes and follows the MSHP principle. The maximum weight is first assigned to the signal class pair with the minimum distance. The IRM algorithm calculates the transition cost from pixel feature $f_i^1$ to pixel feature $f_j^2$ by computing the weight matrix $S=\left[s_{ij}\right]$, as shown below:

$$IRM(f_i^1,f_j^2)={\sum }_{i,j}{s}_{ij}\times d_{ij},i=1,\dots ,n,j=1\dots ,m$$

(2)

$${\displaystyle \sum _{j=1}^m}{s}_{ij}=u_i,i=1,\dots ,n$$

(3)

$${\displaystyle \sum _{i=1}^n}{s}_{ij}=u_j^{\mathrm{\text{'}}},j=1,\dots ,m$$

(4)

$$\sum _{\begin{array}{c}1\le i\le n\\ 1\le j\le m\end{array}}{s}_{ij}=1$$

(5)

$$\sum _{i:1\le i\le n,i\ne i^{\mathrm{\text{'}}}}{s}_{ij}=u_j^{\mathrm{\text{'}}}-u_{i^{\mathrm{\text{'}}}},u_{i^{\mathrm{\text{'}}}}<u_j^{\mathrm{\text{'}}}$$

(6)

In these equations, $d_{ij}$ denotes the distance between signal class centers $v_i$ and $v_j^{\text{'}}$; $S$ represents the matching relationships and weights between the signal classes in pixel features $f_i^1$ and $f_j^2$; and $s_{ij}$ is the matching weight between signal classes $c_i$ and $c_j^{\text{'}}$, where $s_{ij}\ge 0$. Equations (3) and (4) specify that, when matching signal classes between the Time 1 image and the Time 2 image, the total matching weight of a single signal class should be equal to the fuzzy membership degree of the pixel with respect to that signal class. Equation (5) restricts the sum of the matching weights of all signal classes between two pixels to 1. Equation (6) specifies that, after signal class $c_{i^{\text{'}}}$ is matched with signal class $c_j^{\text{'}}$, if the fuzzy membership degree of signal class $c_{i^{\text{'}}}$ is smaller than that of signal class $c_j^{\text{'}}$, the sum of the matching weights between the remaining signal classes of the Time 1 image pixel and signal class $c_j^{\text{'}}$ in the Time 2 image should be equal to $u_j^{\text{'}}-u_{i^{\text{'}}}$.

The iterative process by which the IRM algorithm establishes many-to-many weighted matching relationships between the signal classes of $f_i^1$ and $f_j^2$ is as follows:

1) Set the initial signal class matching set as $W=\left\{\varnothing \right\}$, and define the signal class sets of the pixels in the bi-temporal images as $C_1=\left\{c_1,{\dots c}_i,\dots c_n\right\}$($1\le i\le n)$ and $C_2=\left\{c_1^{\text{'}},\dots c_j^{\text{'}},\dots c_m^{\text{'}}\right\}$($1\le j\le m$).

2) Select the minimum distance $d_{i^{\text{'}}{j}^{\text{'}}}$ from the signal class sets $C_1$ and $C_2$, together with the corresponding signal class pair $\left(c_{i^{\text{'}}},c_{j^{\text{'}}}^{\text{'}}\right)$, where $i^{\text{'}}$ and $j^{\text{'}}$ denote the indices of the signal class pair associated with this minimum distance.

3) Set the matching weight as $s_{i^{\text{'}}{j}^{\text{'}}}=\mathrm{m}\mathrm{i}\mathrm{n}(u_{i^{\text{'}}},u_{j^{\text{'}}}^{\text{'}})$.

4) If $u_{i^{\text{'}}}<u_{j^{\text{'}}}^{\text{'}}$, set $s_{i^{\text{'}}j}=0,\forall j\ne j^{\text{'}}$; otherwise, set $s_{{ij}^{\text{'}}}=0,\forall i\ne i^{\text{'}}$.

5) Update the edge weight of $c_{i^{\text{'}}}$ as $u_{i^{\text{'}}}=u_{i^{\text{'}}}$-$\mathrm{m}\mathrm{i}\mathrm{n}(u_{i^{\text{'}}},u_{j^{\text{'}}}^{\text{'}})$.

6) Update the edge weight of $c_{j^{\text{'}}}^{\text{'}}$ as $u_{j^{\text{'}}}^{\text{'}}=u_{j^{\text{'}}}^{\text{'}}$-$\mathrm{m}\mathrm{i}\mathrm{n}(u_{i^{\text{'}}},u_{j^{\text{'}}}^{\text{'}})$.

7) Update the signal class matching set as $W=W\cup \left\{\right(c_{i^{\text{'}}},c_{j^{\text{'}}}^{\text{'}}\left)\right\}$.

8) When ${\displaystyle {\sum }_{i=1}^n}{u}_i>0$ and ${\displaystyle {\sum }_{j=1}^m}{u}_j^{\text{'}}>0$, return to Step 2); otherwise, terminate the iteration.

In the above pixel-by-pixel signal class matching process, the IRM algorithm supports matching between one signal class and multiple signal classes, which helps improve the accuracy of change detection.

To further illustrate the characteristics of the IRM algorithm, a qualitative analysis is conducted on the weighted many-to-many matching relationship between the signal classes in $f_i^1$ and $f_j^2$.

① Assume that the distance $d_{ij}$ between signal classes $c_i$ and $c_j^{\text{'}}$ is small, and that their corresponding edge weights $u_i\left(p_i^1\right)$ and $u_j^{\text{'}}\left(p_j^2\right)$ are both high. This indicates that signal classes $c_i$ and $c_j^{\text{'}}$ are the typical spectra of pixels $p_i^1$ and $p_j^2$, respectively, and that the spectral difference between them is small. In this case, a larger matching weight $s_{ij}$ is assigned, resulting in a smaller final IRM distance and increasing the possibility that pixel $p_j^2$ is determined as an unchanged pixel.

② Assume that the distance $d_{ij}$ between signal classes $c_i$ and $c_j^{\text{'}}$ is small, but that the corresponding edge weight $u_i\left(p_i^1\right)$ or $u_j^{\text{'}}\left(p_j^2\right)$ is low. This indicates that signal class $c_i$ or $c_j^{\text{'}}$ is not the typical spectrum of pixel $p_i^1$ or $p_j^2$. Although the spectral difference between the signal classes is small, only a smaller matching weight $s_{ij}$ can be assigned due to the constraint of the edge weights, so that $d_{ij}$ accounts for a smaller proportion of the IRM distance.

③ Assume that the distance $d_{ij}$ between signal classes $c_i$ and $c_j^{\text{'}}$ is large, and that $c_i$ and $c_j^{\text{'}}$ represent typical spectra of pixels $p_i^1$ and $p_j^2$, respectively, with high corresponding edge weights $u_i\left(p_i^1\right)$ and $u_j^{\text{'}}\left(p_j^2\right)$. In this case, although the difference $d_{ij}$ between the signal classes is large, a larger matching weight $s_{ij}$ should still be assigned. The calculated IRM distance is therefore large, making pixel $p_j^2$ more likely to be determined as a changed pixel.

④ Assume that the distance $d_{ij}$ between signal classes $c_i$ and $c_j^{\text{'}}$ is large, but that $c_i$ or $c_j^{\text{'}}$ does not represent the typical spectrum of pixel $p_i^1$ or $p_j^2$, resulting in a low corresponding edge weight $u_i\left(p_i^1\right)$ or $u_j^{\text{'}}\left(p_j^2\right)$.In this case, only a smaller matching weight $s_{ij}$ can be assigned due to the constraint of the edge weights, so that $d_{ij}$ accounts for a smaller proportion of the IRM distance.

In this study, the IRM algorithm measures the differences in the membership distributions of pixels at the same spatial locations in bi-temporal images, thereby obtaining pixel-level change intensity information. The change intensity map comprehensively reflects the overall changes at the pixel level and provides reliable and stable input for subsequent HCRF-constrained optimization.

2.4. HCRF

CRF is a discriminative probabilistic graphical model that directly models the posterior distribution of the label field conditioned on the observed data and can incorporate spatial information from the observations.

$$p\left(y\right|x)={\displaystyle \frac{1}{Z\left(x\right)}}exp\left\{-\sum _{c\in C}{\mathrm{Ф}}_c(x,y_c)\right\}$$

(7)

$$Z(\mathit{x})=-\sum _{\mathit{y}}exp\left\{-\sum _{c\in C}{\mathrm{Ф}}_c(x,y_c)\right\}$$

(8)

where C denotes the clique set, ${Ф}_c$ is the potential function defined on clique C, $y_c$ denotes the label field corresponding to clique C, and $Z\left(x\right)$is the partition function. Depending on the specific problem, the potential function may include unary, pairwise, and higher-order terms. In practical tasks such as image segmentation and classification, pairwise CRF models are widely used because they are relatively convenient for modeling and inference.

Traditional pairwise CRF models, however, are limited in their ability to fully exploit ground object change information. For this reason, the HCRF incorporating an object potential function is combined with the FRFCM-IRM algorithm in this study, as shown in Figure 3. Since the change intensity information generated by FRFCM-IRM reduces noise interference to some extent, taking it as the observation-field input of HCRF can improve the noise resistance of the HCRF.

$$p(y|x)={\displaystyle \frac{1}{Z\left(x\right)}}exp\left\{\sum _{i\in N}{\phi }_i(x,y_i)+\lambda \sum _{i\in N}\sum _{j\in {\eta }_{\mu }}{\mathrm{\varnothing }}_{ij}(x,y_i,y_j)+\beta \sum _{s\in S}{\psi }_s(x,y_s)\right\}$$

(9)

2.4.1. Unary Potential Function

The unary potential function represents the probability that a single pixel belongs to the changed or unchanged label. It is usually expressed as follows:

$${\phi }_i=lnp(y_i=l|x_i^d)$$

(10)

where $P(y_i\mid x_i^d)$ represents the probability that pixel $i$ is assigned label $l\in \left\{\mathrm{0,1}\right\}$, with label 0 indicating unchanged and label 1 indicating changed. Different methods can be selected according to specific applications and requirements. In this study, FCM is adopted, and the fuzzy membership degrees obtained through iterative calculation are taken as the probabilities of assigning the changed or unchanged label to each pixel.

2.4.2. Pairwise Potential Function

Considering the strong correlation between neighboring pixels of ground objects in remote sensing images, their change labels tend to remain locally consistent. Therefore, in HCRF, a context-sensitive potential function with boundary constraints is adopted as the pairwise potential function. By considering the differences in change intensity between neighboring pixels and the center pixel, this function determines whether the center pixel should be classified as unchanged or changed. The pairwise potential function constructs contextual information between the center pixel and its neighborhood while penalizing excessive smoothing.

$${\mathrm{\varnothing }}_{ij}(x,y_i,y_j)=\left\{\begin{array}{c}1+exp\{-{\displaystyle \frac{{‖x_i^d-x_j^d‖}^2}{2{\sigma }^2}}\}\\ 0,y_i\ne y_j\end{array}\right.,y_i=y_j$$

(11)

where $i$ and $j$ denote a pair of adjacent pixels, and ${\sigma }^2$ is generally estimated as the mean of the squared change-intensity differences between neighboring pixels. If the change-intensity difference between pixels $i$ and $j$ is large, the probability that the two pixels are assigned the same label decreases, which helps suppress excessive smoothing.

2.4.3. Object Potential Function

The pairwise CRF model constrains pixel-level change labels according to neighborhood relationships, but it is limited in preserving the structural completeness of changed areas. To obtain more accurate results, an object potential function is introduced to enforce label consistency among pixels within the same object. It is defined as follows:

$${\psi }_{is}(x^s,y_s)=1+exp\{-{\displaystyle \frac{{(n_c^s-n_{nc}^s)}^2}{{{\sigma }_s}^2}}\}$$

(12)

where $n_c^s$ denotes the total number of changed pixels within the object containing the pixel, and $n_{nc}^s$ denotes the total number of unchanged pixels within the same object. A small value of $\mid n_c^s-n_{nc}^s\mid$ encourages pixels within the object to take the same change label, whereas a large value penalizes the spatial smoothness of the object.

By incorporating the change-label information, the following inference can be further obtained:

$${\psi }_{is}(x^s,y_s)=\left\{\begin{array}{c}0,y_s=0,\\ {\psi }_s(x^s,y_s),y_s=1\end{array},if{n}_c^s\right.>n_{nc}^s$$

(13)

$${\psi }_{is}(x^s,y_s)=\left\{\begin{array}{c}{\psi }_s(x^s,y_s),y_s=0,\\ 0,y_s=1\end{array},if{n}_c^s\right.\le n_{nc}^s$$

(14)

If the number of changed pixels within an object is greater than the number of unchanged pixels, the probability of assigning the changed label to the pixel is increased; otherwise, the probability of assigning the unchanged label is increased. It can also be seen that ${\psi }_{is}(x^s,y_s)$ decreases gradually as $\mid n_c^s-n_{nc}^s\mid$ increases. This suggests that, when the change labels within an object are relatively consistent in the initial change map, the unary potential function is sufficient to describe the change-label tendency of that object. By contrast, when the labels within an object are more heterogeneous, the object term provides stronger guidance for label assignment.

2.5. SEEDSAM

SAM is a vision foundation model for promptable image segmentation, designed to provide a general and flexible solution for image segmentation tasks. Its core idea is to segment arbitrary targets using different forms of prompt information. During the segmentation process, SAM first generates a large number of candidate masks based on the input prompts. The candidate masks are then filtered according to mask quality and stability, and duplicate or highly overlapping masks are removed to produce a set of segmented regions.

The advantages of SAM are mainly reflected in its category-agnostic property and prompt flexibility. SAM can segment different types of targets without relying on specific semantic labels. It also supports multiple forms of prompt information, including points, boxes, and masks, which enables it to be flexibly applied in different task scenarios.

As shown in Figure 4, Unlike methods that segment the original remote sensing images, SEEDSAM uses the centroids of the regions generated by the SEEDS algorithm as point prompts for SAM. Since SEEDS superpixel segmentation can produce region boundaries that better follow the boundary structures in the change intensity map, the resulting region centroids provide more reasonable and representative point prompts for SAM. These prompts better reflect the change intensity distribution of local regions in the change intensity map. Compared with original dense grid point prompts, this strategy reduces the interference caused by prompt points located in noisy areas or on boundaries, thereby helping delineate the boundaries of truly changed areas more clearly. Subsequently, SEEDSAM is applied to conduct object-level segmentation on the change intensity map without semantic category prompts and under a zero-shot setting. This process enhances the constraint imposed by the object potential function on the consistency of change labels within changed areas.

3. Experimental Setup

Section 3.1 introduces the basic characteristics of the datasets used in the experiments, which are used to evaluate the change detection performance of the proposed FRIH-SEEDSAM algorithm and the comparison algorithms. Section 3.2 describes the comparison algorithms in detail, and Section 3.3 presents the experimental design and the evaluation criteria for algorithm performance.

3.1. Datasets

Five publicly available remote sensing change detection datasets were used in the experiments: Shangtang [59], DSIFN [60], SYSU [61], MSRS [62], and CropSCD [63].

The Shangtang dataset is derived from the SenseEarth platform and was released for the “AI View of the World 2020” Artificial Intelligence Remote Sensing Interpretation Competition organized by SenseTime. The images have a spatial resolution of 3 m and a size of 512 × 512 pixels. All images used in the study area have undergone preprocessing, including radiometric correction, geometric correction, and image registration. The study area represents a rural scene, mainly including farmland, buildings, and woodland.

The DSIFN dataset consists of large-scale high-resolution remote sensing image pairs collected from Google Earth. It covers six cities in China, namely Beijing, Chengdu, Shenzhen, Chongqing, Wuhan, and Xi’an. The original large image pairs are cropped into 512 × 512 pixel patches, with a spatial resolution of 2 m. In the selected study area, the main land cover types are buildings, woodland, and farmland, and the changes mainly occur in farmland areas.

The Sun Yat-Sen University (SYSU) dataset was collected in Hong Kong from 2007 to 2014. It contains 20,000 pairs of aerial images, each with a size of 256 × 256 pixels and a spatial resolution of 0.5 m. The dataset includes several typical change types, such as urban construction, suburban expansion, vegetation change, and road widening. The study area selected in this paper is a mountainous forest region, where the main land cover types are forest, wasteland, and roads. The changed areas are mainly distributed in forest regions.

The MSRS dataset contains 841 pairs of remote sensing images acquired in cities of southern China from 2019 to 2023. Each image has a size of 1024 × 1024 pixels and a spatial resolution of 0.5 m. The main land-cover change types include new buildings, suburban expansion, vegetation change, and road construction. The selected study area mainly consists of buildings, farmland, and woodland.

The CropSCD dataset was collected from rural areas in Guangdong Province, China. It contains 4,141 pairs of bi-temporal remote sensing images and covers eight land-use change categories. Each image has a size of 512 × 512 pixels, with a spatial resolution ranging from 0.5 m to 2 m. The study area used in this paper is a rural region mainly composed of wasteland, woodland, and roads, where the changes mainly occur in wasteland areas.

3.2. Comparison Algorithms

In the comparative experiments, six unsupervised change detection algorithms were selected, namely DeepCVA [64], GMCD [65], KPCAMNet [66], CFRL [67], PSONet [48] and PCAKMeans [68].

Among them, PCAKMeans is a traditional unsupervised change detection algorithm. This method first extracts the band values within the h × h neighborhood of each pixel from the difference image of the bi-temporal images to construct feature vectors. After PCA is applied to reduce the dimensionality of the feature vectors, K-means clustering is used to classify the reduced-dimensional features into changed and unchanged classes. DeepCVA, GMCD, KPCAMNet, CFRL and PSONet belong to unsupervised change detection methods based on deep learning. DeepCVA extracts remote sensing image features with a pre-trained convolutional neural network and combines multi-scale deep features into a feature hypervector. It then identifies changed pixels by calculating the magnitude of the deep vector based on pixel-wise differences. GMCD extracts features from bi-temporal images through a Siamese fully convolutional network and generates a difference map. It introduces Mlt-GCN to capture long- and short-range contextual information in the feature map, which improves the discrimination between changed and unchanged areas. KPCAMNet combines KPCA with a convolutional neural network to extract high-dimensional spatial-spectral feature maps from bi-temporal images layer by layer. It maps the feature difference map into a two-dimensional polar coordinate domain, and then performs clustering and threshold segmentation on changed pixels to obtain the final change detection results. CFRL learns commonality feature representations from multimodal bi-temporal images and generates change magnitude images by measuring feature differences in a shared feature space. PSONet adopts a progressive self-optimization strategy for VHR optical remote sensing imagery, gradually optimizing a lightweight change detection network by capturing change signals from weak to strong.

3.3. Experimental Setup and Evaluation Criteria

All experiments were conducted on a computer equipped with an NVIDIA GeForce RTX 4080 SUPER GPU and a 13th Gen Intel Core i7-13700KF 3.40 GHz CPU. The parameter settings of the proposed FRIH-SEEDSAM algorithm and the comparison algorithms were as follows. 1) For FRIH-SEEDSAM, the number of clusters was set to 10, and the fuzziness parameter was set to 3.5. 2) For PCAKMeans, the local neighborhood window size $h$ was set to 10. 3) GMCD, KPCAMNet, CFRL and PSONet adopted the default parameter settings provided in their open-source codes. 4) Since the default settings of DeepCVA showed limited applicability to the datasets used in this study, its feature extraction layers were set to {5, 8, 10}. All parameters were kept consistent across different datasets and noise conditions, and were not adjusted for any individual dataset.

To evaluate the change detection performance of the proposed algorithm and its robustness to Gaussian noise, four groups of experiments were designed: (1) experiments with Gaussian noise of zero mean and a variance of 0.03; (2) experiments with Gaussian noise of zero mean and variances ranging from 0.005 to 0.05 at an interval of 0.005; (3) ablation experiments; and (4) parameter sensitivity experiments.

To evaluate the performance of different change detection methods, several evaluation indicators were used, including missed alarm rate (MA), false alarm rate (FA), overall accuracy (OA), Kappa, recall, and F1. MA and FA indicate the omission of truly changed areas and the misclassification of unchanged areas, respectively. OA represents the overall classification accuracy of the change detection results. Recall is used to measure the detection completeness of truly changed areas. Kappa measures the consistency between the detection results and the ground truth map. The F1 represents the comprehensive accuracy of the change detection results and reflects the ability of the algorithm to balance false detections and missed detections. A comprehensive evaluation using multiple indicators can provide a basis for comparing the performance of different methods.

4. Experimental Analysis

4.1. Noise Robustness Analysis

To evaluate the robustness of the proposed algorithm and the comparison algorithms under Gaussian noise interference, noise interference experiments were conducted in this study. Gaussian noise with a mean of 0 and a variance of 0.03 was added to five groups of study-area images, and the above change detection algorithms were then used for detection. The performance of each algorithm under noise interference was analyzed by comparing detection accuracy. In the evaluation indicator tables, the best result for each indicator is highlighted in bold, and the second-best result is underlined. The experimental results show that the FRIH-SEEDSAM algorithm achieved the best change detection results on multiple datasets, as shown in Figure 5, Figure 7 and Figure 8. Under Gaussian noise interference, the FRIH-SEEDSAM algorithm can effectively suppress missed detections and false detections, showing strong robustness against Gaussian noise.

As shown in Table 1, in the selected study areas of the Shangtang and CropSCD datasets, FRIH-SEEDSAM achieved the best results for all evaluation indicators. In particular, in the selected study area of the CropSCD dataset, the MA was only 0.0042, indicating that the FRIH-SEEDSAM algorithm has a strong ability to detect truly changed areas. This is because, under Gaussian noise contamination, the FRFCM clustering algorithm can preserve the main data distribution characteristics of the images through morphological reconstruction and membership filtering, allowing it to identify changed areas more accurately and reduce the occurrence of false detections and missed detections. As illustrated in Figure 5, in the Shangtang dataset, the DeepCVA algorithm achieved the second-best comprehensive performance. However, obvious false alarm patches appeared in its detection results, causing its Kappa and F1 to be 0.1503 and 0.0856 lower than those of FRIH-SEEDSAM, respectively. As illustrated in Figure 6, in the DSIFN dataset, the changed areas mainly appear as large and continuous regions where farmland is converted into buildings. PCAKMeans can extract the main structural information through principal component analysis while reducing the influence of noise, and therefore obtained the lowest FA of 0.1290, which is 0.0124 lower than that of FRIH-SEEDSAM. CFRL achieved the second-lowest FA. However, due to its relatively high MA, its Kappa was 0.1163 lower than that of PCAKMeans. FRIH-SEEDSAM achieved the best results for all evaluation indicators except FA, with Recall and F1 being 0.1427 and 0.0705 higher than those of PCAKMeans, respectively. By contrast, under noise interference, GMCD, KPCAMNet, and PSONet produced many scattered false detections and missed detections, with F1 reaching only 0.6360, 0.5705, and 0.4024, respectively. In particular, the MA of PSONet was as high as 0.7142, indicating that it suffered from a relatively severe missed detection problem. The experimental data show that FRIH-SEEDSAM performs stably on datasets with a size of 512 × 512, accurately identifies changed areas in bi-temporal images under Gaussian noise interference, and suppresses false detections and missed detections, showing strong resistance to Gaussian noise.

Figure 5. Change detection results on the Shangtang dataset.(a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 5. Change detection results on the Shangtang dataset.(a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 6. Change detection results on the DSIFN dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 6. Change detection results on the DSIFN dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 7. Change detection results on the CropSCD dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 7. Change detection results on the CropSCD dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

As shown in Figure 8, the FRIH-SEEDSAM algorithm achieved the best detection performance on the MSRS dataset, with more complete detected changed areas and relatively fewer missed detections and false detections. Its Kappa and F1 reached 0.8526 and 0.8718, respectively. As shown in Figure 8, the detection results of the other comparison algorithms showed more serious false detections or missed detections. Among the comparison algorithms, CFRL obtained the lowest MA, but its MA was still 0.1902 higher than that of FRIH-SEEDSAM. PCAKMeans obtained the lowest FA; however, obvious missed detection regions appeared in its detection results, which affected its overall detection performance, and its F1 was only 0.7238. These phenomena can be attributed to the larger image size of the study area in the MSRS dataset and its richer land-cover information. Therefore, after Gaussian noise was added, the comparison algorithms had difficulty distinguishing noise from real changes. In contrast, FRIH-SEEDSAM introduces HCRF to further process the change intensity information. By imposing multi-level constraints on change labels at the pixel, neighborhood, and object levels, it effectively improves the accuracy and completeness of the change detection results.

Figure 8. Change detection results on the MSRS dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Figure 8. Change detection results on the MSRS dataset. (a) Time 1 image with noise; (b) Time 2 image with noise; (c) Ground truth; (d) Ours; (e) DeepCVA; (f) GMCD; (g) KPCAMNet; (h) CFRL; (i) PSONet; (j) PCAKMeans.

Table 2. Accuracy of change detection results on the MSRS dataset.

Dataset	Method	Evaluation indicators
		FA	MA	OA	Kappa	Recall	F1
MSRS	Ours	0.2207	0.0107	0.9661	0.8526	0.9893	0.8718
	DeepCVA	0.8354	0.4953	0.6440	0.0881	0.5047	0.2483
	GMCD	0.6049	0.3413	0.8428	0.4077	0.6587	0.4939
	KPCAMNet	0.5130	0.2614	0.8789	0.5195	0.7386	0.5869
	CFRL	0.4708	0.2009	0.8937	0.5774	0.7990	0.6366
	PSONet	0.5796	0.8593	0.8773	0.1618	0.1406	0.2108
	PCAKMeans	0.2453	0.3046	0.9382	0.6891	0.6954	0.7238

Table 2. Accuracy of change detection results on the MSRS dataset.

Dataset	Method	Evaluation indicators
		FA	MA	OA	Kappa	Recall	F1
MSRS	Ours	0.2207	0.0107	0.9661	0.8526	0.9893	0.8718
	DeepCVA	0.8354	0.4953	0.6440	0.0881	0.5047	0.2483
	GMCD	0.6049	0.3413	0.8428	0.4077	0.6587	0.4939
	KPCAMNet	0.5130	0.2614	0.8789	0.5195	0.7386	0.5869
	CFRL	0.4708	0.2009	0.8937	0.5774	0.7990	0.6366
	PSONet	0.5796	0.8593	0.8773	0.1618	0.1406	0.2108
	PCAKMeans	0.2453	0.3046	0.9382	0.6891	0.6954	0.7238

As shown in Figure 9, the changed areas in the selected image from the SYSU dataset are mainly located in forest areas and show irregular shapes, which places higher requirements on algorithm performance. As shown in Table 3, the MA of the FRIH-SEEDSAM algorithm is only 0.0662, while its OA and Kappa reach 0.9155 and 0.8300, respectively. Meanwhile, its Recall and F1 are 0.1357 and 0.0595 higher than those of the corresponding second-best algorithms, CFRL and PCAKMeans, respectively. Since each image in the SYSU dataset is only 256 × 256 pixels, the available spatial contextual information is limited. Under Gaussian noise interference, real change information is more easily affected by background texture and noise. By introducing SEEDSAM segmentation, FRIH-SEEDSAM uses the centroids of the regions obtained from SEEDS superpixel segmentation as point prompts for SAM. This prompt strategy makes the SEEDSAM segmentation results better conform to the local change intensity distribution in the change intensity map, allowing the algorithm to more effectively extract change information from the change intensity map and improve the comprehensive detection performance by imposing object-region constraints.

4.2. Sensitivity Analysis to Gaussian Noise

In this section, noise sensitivity experiments were conducted for FRIH-SEEDSAM and the comparison algorithms, including DeepCVA, GMCD, KPCAMNet, CFRL, PSONet, and PCAKMeans. In the experiments, Gaussian noise with different intensities was added to images from the Shangtang, DSIFN, CropSCD, MSRS, and SYSU datasets. The mean was set to 0, and the variance ranged from 0.005 to 0.05 with a step size of 0.005. By comparing the changes in detection accuracy under different Gaussian noise intensities, the performance of each algorithm was further evaluated.

As shown in Figure 10, with the increase in Gaussian noise intensity, the FRIH-SEEDSAM algorithm consistently maintained stable change detection performance. Its Kappa remained at 0.8 or above on multiple datasets, showing strong robustness against Gaussian noise. The comparison algorithms showed different advantages and disadvantages on different datasets, but their overall performance was inferior to that of FRIH-SEEDSAM.

The Kappa values of DeepCVA and PSONet showed large fluctuations on some datasets and generally tended to decrease as the Gaussian noise variance increased. As presented in Table 4, in the CropSCD dataset, when the Gaussian noise variance was 0.005, DeepCVA reached a Kappa of 0.8920, which differed from FRIH-SEEDSAM by only 0.0012. However, when the Gaussian noise variance increased to 0.015, its Kappa dropped to 0.6552, and the difference from FRIH-SEEDSAM increased to 0.2315. In the SYSU dataset, PSONet achieved Kappa values of 0.7058 and 0.6912 at Gaussian noise variances of 0.015 and 0.025, respectively, with a difference of only 0.0146. However, when the Gaussian noise variance was 0.02, its Kappa sharply decreased to 0.3517, indicating that PSONet is sensitive to Gaussian noise interference. KPCAMNet also showed unsatisfactory accuracy on multiple datasets, with its Kappa exceeding 0.5 only on the MSRS dataset. As the Gaussian noise variance increased, the noise influence in the images was further amplified, which instead reduced the detection of some weak non-real change regions by KPCAMNet. As a result, its FA decreased from 0.5914 to 0.4957 with increasing Gaussian noise intensity, but this cannot be regarded as evidence that the detection performance of KPCAMNet improved.

The Kappa values of CFRL on the DSIFN, CropSCD, and SYSU datasets show a relatively flat trend as the Gaussian noise variance increases. However, on the Shangtang and MSRS datasets, its Kappa values fluctuate more markedly, indicating that the detection stability of CFRL is influenced to some extent by dataset characteristics. In contrast, the Kappa of GMCD and PCAKMeans was generally stable across all datasets. On the Shangtang dataset, the Kappa of the two algorithms was relatively close, with a minimum difference of only 0.0003. When the Gaussian noise variance increased to 0.05, the accuracy of PCAKMeans declined to some extent due to the influence of noise, and its Kappa was 0.0629 lower than that of GMCD. However, on images from the other datasets, PCAKMeans performed significantly better than GMCD overall. In particular, on the CropSCD dataset, the average Kappa of PCAKMeans was 0.4842 higher than that of GMCD. This is because the images in the CropSCD dataset contain certain brightness differences, causing GMCD to easily misidentify texture details and brightness interference as changed areas, which greatly affected the accuracy of the detection results.

The experimental data show that all comparison algorithms exhibited certain limitations in the noise sensitivity experiments. In contrast, in the Gaussian-noise-robust change detection task, FRIH-SEEDSAM obtains stable change intensity information by combining FRFCM and IRM, and further introduces HCRF and SEEDSAM to impose multi-level constraints on the change intensity information. This enables FRIH-SEEDSAM to identify truly changed areas effectively even when the Gaussian noise intensity increases, while suppressing false detections and missed detections caused by Gaussian noise. FRIH-SEEDSAM maintained high and stable Kappa on all five datasets, indicating that it has stronger robustness under varying Gaussian noise intensities.

4.3. Ablation Experiments

To explore the contribution of each functional module in the FRIH-SEEDSAM algorithm to change detection performance, this section removes or replaces the FRFCM, HCRF, and SEEDSAM components of FRIH-SEEDSAM, and constructs the following models:

(A1) the complete change detection model.

(A2) the SEEDSAM segmentation method in the complete change detection model is replaced with Simple Linear Iterative Clustering (SLIC) [69] algorithm .

(A3) based on the complete change detection model, the HCRF is replaced with a pairwise CRF.

(A4) the HCRF component is removed from the complete change detection model.

(A5) based on the complete change detection model, FRFCM is replaced with standard FCM.

(A6) based on A5, the SEEDSAM segmentation method is replaced with SLIC algorithm.

(A7) based on A5, the HCRF is replaced with a pairwise CRF.

(A8) based on A5, the HCRF component is removed.

The Shangtang dataset images with Gaussian noise of zero mean and a variance of 0.03 were used as the study area. Algorithms A1–A8 were used to validate the effectiveness of each module in FRIH-SEEDSAM. The fixed parameter settings of FCM and FRFCM were kept consistent, with the fuzziness set to 3.5 and the number of clusters set to 10. The weights of the potential functions in CRF and HCRF were searched within the range of [0, 1], and the weight combination with the best performance was used in the ablation experiments.

As shown in Figure 11 and Table 5, the complete model A1 achieved the best results for OA, Kappa, and F1, while the other evaluation indicators were also the second-best, indicating that FRIH-SEEDSAM achieved the best comprehensive change detection performance. Due to the different clustering methods, the two groups of models, A1–A4 and A5–A8, showed obvious differences in the detection results. For example, A8 showed obvious false detections, whereas A4, which only replaced FCM with FRFCM, effectively reduced false positive patches in the detection results and significantly improved OA, Kappa, and F1. In particular, its Kappa was 0.3040 higher than that of A8. The experiments demonstrate that, compared with traditional FCM, FRFCM can suppress the interference of noise with images to a certain extent through morphological reconstruction and membership filtering, and can obtain more stable change intensity information.

A7 builds upon A8 by adding a pairwise CRF. By incorporating neighborhood information to suppress the influence of image noise, its detection accuracy is significantly improved. A6 further introduces an object potential function into the pairwise CRF to form an HCRF, and uses SLIC algorithm to segment the change intensity map. Although the improvement of A6 over A7 is not significant, its Kappa and F1 are still 0.2005 and 0.0831 higher than those of A8, respectively. This indicates that introducing HCRF can optimize the change detection results by incorporating neighborhood information and adding object constraints. However, constructing the object potential function based on SLIC superpixel segmentation provides only limited improvement in detection accuracy.

To analyze the improvement in detection accuracy brought by SEEDSAM segmentation, we also compare two groups of models, A1–A2 and A5–A6. It can be observed that A1 shows only a slight improvement over A2 in all evaluation indicators. This is because FRFCM-IRM has already detected the main changed areas, leaving limited room for further accuracy improvement. In contrast, the comparison between A5 and A6 better reflects the superiority of SEEDSAM segmentation over SLIC superpixel segmentation. A5 uses the centroids of the regions obtained from SEEDS superpixel segmentation as point prompts for SAM, and calculates the object potential function based on the SEEDSAM segmentation results, which effectively suppresses false detections. Its Kappa and F1 are 0.0779 and 0.0373 higher than those of A6, respectively. The experimental results show that SEEDSAM segmentation can better extract changed areas from the change intensity map and provide clearer object information. However, SEEDSAM segmentation is also relatively dependent on the quality of the change intensity map. If the change intensity of the truly changed areas is weak, its improvement in detection accuracy may be limited.

In summary, each module of the FRIH-SEEDSAM algorithm plays a positive role in the change detection task. After removing or replacing any part of FRFCM, HCRF, or SEEDSAM, the detection accuracy decreases to a certain extent. FRIH-SEEDSAM achieves the best or second-best results for all evaluation indicators and shows the highest comprehensive detection accuracy. The experimental results indicate that the noise-resistant clustering of FRFCM, the spatial constraints of HCRF, and the SEEDSAM segmentation work together to improve the accuracy and stability of the change detection algorithm.

4.4. Parameter Sensitivity Analysis

Considering that the performance of HCRF is relatively dependent on the weights of the potential functions, Gaussian noise with a mean of 0 and a variance of 0.03 was added to the five datasets to analyze the influence of each potential function weight on the accuracy of the change detection results. The locally optimal parameters obtained through pattern search [70] were used as the reference. Using the control variable method, the weights of the unary potential function, pairwise potential function, and object potential function were sequentially set from 0 to 1 with a step size of 0.1. When one weight was changed, the remaining weights were kept at their local optima, and the influence of each weight on the detection results was observed. To highlight the influence of the weights on the detection results, no post-processing operation was used in this section, so as to avoid eliminating the differences between different weight settings.

The unary potential function is mainly used to describe the correspondence between pixel features and change labels. As shown in Figure 12, on the Shangtang and DSIFN datasets, changes in the weight of the unary potential function have little influence on Kappa, and the accuracy curve shows a relatively flat trend. This is because the detection results of the selected images from these two datasets rely more on neighborhood information and object-level constraints, so changes in the weight of the unary potential function have little influence on the determination of change labels. The Kappa of the detection results on the MSRS and SYSU datasets decreases to different degrees as the weight of the unary potential function increases. This is because the change intensity map is affected by Gaussian noise, which reduces the reliability of pixel-level change intensity information. As shown in Table 6, when the weight is in the range of 0–0.8, the Kappa of the detection results on the CropSCD dataset remains unchanged. However, when the weight continues to increase and approaches 1, Kappa sharply drops to 0.5700. This indicates that, when pixel-level change intensity information is overly relied on, Gaussian noise interference is easily identified as real change information, resulting in obvious false detections in the detection results. The above phenomena indicate that, under Gaussian noise interference, relying only on pixel features is unreliable, and neighborhood information and object-level constraints need to be introduced to improve robustness.

Compared with the unary potential function, changes in the weight of the pairwise potential function have a more obvious influence on Kappa. The pairwise potential function is mainly used to describe the relationship between the change labels of neighboring pixels. When the change intensities of adjacent pixels are similar, it enhances the consistency of change labels and can suppress noise to a certain extent. When the weight of the pairwise potential function is small, the constraint ability of spatial neighborhood information is weak. Therefore, as the weight increases, Kappa improves to a certain extent. However, when the weight of the pairwise potential function exceed certain threshold, the true boundaries of ground objects are smoothed because the consistency of change labels among neighboring pixels is overemphasized. As the weight of the pairwise potential function increases, the Kappa of the detection results on the Shangtang, DSIFN, and SYSU datasets first increases and then decreases, indicating that appropriate neighborhood constraints can suppress local noise interference. On the MSRS and CropSCD datasets, when the weight of the pairwise potential function is high, some noise-affected regions are assimilated into changed labels by neighboring real change information because the consistency of change labels among neighboring pixels is overemphasized, resulting in relatively serious false detections. The experimental results show that weights of the pairwise potential function that are too high or too low lead to obvious missed detections and false detections in the change detection results. Therefore, an appropriate weight range should be selected according to different images to balance boundary preservation and noise suppression.

In the sensitivity analysis of the object potential function weight, the detection accuracy on all dataset images shows an increasing trend as the weight of the object potential function increases. This trend is particularly evident on the MSRS and CropSCD datasets, where Kappa increases from 0.5400 and 0.6195 to 0.8641 and 0.8908, respectively. This indicates that the object potential function can enhance the internal consistency of changed areas, reduce fragmented false detections caused by noise contamination, and improve the detection accuracy of large changed areas. Under Gaussian noise conditions, the object potential function can suppress noisy regions by considering the overall change labels of segmented objects. However, when the segmentation quality of the change intensity map under noise interference is poor, real change information and unchanged information may coexist within the same segmented object. In this case, coordination between the unary and pairwise potential functions is required.

The overall experimental results show that the unary potential function, pairwise potential function, and object potential function play mutual complementary roles in HCRF. Specifically, the unary potential function focuses on the pixel’s own features, the pairwise potential function incorporates neighborhood information, and the object potential function enhances the consistency of change labels within objects. A reasonable combination of weights can jointly consider the above information, improving the completeness of change detection results and the ability to preserve boundaries while reducing missed detections and false detections.

5. Conclusions

To address the interference of Gaussian noise in remote sensing change detection, we propose FRIH-SEEDSAM, an unsupervised Gaussian-noise-robust change detection algorithm. The proposed method generates a pixel-level change intensity map through FRFCM-IRM, uses SEEDS-based superpixel centroids as point prompts for SAM segmentation, and constructs the potential function in HCRF from the SEEDSAM segmentation results. The HCRF potential functions jointly constrain pixel-level change labels, improving the change detection performance of FRIH-SEEDSAM under Gaussian noise conditions. Experimental results show that FRIH-SEEDSAM maintains relatively stable detection performance across different dataset images and Gaussian noise intensities. When the variance of Gaussian noise increases to 0.05, the algorithm can still maintain Kappa of 0.8 or above on multiple datasets. Compared with the competitive algorithms, the proposed method is more effective in identifying truly changed areas and suppressing missed detections and false detections caused by Gaussian noise. The ablation experiments show that FRFCM, HCRF, and SEEDSAM all yield positive contribution to change detection accuracy, confirming the effectiveness of the algorithmic framework.

However, the proposed algorithm still has some limitations. On the one hand, the SEEDSAM segmentation results are affected by the change intensity map. When the difference information within truly changed areas is not obvious, the constraint effect of the object potential function on change labels may be limited. On the other hand, the weights of the potential functions in HCRF still require parameter search, and the adaptability of the method can be further improved. Future work can focus on enhancing change intensity information and improving the adaptive adjustment of potential function weights, so as to further improve the generalization ability of the algorithm.