Multiresolution-Based Rough Fuzzy Possibilistic -Means Clustering Method for Land Cover Change Detection

Object-oriented change detection (OOCD) plays an important role in remote sensing change detection. Generally, most of current OOCD methods adopt the highest predicted probability to determine whether objects have changes. However, it ignores the fact that only parts of an object have changes, which will generate the uncertain classification information. To reduce the classification uncertainty, an improved rough-fuzzy possibilistic $c$-means clustering algorithm combined with multiresolution scales information (MRFPCM) is proposed. First, stacked bitemporal images are segmented using the multiresolution segmentation approach from coarse to fine scale. Second, objects at the coarsest scale are classified into changed, unchanged, and uncertain categories by the proposed MRFPCM. Third, all the changed and unchanged objects in previous scales are combined as training samples to classify the uncertain objects into new changed, unchanged, and uncertain objects. Finally, segmented objects are classified layer by layer based on the MRFPCM until there are no uncertain objects. The MRFPCM method is validated on three datasets with different land change complexity and compared with five widely used change detection methods. The experimental results demonstrate the effectiveness and stability of the proposed approach.

geographical phenomenon by observing it at different times [1], [2]. LCCD plays an essential role in many fields, such as disaster monitoring [3], environmental protection [4], and earth resource management [5]. It has become one of the most popular applications of remote sensing technology. With the development of satellite technology, there is an increasing number of studies, which use remote sensing images (RSIs) to obtain and monitor land cover change information on the surface of the Earth [6], [7], [8], [9], [10].
Although the increased spatial resolution of RSIs has provided a more convenient and detailed source of data, it has also brought a significant challenge for the traditional pixel-based change detection (PBCD) approach [11]. PBCD approach can obtain "salt and pepper" noise in change detection (CD) maps [12] and results with poor accuracy [13], [14] in RSIs of high-spatial resolution. To overcome the drawback, CD approaches considering spatial information are proposed. Spatial contextual information extraction-based pixel [15], [16] and object-oriented approaches [17], [18] are effective to extract spatial information for RSIs.
The pixel methods based on spatial contextual information use an image block [15], network structure [19], and Markov random field model [20], etc. to obtain spatial information about the pixel context. For instance, Celik [8] proposed the PCA-Kmeans method, which uses "h × h" image block to explore the spatial contextual information and reduce the noise of CD results. Deep learning-based unsupervised methods, such as MAU-Net [21], GDCN [22], and FDCNN-based CD approach [19] use convolutional network structure to extract the pixel neighborhood information and obtain the change information of the Earth's surface. Lv et al. [23] proposed the hybrid conditional random field to model the spatial information and achieved great CD results. However, it is still a difficult task to detect changes in clarifying the boundaries among different geographic objects [24], which can cause the over-smoothing problem [25].
The object-oriented change detection (OOCD) methods adopt geographic objects as the basic processing unit, which can alleviate the abovementioned problems effectively due to their rich spectrum, shape, spatial, and texture information. Image segmentation plays an essential role in the performance of the OOCD method. Image segmentation aims to obtain "common objects" between bitemporal RSIs in OOCD. Due to the scale effect of RSIs, most of image segmentation algorithms, such as mean shift [26], multiresolution segmentation [27], and fractal This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ net evolution approach [28] acquire geographic objects at a specified scale. Many studies focused on how to find the best scale in segmentation by comparing the CD results with different scale parameters [29], [30], [31] or by using the existing segmentation evaluation index [32]. Nevertheless, the single-scale information greatly limits the generalization ability of the CD algorithm, particularly in RSIs with complex changes and significant differences in feature size scales. Therefore, CD methods combining feature information from different scales are developed, which could break the abovementioned limitation and improve CD accuracy [33], [34].
After image segmentation, classifiers are employed to classify objects into changed and unchanged categories. Classification methods usually have two branches in unsupervised methods: threshold and clustering methods. Threshold methods, such as maximum entropy thresholding [35], fuzzy thresholding [36], and OTSU [37] obtain changed and unchanged feature objects by automatically dividing thresholds [38], [39]. Meanwhile, clustering approaches including K-means [40], fuzzy c-means [41], and Gaussian mixture model [42] acquire changed and unchanged clusters by calculating the proximity of distances [43]. However, the category with the highest predicted probability is regarded as the final category in the abovementioned approaches, which can introduce uncertainties when the predicted probabilities of the changed and unchanged are close [44]. For instance, P c and P u represent the probability of an object belonging to changed and unchanged, respectively (P c is greater than P u ). If the difference between P c and P u is significant, it is reasonable to determine the geographic object as changed. However, it is likely that only parts of the object have changed while P c is pretty close to P u .
To address the aforementioned problems, this article proposes an improved multiresolution-based on rough fuzzy possibilistic c-means clustering approach (MRFPCM) to reduce the classification uncertainty layer by layer. A state-of-the-art change characteristics extraction method, key point vector distance (KPVD) [24], is employed to measure the change magnitude between the pairwise objects. Then, MRFPCM is applied in three pairs of RSIs with different change complexity to test the stability and reliability of the algorithm. In the end, five widely used CD methods, namely, CVA [45], MAD [46], PCA-Kmeans [8], SFA [47], and KPVD-based [24] are compared with the proposed method to evaluate its feasibility.
The rest of this article is organized as follows. Section II provides a comprehensive description of the proposed MRFPCM method. Section III presents the experiments and analysis. Some discussions on the proposed method are presented in Section IV. Finally, Section V concludes this article.

II. METHODOLOGY
The proposed method integrates the information from multiple scales and employs the improved rough fuzzy possibilistic c-means clustering (MRFPCM) approach to reduce the classification uncertainty layer by layer. As shown in Fig. 1, the proposed MRFPCM approach comprises the following steps.
1) Select a series of scale parameters from coarse to fine. Stacked bitemporal images are segmented to generate "common objects" at the coarsest scale. 2) KPVD is used to measure the change magnitude between bitemporal objects. Then, the improved RFPCM (MRFPCM) approach classifies bitemporal objects into changed, unchanged, and uncertain objects based on change magnitudes. 3) The uncertainty objects are segmented at a fine scale. The MRFPCM approach recalculates the change magnitude centers (CMCs) of the changed and unchanged from the objects at the previous scales as the training data and classifies the uncertain objects into changed, unchanged, and uncertain objects. The changed and unchanged objects at the fine scale would be combined with the changed and unchanged objects at all the previous scales to generate new CMCs of changed objects at a finer scale.

4)
Step 3) is repeated until all the uncertain objects are classified into changed and unchanged categories. 5) Integrate all the changed and unchanged objects from the different scales to generate the CD results.

A. Multiresolution Segmentation Method
Image segmentation is the process of converting RSIs into discrete regions or objects with uniform spatial or spectral characteristics [27], [29]. Due to the complexity of the geographic objects, it is difficult to describe them at a specific scale and a single image in bitemporal images. To generate the "common objects" at different scales, the multiresolution segmentation method in eCongnition 9.0 is applied in this article. The multiresolution segmentation method has the following advantages: 1) it can generate different objects using the scale parameter, which is essential to control the internal (spectral) heterogeneity of objects; 2) it can use the stacked bitemporal image information as the image layer weights parameters [28], [48], [49]. In order to achieve the spectral and shape features of geographical objects in different periods, two RSIs in different periods are combined into one stacked bitemporal image. Subsequently, the stacked bitemporal image information is segmented into "common objects" from different scales by the multiresolution segmentation method.

B. Key Point Vector Distance (KPVD)
To describe the discrete and biased characteristics of the spectral values within an object in RSIs, the key point vectors (KPVs) of an object is generated by employing a set of interest pixels to characterize the characteristics of an object instead of considering all its pixels [24]. The steps for obtaining the key points are as follows. First, the spectral values of an object in a specific band are sorted from smallest to largest, denoted as set A. Second, five points including the minimum, lower quartile, median, upper quartile, and maximum values in set A are selected, which are represented as k 0 , k 1 , k 2 , k 3 , and k 4 , respectively.
Based on the selection of KPV, the KPVD can be calculated as follows: where Δd i is the change magnitude of the object i from t 1 to t 2 ; m is the number of spectral bands in one of the bitemporal images; l indicates a specific band in the image; j represents the jth element within a KPV; 1 indicates KPVD between two objects in the l-band and 1 2 ||k t 1 j (l) − k t 2 j (l)|| represents the distance between two objects using the jth KPV element in the l-band.

C. Rough Fuzzy Possibilistic C-Means Clustering Algorithm (RFPCM)
The RFPCM method introduces rough-set theory based on the possibilistic C-means (PCM) method [50]. The rough sets theory was proposed by Pawlak [51], and it could deal with uncertainty in class definition of CD. Let a pair < U, R > be an approximation space, where U = {u 1 , . . . u j , . . . u n } is the set of n objects, and R is an equivalence relation on U . Let U/R represents the quotient set of U by the equivalence relation R, For an equivalence class X, the lower and upper approximations (R(X) and R(X)) are defined as follows: Based on the concept of lower and upper approximations, the positive, negative, and boundary regions of X for the equivalence relation R (POS R (X), NEG R (X), and BND R (X)) are defined as follows: The concept of positive, negative, and boundary regions can solve the uncertainty of the classification in the CD based on RSIs. As shown in Fig. 2, the positive region indicates that there is high confidence that the objects are changed; conversely, the negative region means that objects are likely to be unchanged; and the boundary region represents that it is uncertain to determine whether objects are changed or unchanged. Based on the positive, negative, and boundary regions, the RFPCM algorithm divides U into c clusters by minimizing the objective function where ω is the relative importance of lower approximation region; m 1 and m 2 indicate the fuzzifiers (generally, m 1 = m 2 = 2); a and b are the constants which represent the relative importance of probabilistic membership μ ij and possibilistic membership υ ij . Therefore, the following equations can be obtained: where η i represents the zone of influence of cluster X; υ i indicates the center of the cluster. The calculations are as follows: where C 1 and D 1 indicate changed and unchanged regions, which are defined as follows: The key to solving (8) is to determine whether x j belongs to R(X) or R(X). Classical RFPCM used a fixed threshold threshold to classify the objects into two categories: changed, unchanged, and uncertainty. μ c and μ u are the memberships of an object belonging to the changed and unchanged categories. If (μ c − μ u ) is greater than a threshold T , the object belongs to the changed categories; if (μ u − μ c ) is greater than T , the object belongs to the unchanged categories; otherwise, it belongs to the uncertain categories.

D. Multiresolution-Based Rough Fuzzy Possibilistic C-Means Clustering Algorithm (MRFPCM)
The above RFPCM method applies to the PBCD method but does not extend it to the OOCD method. Inspired by the RFPCM method and the uncertainty-refining strategy layer by layer [33], an improved RFPCM approach combined with multiresolution information (MRFPCM) is proposed to reduce the classification uncertainty in the OOCD method.
In image segmentation, there exist some incompletely segmented objects, which can make it difficult to determine whether they are changed or not. As shown in Fig. 3, there are three hypothetical cases with two images in T 1 and T 2 : case A), the tiny object on the right side has not changed; case B), only one tiny object on the right has changed; case C), the tiny object on the right side has changed. Two images are segmented at a specific scale to obtain the common object, the results in the tiny object on the right side of the image not being completely segmented. α 1 , α 2 , and α 3 represent change magnitude of three objects between two periods. According to the real change of the ground surface, we assume α 1 ≈ α 3 < α 2 in case A), α 1 < α 3 < α 2 in case B), and α 1 < α 2 ≈ α 3 in case C). Most of the classification methods can accurately classify in cases A) and C). However, it is difficult to classify the images in case B) based on the predicted probabilities due to the partial change in the geographical object.
To overcome the drawback, a shrinkable threshold variable and the uncertainty-refining strategy layer by layer are introduced into the RFPCM method. The improved RFPCM approach adopts a shrinkable threshold variable to classify the image into the following three categories: changed, unchanged, and uncertainty. The threshold will gradually decay as segmentation scales decrease. Then, the uncertainty will be reclassified into three categories at a fine scale. To integrate the multiresolution information, the CMCs of the changed and unchanged will be recalculated based on the previous changed and unchanged objects. By this improved method, the objects of the case B) with the change magnitude α 1 and α 2 will be classified into the changed and unchanged categories, while the object with α 3 into the uncertain category. Additionally, in case A), the objects with α 1 and α 3 will be determined as the unchanged category, and the object with α 2 will be classified into the changed category by this method. In case C), the improved MRFPCM approach will classify the object where the value of α 2 and α 3 into the changed category.
1) Shrinkable Membership Threshold: The improved RF-PCM approach uses a membership threshold to indicate that objects have great confidence in being classified as changed categories. At the coarsest scale, an initial threshold is set to classify objects as changed, unchanged, and uncertain categories. Then, the uncertain objects will be segmented into tiny objects, and the tiny objects will be continuously classified as new changed, unchanged, and uncertain categories. In this classification, if the initial threshold is not changed, there will always be uncertain objects no matter how many times doing segmented. Therefore, a threshold decay strategy is set to remove the uncertain categories at a special scale. The formula for threshold classification and decay is as follows: where n and i represent the nth segmentation and the ith object, respectively; μ ic_n is the membership of the ith object belonging to the change category in the nth segmentation; n denotes the threshold value of the nth segmentation, denotes the initial threshold; η is the fuzzy reduction factor. While n is equal to 0.5, all the objects will be divided into changed and unchanged classes. There are two cases where n is equal to 0.5: natural decay to 0.5 and segmentation to the finest scale. For the second case, although n is greater than 0.5, there is no finer scale information. Therefore, to classify all objects into changed and unchanged categories, n is changed to 0.5.

2) CMCs Based on Multiresolution Information:
To describe the CMCs comprehensively, the information at different scales should be integrated. Therefore, we combine the changed and unchanged objects at the current scale and all the previous scales. Subsequently, the CMCs of the changed and unchanged classes at a finer scale are calculated based on the integrated changed and unchanged objects. By (15), new changed and unchanged objects are classified based on the calculated CMCs of the changed and unchanged classes. The calculations are defined as follows: where v n_c_mean and v n_unc_mean are the CMCs of all changed and unchanged objects after nth segmentation, respectively; m is the number of all changed objects after (n − 1)th segmentation; v n_c and v n_unc are the CMCs of changed and unchanged objects at the nth segmentation scale, respectively; n is the number of changed objects at nth segmentation scale; p represents the number of all unchanged objects after (n − 1)th segmentation; q represents the number of unchanged objects at nth segmentation scale.

E. Evaluation Indicators
To evaluate the accuracy of the proposed MRFPCM, four popular evaluation indicators, including false alarm (FA), missed alarm (MA), total error (TE), and binary classification Kappa coefficient (Ka) are employed [15]. The calculation equations are as follows: where the true positive (TP) and false negative (FN) indicate that the detected results are actually changed and unchanged in the real case that the pixel is changed, respectively; the true negative (TN) and false positive (FP) represent that the detected results are actually unchanged and changed in the real case that the pixel is unchanged, respectively; k 1 = TP + FP, k 2 = FP + TN, k 3 = TP + FN, k 4 = FN + TN. In addition, FA denotes the ratio between the number of incorrectly identified change pixels in the CD map and the ground reference map; MA means the ratio between the number of missing change pixels in the CD map and the ground reference map; TE demonstrates the ratio of the total number of FA and missing detections to the total number of pixels in the ground reference map; Ka measures the internal reliability of the qualitative items of detection results with a threshold value between 0 and 1.

A. Data Description
As shown in Fig. 4, three pairs of RSIs with different levels of change complexity are used to verify the reliability and stability of the proposed method. Dataset I includes two Landsat 7 images with 400 × 400 pixels, which were acquired in Liaoning Province in August 2001 and August 2002, respectively. The spatial resolution of the bitemporal images was 30 m/pixel, and the changed lands are farmland, which means that the changes in dataset I are relatively homogeneous and straightforward. The datasets II and III with a high-spatial resolution of 0.5 m/pixel In addition, the ground reference map of each dataset was manually interpreted in ArcGIS 10.6 software.

B. Experimental Setup
Five LCCD approaches, including a traditional pixel-based approach, three kinds of change magnitude description or spatial context enhanced pixel-based approaches, and one widely used object-oriented approaches, namely, CVA [45], MAD [52], PCA-Kmeans [8], SFA [47], and KPVD-based [24] are compared with the proposed MRFPCM approach to evaluate its effectiveness.
In the parameters setting of image segmentation, the bands used for the three datasets are red, green, and blue bands, and the weight of each band layer was 1. In addition, the shape and compactness indices are set to 0.1 and 0.5 for all the datasets, respectively; the scale parameters for the KPVD-based approach are 10, 50, and 30 for datasets I, II, and III, respectively. According to the sensitivity analysis, the coarsest segmentation scales for the three datasets are 10, 50, and 30, and the initial membership thresholds are set to 0.90, 0.70, and 0.85 in the proposed MRFPCM, respectively. The finest scales for datasets I, II, and III are set to 5, 20, and 20 based on the complexity  Fig. 5. By comparing the visual results of the PBCD methods, the results based on CVA, SFA, and PCA-Kmeans contain less "salt-and-pepper" noise and a large amount of pretzel noise exists in the CD results based on MAD due to the low resolution of the dataset. Moreover, PCA-Kmeans performs poorly in the classification of large objects. For example, the actual change areas in the red boxes in Fig. 5(d) are larger than the detection results. The KPVD-based and MRFPCM approaches achieve an outstanding performance on removing "salt-and-pepper" noise because their basic analysis unit is a geographic object. Additionally, due to considering the uncertainty in classification, MRFPCM performs better than the KPVD-based method in small objects classification (e.g., the results in the red boxes), which also proved the feasibility of the hypothesis in Fig. 3. Table I shows the quantitative evaluation of the results achieved based on dataset I. The results show that the MRF-PCM has a performance second only to the CVA in the images with a low spatial resolution. Moreover, the OBCD approaches (KPVD-based and MRFPCM) perform better than the other PBCD approaches in general. Specifically, the MA, and TE for MRFPCM are only 0.755%, and 0.153% higher than the CVA, respectively, and are lower than the SFA (1.542% and 1.300%,  respectively), MAD (1.118% and 9.121%, respectively), PCA-Kmeans (7.095% and 6.416%, respectively), and KPVD-based approaches (0.600% and 0.401%, respectively). The KA for MRFPCM are improved by 0.051, 0.246, 0.291, and 0.016 over the SFA, MAD, PCA-Kmeans, and KPVD-based methods, respectively, and is only reduced by 0.009 over the CVA. As the proposed MRFPCM approach considers contextual information and classification uncertainty, it performs better than most PBCD approaches and the other OOCD method (KPVD-based method).
2) Datasets II and III: For complex datasets II and III, the CD results are shown in Figs. 6 and 7, respectively. It can be found that CVA, SFA, and MAD perform poorly in datasets II and III due to the absence of contextual information, especially for CVA. Since PCA-Kmeans considers the pixel neighborhood relationship within the "h × h" block, and the KPVD-based and MRFPCM methods take the object as the unit of analysis, they have an excellent performance on removing "salt-and-pepper" noise. In addition, the OOCD methods (MRFPCM and KPVDbased) perform almost the same in the CD of large objects. The differences between the MRFPCM and KPVD-based approaches exist in the classification results of small objects. From   TABLE II  COMPARISON BETWEEN OTHER METHODS AND THE PROPOSED MRFPCM  APPROACH FOR DATASET II; THE ACCURACIES OF FA, MA, AND TE ARE  PRESENTED IN PERCENTAGE (%), AND KA IS RANGED FROM 0 TO 1   TABLE III  Based on the abovementioned experimental analysis and comparison, the MRFPCM method maintains a more stable accuracy than the PBCD methods in detecting land changes with different complexities. Meanwhile, it can extract the land changes better than the other OOCD method (KPVD-based) because the MRF-PCM method takes into account the classification uncertainty.

A. Sensitivity of Different Coarsest Scales and Initial Thresholds on the Proposed MRFPCM Method
To test the sensitivity of different parameter settings, this section explores the relationship between the coarsest scale, initial threshold, and CD accuracy (FA, MA, TE, and Ka) in  IV  PARAMETERS SETTINGS WITH THE PROPOSED MRFPCM METHOD FOR  DATASET I   TABLE V  PARAMETERS SETTINGS WITH THE PROPOSED MRFPCM METHOD FOR  DATASET II datasets I, II, and III. For simple and complex datasets, the coarsest segmentation scale ranges are set from 10 to 40, and 30 to 60, respectively, and the scale increases in steps of 10. Initial thresholds are set from 0.70 to 0.90, and other basic parameters are the same as described in Section III. As shown in Tables IV, V, and VI, the setting of the coarsest scale plays an important role in the CD for datasets I, II, and III. In the test for dataset I, the lowest Ka is 0.812 when the coarsest scales are 10 and 20, while the highest Ka is 0.770 when the coarsest scales are 30 and 40. For datasets II and III, the MRFPCM method achieves the best result with the coarsest segmentation scales of 50 and 30, respectively. Therefore, it is necessary to detect a sensible coarsest segmentation before the CD based on the proposed MRFPCM is performed in the RSIs. When the selected coarsest scale is too large, a large amount of partial changed objects can be generated in the segmentation process, which will increase the uncertainties in classification and lead to a low CD. In addition, the CD results are better when the coarsest scale is small in the RSIs with a low resolution and complex land changes compared with the ones with a higher resolution and simple land changes. The best performance in the datasets I and III is achieved with the coarsest scale of 10 and 30, respectively, which are the finest scales in the tests.
To explore the effect of the initial threshold on the results, the results based on the different initial thresholds are presented in Figs. 8-10 corresponding to the datasets I, II, and III, respectively. For dataset I, at the same coarsest scale, FA, MA, and TE show a gradually decreasing trend with the increase of the initial membership threshold, while the results of Ka have an increasing trend. The reason might be that the classification for the changed and unchanged categories is stricter as the initial threshold increases, which would produce more accurate classification information at the coarsest scale. However, the performance of the MRFPC has a peak when dataset I is segmented at the coarsest scale of 20. Although more accurate classification information is produced when the initial threshold value is larger, it would lead to a decrease in the number of changed and unchanged training samples, which will make the CD accuracy decrease. There are similar situations in datasets II and III (e.g., the coarsest scales are 30 and 40 in dataset II and the coarsest scales are 40, 50, and 60).

B. Comparison of the KPVD-Based Method and Proposed MRFPCM Method With Different Parameters
The proposed MRFPCM method is improved based on the KPVD-based method by the classifier. The superiority of the two algorithms is compared in the case that the coarsest scale of the MRFPCM method was the same as that of the KPVDbased method. The results of different scale parameters with the KPVD-based method are shown in Figs. 11-13 and the results   Tables IV-VI,  respectively. For dataset I, the Ka of the MRFPCM approach is generally higher than the KPVD-based approach in the cases with the same coarsest scale. In addition, the FA, MA, and TE of the MRFPCM approach are mostly lower than the KPVD-based approach. The CD results in dataset I demonstrate that the proposed MRFPCM has a better performance than the KPVD-based method in the RSIs with a low resolution. For dataset II, with the coarsest scale of 40, the performance of the KPVD-based method is better than the MRFPCM method by a small margin. On other scales, the performance of the MRFPCM method is better than the KPVDbased method. For dataset III, the Ka of the MRFPCM method is higher than the KPVD-based method overall. Meanwhile, the FA, MA, and TE of the MRFPCM method also achieve better results than the KPVD-based method in the dataset. Based on the abovementioned comparison, the MRFPCM method generally performed better with the same coarsest scale.

V. CONCLUSION
To reduce the classification uncertainty in CD based on RSIs, this article proposed an improved RFPCM method (MRFPCM) by integrating multiresolution information. First, the multiresolution segmentation approach is employed to segment stacked images into objects from coarse to fine scales. Second, the improved RFPCM is used to classify the objects into changed, unchanged, and uncertainty categories by a shrinkable threshold T . Third, all the changed and unchanged objects at the previous scales are combined as the training sample in the proposed MRFPCM to generate new CD results at a fine scale. Finally, the RSIs are interpreted as changed and unchanged targets layer by layer until there are no uncertain objects.
Five widely used CD approaches including CVA [45], MAD [46], PCA-Kmeans [8], SFA [47], and KPVD-based [24] were compared with the MRFPCM approach in three datasets with different spatial resolution and land change complexity to verify its stability and reliability. The results show that the proposed MRFPCM can detect object changes effectively and maintain reliable accuracy in simple and complex change datasets. Meanwhile, it is found that the accuracies had a significant relationship with the coarsest scale parameters by the tests with different coarsest scale parameters and initial thresholds. If the coarsest scale is appropriately set finer, the MRFPCM can achieve a great performance in RSIs. Although a larger initial threshold can generate more accurate classification information of changed and unchanged, it brings in a decrease of training samples. Therefore, the initial threshold needs to be set in a reasonable range.
However, the performance based on the proposed method needs to be enhanced in complex land cover changes, although many algorithms are not very accurate in complex land cover changes. In future research, we will focus on the automatic coarsest scale and initial threshold selection process to improve the CD performance instead of using enumeration for selection.