High-Resolution Remote-Sensing Image-Change Detection Based on Morphological Attribute Profiles and Decision Fusion

Key Laboratory of Meteorological Disaster, Ministry of Education (KLME)/Collaborative Innovation Center on Forecast and Evaluation of Meteorological Disasters (CIC-FEMD)/Joint International Research Laboratory of Climate and Environment Change (ILCEC), Nanjing University of Information Science and Technology, Nanjing 210044, China Jiangxi Province Key Laboratory of Water Information Cooperative Sensing and Intelligent Processing Nanchang Institute of Technology, Nanchang 330099, China College of Food, Agricultural, and Environmental Sciences, 3e Ohio State University, Wooster 44691, USA College of Computer and Information Engineering, Hohai University, Nanjing 211100, China


Introduction
With the development of remote sensing system, change detection (CD) has attracted widespread interest as one of the most important applications in remote sensing [1]. e accurate processing and understanding of the changes of land covers is a significant issue in different applications pertaining human activities, such as dynamic monitoring of land use, vegetation health, and environment [2][3][4]. e wild use of the new generation of high-resolution sensors (e.g., IKONOS, QuickBird, and GF2) has further broadened the applications of CD technology [5]. Compared with mediumand low-resolution remote sensing images, a greater amount of spatial and thematic information of land covers is contained in high-resolution remote sensing (HRRS) images, which makes it feasible to recognize different types of complex structures within a scene [6]. However, due to that, an object with a variety of shapes is composed by many pixels and the spectral information is very limited, these properties of HRRS images make the traditional pixel-based CD methods which are based on spectral differences ineffective [7].
In order to address this issue, numerous studies have focused on importing spatial structure information as a supplement [8,9]. It has been proved that such information is highly effective to improve the recognition ability of CD in HRRS images [10]. In the current literature, supervised machine learning methods are most widely used for feature extraction in CD applications [11,12]. However, these methods require a large number of labeled examples to identify model parameters and avoid overfitting [13]. Meanwhile, a variety of unsupervised spatial structure information extraction methods for CD in HRRS images have been proposed. Different strategies, such as object-based methods combined with image segmentation [14], linear transformation-based methods [15], Markov Random Field-(MRF-) based methods [16], multiscale analysis methods [17], and a number of indicators as the change intensity measurement [18][19][20], have been employed in these studies. In recent years, in order to deal with a high level of details due to the increased resolution of HRRS images that are not significant or even disadvantageous for CD, the Morphological Attribute Profiles (MAPs) have been introduced into CD applications [7,21].
Among the most effective methods of spatial modeling for the analysis of HRRS images, the operators in MAPs can be efficiently implemented based on the multiscale representation of land covers via tree structures [22,23]. Compared with traditional feature extraction strategies based on the given filter windows, the MAPs can expand the analysis unit to all connected pixels with similar attribute, which is helpful to accurately extract the spatial structure information of the object that the pixel belongs to. Moreover, their effectiveness has been proved in decreasing the complexity of image and extracting spatial structure information in CD applications [24]. Even so, there are still several issues in most MAPs-based CD methods [25,26]: (1) In order to highlight the representative spatial structure information while reducing the reductant information in a limited number of Attribute Profiles (APs), a reasonable set of scale parameters should be adaptively determined. However, the theory of MAPs does not give explicit criteria and the scale parameters are currently determined manually by experience. (2) In view of the complexity of land cover changes within a scene, when combining multiple change information for APs and other features, few studies take the uncertainty of change information from different sources into consideration.
Concerning the above challenges, a novel method for CD in HRRS images based on morphological attribute profiles and decision fusion is proposed, and the contributions of this study can be summarized as follows: (1) A morphological attribute profile with adaptive scale parameters (ASP-MAPs) is presented to extract representative APs while reducing redundant information. By establishing the objective function based on the minimum of average interscale correlation, the scale parameter set for each attribute can be adaptively determined through iterative computations. (2) In addition, a multifeature decision fusion framework based on Dempster-Shafer (D-S) theory [27] is constructed. In this framework, change intensity indicator (CII) and confidence indicator of evidence (CIE) are presented to describe the change information and the corresponding belief degree, respectively, and the decision fusion strategy has been proved efficiently to improve the reliability of decisions through reducing the uncertainty of change information from different sources. e rest of this paper is organized as follows: Section 2 briefly introduces the MAPs theory and the adopted attributes; in Section 3, the detailed implementation process of the proposed method is demonstrated; Section 4 contains an analysis and discussion of the experiments; the conclusion is drawn in Section 5.

MAPs Theory and the Adopted Attributes
MAPs theory is developed from set theory, in which the connected region corresponding to a pixel is extracted though spectral similarity and spatial connectivity as the basic analysis unit, and then, multiscale operators are designed with different attributes. e calculation process of MAPs is briefly introduced as follows [28]: let B denote a gray image, i denote a pixel in B, and k denote a gray level. en, a binary image Th i k (B) can be obtained: Traverse all pixels in B to get a series Th k (B) and set Γ i (B) � max(k) as the result of the opening operation of i. On this basis, by using the symmetry of attribute transformation, the closing operation Φ i (B) � min(k) of i can be obtained. Let T w ∈ T 1 , T 2 , . . . , T W denote the wth scale parameter, W denote the total number of scales, and the opening profile Ψ(Γ(B)) and closing profile Ψ(Φ(B)) are represented as follows: By combining Ψ(Γ(B)) and Ψ(Φ(B)), the MAPs can be obtained.

Adopted
Attributes. Based on the research outcomes related to MAPs, four attributes have proved to be effective in HRRS image classification and CD applications are adopted in this study, including Area, Diagonal, Standard Deviation, and Normalized Moment of Inertia (NMI) [25,28].
For the connected region corresponding to pixel i, Area reflects the area size; Diagonal describes the diagonal length of the minimum external rectangle attribute; Standard Deviation describes the degree of gray variation; and NMI reflects the shape and gravity position.

Method
Based on the image registration and radiation normalization of multitemporal HRRS images, the implement of the 2 Complexity proposed method mainly includes ASP-MAPs construction, change information description based on CII, and multifeature decision fusion. A specific description of the implementation process is shown in Figure 1.

ASP-MAPs Construction.
As shown in Figure 1, during the process of ASP-MAPs construction, the scale parameters are firstly determined by the following objectives: a limited number of APs with different scale parameters should highlight the representative spatial structure features of typical land covers within a scene, thus improving the recognition ability of the changes that happen in these land covers; besides, reducing the redundant information between APs also requires a reasonable scale parameter set [29,30]. On this basis, it is expected that the smaller the average interscale correlation of APs is, the more representative the APs are. Based on this principle, the specific process of ASP-MAPs construction is as follows.

Gradient Similarity (GRSIM).
In order to measure the interscale correlations of APs, an appropriate similarity measurement is needed. According to the theory of MAPs, the pixels that conform to the attribute range determined by the corresponding scale parameter have the greatest response, which are presented as newly generated edges (or objects). erefore, the similarity measurement should be sensitive to the edge changes. Based on the above analysis, a gradient vector-based similarity measurement, GRSIM, is presented: e third-order Sobel filter [31] is used to extract the gradient information and define the GRSIM index between images B1 and B2 as follows: where Z1 and Z2 denote the gradient amplitude matrix of B1 and B2, respectively; M1 and M2, respectively, denote the gradient direction matrix of B1 and B2; σ Z1, σ Z2, σ M1, σ M2, σ 2 Z1 , σ 2 Z2 , and σ M1,M2 denote the standard deviation, variance, and covariance, respectively. e greater the value of GRSIM B1,B2 is, the higher the correlation between B1 and B2 will be.

Adaptive Scale Parameter Extraction Based on GRSIM.
e steps of the adaptive scale parameter extraction strategy are as follows: Step 1: set the interval [T min , T max ] and the number of scales W for each attribute to adaptively search the optimal scale parameter set. According to suggestions in [8,28,32], set Area interval as [500, 28000], Diagonal interval as [10,100], Standard Deviation interval as [10,70], NMI interval as [0.2, 0.5], and W as no more than 10. In addition, according to the results of the following multiple experiments, it is suggested to set W as 6 in this study.
Step 2: in order to avoid trapping in the local optimum, the wth (w ∈ 1, 2, . . . , W { }) scale parameter should be located within the interval Sub w . Set Sub w as in the following equation: Step 3: define objective function as follows: where GRSIM w,w+1 denotes the GRSIM of two adjacent APs. According to equations (3)-(5), iteratively compute the GRSIM sum with all combinations of scale parameters and regard the combination corresponding to the minimum of GRSIM sum as the extracted optimal scale parameter set. On this basis, the ASP-MAPs of multitemporal images can be obtained according to equation (2) in Section 2.1.

Change Information Description Based on CII.
In order to uniformly describe the change information extracted from both ASP-MAPs and original spectra, a change intensity indicator, CII, is calculated as follows: Step 1: extract the difference image between different temporal APs of the same scale parameter by difference disposal, and the difference image set based on ASP-MAPs for each attribute can be obtained.
Step 2: extract the difference image between different temporal images of the same band by difference disposal, and the difference image set based on the original spectra can be obtained.
Step 3: in the difference image, since the gray value of pixel i reflects the possibility of whether i is a changed pixel, it is given a normalized treatment in the interval of [0, 255] as one of CIIs corresponding to i. Computing the CIIs based on ASP-MAPs and all bands in original images, then five CII sets based on Area, Diagonal, Standard deviation, NMI, and original spectra corresponding to i can be obtained.

Multifeature Decision
Fusion. D-S theory is a decision theory of multisource evidence fusion, and one significant advantage of D-S theory is the strong ability in explicit estimations of uncertainty of multisource evidences [26,33]. erefore, a decision fusion framework is constructed in this study for fusing change information from ASP-MAPs and original spectra.

Basic Probability Assignment Formula (BPAF).
According to D-S theory, denote A as a nonempty subset of 2 Θ , Θ as a hypothesis space, and the BPAF of A as m(A). e BPAF m: 2 Θ ⟶ [0, 1] should satisfy the following constraints: where m(A) represents the belief degree of A, and the computation of m(A) is shown as follows: where N denotes the total number of evidences, m n (F n ) denotes the BPAF computed from the nth evidence F n ∈ 2 Θ , and F n ≠ ∅.

Calculation of CIE.
In order to measure the belief degree of CIIs from different sources (including Area, Diagonal, Standard deviation, NMI, and the original spectra), a confidence indicator of evidence, CIE, is presented. For each evidence, the CIE can be calculated with equation (8). For each CII, the bigger CIE means that the higher relief degree should be given in the decision fusion process:

Construction of Decision Fusion
where CII n and CIE n represent the nth CII and CIE corresponding to pixel i. On this basis, calculate m( CT { }), m( NT { }), and m( CT, NT { }) for pixel i through equation (7), and the decision rules are shown as follows: If i satisfies the above rules, i is recognized as a changed pixel; else, i is recognized as an unchanged pixel. Finally, the CD map can be obtained by traversing all pixels based on the above decision procedure.

Experiment and Analysis
In the experiments, three datasets of multitemporal HRRS images were used. By combining quantitative evaluation and visual inspection, the performance of the proposed method was verified by comparison with a variety of advanced CD methods.  2012, respectively; the spatial resolution was 0.5 m, and the image size was 512 × 512 pixels, as shown in Figure 2(a). Dataset 2 was a set of QuickBird images with red, green, and blue bands of Chongqing, China; the acquisition times were September 2007 and August 2011, respectively; the spatial resolution was 2.4 m, and the image size was 512 × 512 pixels, as shown in Figure 2(b). Dataset 3 was a set of SPOT-5 pansharpened images with red, green, and blue bands of Shanghai, China; the acquisition times were June 2004 and July 2008, respectively; the spatial resolution was 2.5 m, and the image size was 512 × 512 pixels, as shown in Figure 2(c). Besides, a number of representative areas marked in red boxes (patches I1, I3, and I5) and blue boxes (patches I2, I4, and I6) in Figure 2 were chosen for detailed comparison and analysis.
e reasons for selecting these three datasets for the experiments were as follows: these datasets represented different urban scenes and were mainly composed of buildings, roads, vegetation, wasteland, etc., which were helpful to verify the ability of the proposed method in recognizing the changes happened on these typical land covers; moreover, using these datasets was beneficial to evaluate the applicability and stability of the proposed method in CD applications.

Experimental Setup.
In order to evaluate the performance of the proposed method synthetically, five advanced CD methods were adopted for comparison experiments: the improved change vector analysis (CVA) methods, including CVA-Expectation Maximum (CVA-EM) method (Method 1) [3], spectral angle mapper-based method (Method 2) [7], and spectral and texture features-based method (Method 3) [34]; the MAPs-based method (Method 4) [8]; and the Deep Learning-(DL-) based method (Method 5) [13]. e implementation steps and parameter settings of comparison methods were consistent with the original references, and the adaptively extracted scale parameter sets of the proposed method are reported in Tables 1-3.

General Results and Analysis of Datasets.
e CD maps and the reference maps of three datasets are shown in Figures 3-5, in which white pixels represent changed pixels and black pixels represent unchanged pixels. In addition, the reference maps were manually delineated by field investigation and visual interpretation. e quantitative evaluation results of the different methods are reported in Tables 4-6. In all three datasets, the overall accuracy (OA) of the proposed method reached more than 83.9%, and the fluctuation range was less than 1.5%, which were significantly better than that of the comparison methods. erefore, among the challenges brought by the different data sources, the proposed method possessed advantages of high accuracy and stability.
Among three CVA-based CD methods, Methods 1 and 2 only used spectral difference as the basis of CD and had weak ability in identifying false changes that were produced by insignificant detail changes; hence, the false positive (FP) rate and false negative (FN) rates were over 30% and 20%, respectively. Since the texture difference was introduced as a supplement, the three evaluation indicators showed an obvious improvement in Method 3. erefore, it was necessary to handle the information of a pixel considering its spatial neighborhood system in order to generate more accurate CD maps. However, in Method 3, a series of specified filter windows were defined manually to extract the texture features, which made it hard to be in consistent with the inherent shape and area of the corresponding object the current pixel belongs to. By contrast, the MAPs could extract more accurate spatial structure information based on unfixed local regions constituted of all connected pixels with similar attribute.
Compared with the proposed method, although Method 4 adopted APs to extract the change information, the results of OA were significantly lower and fluctuated by more than 8% in all three datasets in this study. ese may be mainly due to that in Method 4, the scale parameters were set manually, which neglected to highlight the representative spatial structure information while reducing reductant information in APs; and the final CD map was obtained by a single threshold based on the change information from different sources with the same weight, which ignored uncertainty of change information. Based on this analysis, additional experiments and discussion about the impact on OA with adaptive scale parameter extraction and decision fusion are presented in Section 4.5.
As one of the DL-based methods, Method 5 utilized the dense skip connections within the UNet++ architecture to learn multiscale feature maps from different semantic levels. It had shown outstanding performance in terms of CD based on the satellite image pair set which was presented by Lebedev [35], and the OA could reach more than 89%. However, Method 5 showed low accuracy and bad stability in all three datasets in this study. It was expected that the lack of training samples was the primary reason why there was a huge difference of OA among different datasets. erefore, DP-based methods could not be implemented or obtain reliable results in CD applications without sufficient training samples. However, it is certain that with the increase of training samples, the performance of Method 5 would be significantly improved.

Visual Inspection of Representative Patches.
e results of the representative patches in each dataset are reported in Figure 6 (patches I1 and I2), Figure 7 (patches I3 and I4), and Figure 8 (patches I5 and I6). e CD maps for each representative patch were discussed as follows.
As shown in Figures 6-8, the proposed method showed better performance than the other comparison methods in most patches, especially for the changes happened in typical urban land covers such as buildings, roads, uncultivated lands, and vegetations, which were mainly embodied in the following: in the yellow rectangle of I1, only Methods 1, 3, and 4 and the proposed method almost extracted the complete contour of the new gymnasium; for the area severely affected by the shadows as shown in the purple rectangle of I1, a large number of false positives existed in all

Efficiency Analysis of Adaptive Scale Parameters and Decision Fusion.
In order to verify the effectiveness of the proposed adaptive scale parameter extraction strategy and decision fusion framework, respectively, the following two          [25], respectively, and the remaining steps were consistent with the proposed method (Method 6); (2) average the extracted CIIs corresponding to pixel i, and traverse all pixels in the image, and make use of EM method [3] to determine a threshold for obtaining the CD map (Method 7). e OA of the different methods are reported in Table 7. As shown above, the OA of the proposed method was significantly higher than of the other two methods. erefore, the proposed adaptive scale parameter extraction (g) (h) (i)       (g)   14 Complexity strategy and decision fusion framework were necessary and effective for improving CD accuracy: the former was helpful to highlight the representative spatial structure information while reducing the reductant information in APs; the latter could improve the reliability of decisions by reducing the uncertainty of change information from different sources.

Analysis of the Impact on OA with Different W.
In the process of adaptive scale parameter extraction, the number of scales, W, was the only the subordinate parameter which should be set manually. In order to specify the setting basis of W, the impact on OA with different W was analyzed in this section. As shown in Figure 9, the horizontal coordinate is W, the longitudinal coordinate is OA, and the results of three datasets are represented by curves in different styles. As shown above, in the three dataset experiments, with the continuous increase of W, OA shows a similar general   Complexity trend of gradual rising at first, then steady, and decreasing in the end. Among them, W � 6, W � 4, and W � 6 are corresponded to the peaks of OA curves with 83.9%, 84.9%, and 85.1% in the experiments of Datasets 1, 2, and 3, respectively. e detailed values are shown in Table 8.
As shown above, in the experiment of Dataset 2, when W was set as 6, OA could reach 84.5% and was only slightly lower by 0.4% than the corresponding highest OA. is meant the ideal results could be obtained in all experiments of three datasets by setting W as 6. erefore, considering the automation and reliability, it was suggested to directly set W as 6 in CD applications.

Conclusion
In this paper, a novel decision fusion framework based on ASP-MAPs was proposed for CD in HRRS images. By establishing the objective function based on the minimum of average interscale correlation, a set of scale parameters could be adaptively obtained to extract the representative APs while reducing redundant information. On this basis, a multifeature decision fusion framework based on D-S theory was constructed to improve the reliability of decisions by reducing the uncertainty of change information from different sources. e effectiveness of the proposed method was elaborately examined through the experiments on the multitemporal HRRS image datasets. By comparison with five advanced CD methods of different types, the proposed method showed outstanding performance in both quantitative evaluation and visual inspection, and OA reached more than 83.9%, while the fluctuation range was less than 1.5%.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.