Change Detection Using a Texture Feature Space Outlier Index from Mono-Temporal Remote Sensing Images and Vector Data

: Multi-temporal remote sensing images are the primary sources for change detection. However, it is difﬁcult to obtain comparable multi-temporal images at the same season and time of day with the same sensor. Considering texture homogeneity among objects belonging to the same category, this paper presents a new change detection approach using a texture feature space outlier index from mono-temporal remote sensing images and vector data. In the proposed approach, a texture feature contribution index (TFCI) is deﬁned based on information gain to select the optimal texture features, and a feature space outlier index (FSOI) based on local reachability density is presented to automatically identify outlier samples and changed objects. Our approach includes three steps: (1) the sampling method is designed considering spatial distribution and topographic properties of image objects extracted by segmenting the recent image with existing vector map. (2) Samples with changed categories are reﬁned by an iteration procedure of texture feature selection and outlier sample elimination; and (3) the changed image objects are identiﬁed and classiﬁed using the reﬁned samples to calculate the FSOI values of the image objects. Three experiments in the two study areas were conducted to validate its performance. Overall accuracies of 95.94%, 96.36%, and 96.28% were achieved, respectively, while the omission and commission errors for every category were all very low. Four widely used methods with two-temporal images were selected for comparison, and the accuracy of the proposed method is higher than theirs. This indicates that our approach is effective and feasible.


Introduction
Change detection of the Earth's surface features is the process of measuring the landscape changes of the same geographical area at different times [1][2][3]. It is extremely important for monitoring disasters and observing urban expansion as well as ecosystem and land-use/land-cover changes [4][5][6][7][8]. Due to the advantages of repetitive data acquisition, its synoptic view, low cost, and fast response capacities, remote sensing has long been recognized as an effective tool for a variety of change detection applications [9][10][11].
The remainder of this paper is organized such that Section 2 outlines the proposed change detection method, including the sampling design, sample refinement by the iteration of texture feature selection and outlier sample elimination, and the changed object detection. The results and discussion are presented in Sections 3 and 4, respectively. Finally, the main conclusions are drawn in Section 5.

Methods
The framework of the proposed change detection approach from mono-temporal remote sensing images and vector data is shown in Figure 1. Our approach involves three main steps. (1) The sampling design is based on a priori information. Image objects are first extracted by segmenting the recent images with the existing vector map, which can significantly reduce the difficulty and improve accuracy of image segmentation. The extracted image objects are bundled with a priori information (e.g., shape and category) from vector data and spectral information from the images. Then, the sampling method is designed considering the spatial distribution and topographic properties of the objects (DEM data are used to represent the topographic properties), and the initial samples are obtained, although there may be some samples with changed categories. (2) Samples with changed categories are refined by an iteration procedure in which texture features are selected and outlier samples are eliminated. In the iteration procedure, a TFCI is defined based on information gain to select the optimal texture features, and an FSOI based on local reachability density is presented to automatically identify outlier samples. After the iteration, the optimal texture features for each category can be determined, and the samples with unchanged categories can be obtained. (3) The detection and classification of the changed objects are conducted. The changed objects are identified with the refined samples by calculating the FSOI values of image objects. The changed image objects are resegmented based on the existing multi-resolution segmentation algorithm [46,47], and the resegmented changed image objects are classified with the refined samples by calculating the FSOI values of the image objects. In this paper, the sampling design, sample refinement (including TFCI and FSOI), and changed object detection are all discussed in detail.
Remote Sens. 2021, 13, x FOR PEER REVIEW 3 of 26 on local reachability density is presented to automatically identify outlier samples and changed objects. Samples with changed categories are refined by an iteration procedure of texture feature selection and outlier sample elimination. The types of the changed objects are determined with the refined samples. The remainder of this paper is organized such that Section 2 outlines the proposed change detection method, including the sampling design, sample refinement by the iteration of texture feature selection and outlier sample elimination, and the changed object detection. The results and discussion are presented in Section 3 and Section 4, respectively. Finally, the main conclusions are drawn in Section 5.

Methods
The framework of the proposed change detection approach from mono-temporal remote sensing images and vector data is shown in Figure 1. Our approach involves three main steps. (1) The sampling design is based on a priori information. Image objects are first extracted by segmenting the recent images with the existing vector map, which can significantly reduce the difficulty and improve accuracy of image segmentation. The extracted image objects are bundled with a priori information (e.g., shape and category) from vector data and spectral information from the images. Then, the sampling method is designed considering the spatial distribution and topographic properties of the objects (DEM data are used to represent the topographic properties), and the initial samples are obtained, although there may be some samples with changed categories. (2) Samples with changed categories are refined by an iteration procedure in which texture features are selected and outlier samples are eliminated. In the iteration procedure, a TFCI is defined based on information gain to select the optimal texture features, and an FSOI based on local reachability density is presented to automatically identify outlier samples. After the iteration, the optimal texture features for each category can be determined, and the samples with unchanged categories can be obtained. (3) The detection and classification of the changed objects are conducted. The changed objects are identified with the refined samples by calculating the FSOI values of image objects. The changed image objects are resegmented based on the existing multi-resolution segmentation algorithm [46,47], and the resegmented changed image objects are classified with the refined samples by calculating the FSOI values of the image objects. In this paper, the sampling design, sample refinement (including TFCI and FSOI), and changed object detection are all discussed in detail.  The results of change detection

Sampling Design with a Priori Information from Vector Data and DEM
It is well known that the quality of samples determines the success of the change detection process, while the quality of samples is affected by the size and location distribution of sample objects [48]. Besides, the quality of samples is also affected by their representativeness. When the vector map is available, all objects can be theoretically used as samples. However, this will decrease the representativeness of samples. Considering the above reasons, we choose the representative objects as the samples. Therefore, the sampling design is one of the key steps in implementing automatic sampling for change detection. Since samples are taken from image objects that have the same a priori categories, the image objects that have changed in a posteriori category are inevitably sampled. Compared to the number of unchanged objects, the number of changed objects is usually expected to be small. The aim of sampling design is to obtain as few as possible changed samples and enough statistical power to detect texture homogeneity among objects belonging to the same categories. The appropriate sampling area, density of sampling, and allocation of sampling sites are three important characteristics to be considered when designing a sampling program. The sampling area selection should be based on requirements for outlier data and specific study areas. The probability of image objects with homogeneous texture features being sampled will increase with the enlargement of the sampling range, so the sampling design requires sampling at a global range in the study area. The density of sampling (i.e., the number of samples per unit area) is usually dictated by the practical constraints of the landscape and topographic properties. Sampling sites must be distributed in a purely random fashion. Consequently, sampling design is achieved according to sampling areas, spatial distribution, and the topographic properties of the objects.
A uniform grid that covers the sampling area is used to allocate samples. First, the sampling area is divided into a uniform grid. The size of the grid can be properly determined according to the size of the sampling area, the total number of image objects, and the number of samples taken. Second, the sampling area is divided into t levels according to topographic properties based on DEM data, and then the number of samples is calculated in each cell. The number of samples in row r and column c of the grid, SN r×c , is calculated as follows: where Ion is the number of objects and STN is the number of samples taken in the sampling area. Ion j r×c is the number of objects in row r and column c of the terrain level j. The principle of sampling design is shown in Figure 2. Finally, samples for each cell are randomly taken from objects included in each cell, and the initial samples containing outlier samples (i.e., changed sample objects) are obtained.

Refining Samples by Iteration of Texture Feature Selection and Outlier Sample Elimination
To improve the accuracy of the change detection results, a TFCI is defined by information gain to select the optimal texture features for each category, and an FSOI based on local reachability density is presented to automatically identify outlier samples and changed objects. However, the optimal texture features need to be identified from samples with unchanged categories, and samples with unchanged categories need to be extracted according to the optimal texture features. Therefore, automatically identifying the optimal texture features is in contradiction with automatically detecting outlier samples. Consequently, in order to implement automatic sampling for change detection, samples with changed categories must be refined by an iteration procedure of texture feature selection and outlier sample elimination.

Refining Samples by Iteration of Texture Feature Selection and Outlier Sample Elimination
To improve the accuracy of the change detection results, a TFCI is defined by information gain to select the optimal texture features for each category, and an FSOI based on local reachability density is presented to automatically identify outlier samples and changed objects. However, the optimal texture features need to be identified from samples with unchanged categories, and samples with unchanged categories need to be extracted according to the optimal texture features. Therefore, automatically identifying the optimal texture features is in contradiction with automatically detecting outlier samples. Consequently, in order to implement automatic sampling for change detection, samples with changed categories must be refined by an iteration procedure of texture feature selection and outlier sample elimination.

TFCI Computation Based on Information Gain
Texture is an innate property of all types of surface objects and contains important information about the structural arrangement of surfaces and their relationship to the surrounding environment [49,50]. Texture information is widely used to help in segmentation or classification. Among multitudinous texture analysis methods, a gray-level co-occurrence matrix (GLCM) has been proven to be an effective tool for capturing numerical features of remote sensing images using spatial relations of similar gray tones [51,52]. The 14 texture features have been defined based on the GLCM [50], as shown in Table 1. Variance (VAR) f8 Sum Variance (SVAR) f9 Sum Average (SAVE) f10 Sum Entropy (SENT) f11 Difference Entropy (DENT)

TFCI Computation Based on Information Gain
Texture is an innate property of all types of surface objects and contains important information about the structural arrangement of surfaces and their relationship to the surrounding environment [49,50]. Texture information is widely used to help in segmentation or classification. Among multitudinous texture analysis methods, a gray-level co-occurrence matrix (GLCM) has been proven to be an effective tool for capturing numerical features of remote sensing images using spatial relations of similar gray tones [51,52]. The 14 texture features have been defined based on the GLCM [50], as shown in Table 1. Directly applying all of the texture features from the GLCM to describe the texture information results in some redundancy because some of the features may not have a clear contribution to distinguishing different categories of image objects. The redundancy is related to the uncertainty of texture feature values. Therefore, identifying the optimal texture features can be accomplished by analyzing the uncertainty of different texture features. It is well known that information entropy is regarded as an effective tool to measure the uncertainty [27,53], and thus, information entropy is used to measure the contribution of a texture feature to distinguish different categories of image objects.
The information gain is a measure of the decrease in the amount of information entropy that one feature has about all other features [54]. It can be used as an index to measure the importance of texture features. Assume that Gain(c i , f j ) indicates the information gain of texture feature f j belonging to category c i , and the expression of Gain(c i , f j ) can be written as: where H(c i ) is information entropy and H(c i / f j ) is conditional information entropy of category c i . N is the total number of objects and N c i is the number of objects belonging to category c i . N c i f j is the number of objects whose values of texture feature f j belong to the texture feature space of the category c i . However, applying information gain may result in a biased estimation that the optimal texture features tend to have a larger range of the feature vector [55]. Hence, the information gain ratio is employed to eliminate this effect. Assuming that GainRat(c i , f j ) represents the information gain ratio of texture feature f j belonging to the category c i , and GainRat(c i , f j ) can be written as: where H( f j ) is the information entropy of texture feature f j . Therefore, a texture feature contribution index (TFCI) based on information gain ratio can be defined as: where TFCI f j c i indicates the TFCI of the texture feature f j belonging to the category c i . The TFCI value is between 0 and 100%, and the higher its value, the greater the contribution of texture feature f j on category c i . Hence, it is easy to determine which texture features can be selected as the optimal features to identify changed objects. In order to quantify the contribution levels of texture features, analytic hierarchy process (AHP) is used to determine the priorities of texture feature selection. In AHP for texture features, the equal interval method is applied to divide the TFCI interval into five sub-intervals, and each sub-interval width is equal to all other sub-interval widths [56,57]. Table 2 shows the five sub-intervals and their contribution levels. The optimal texture features can be selected according to the TFCI value. Generally, the texture features with very low and low contribution levels must be eliminated, texture features with moderate contribution levels can be selected appropriately, and texture features with high and very high contribution levels must be selected. The texture feature space vector (TFSV) for types of surface objects can be established according to the results of the optimal texture feature selection. Assume that TFSV(c j ) indicates the TFSV of the category c j . The expression of TFSV(c j ) can be written as: where w j i (i = 1, 2, · · · , 14) is TFCI value of texture feature f i in the category c j . In Equation (5), if TFCI values of texture feature f i are below 60%, texture feature f i should not be chosen, and the w j i value is set as zero.

FSOI Computation Based on Local Reachability Density
In remote sensing images, there are many factors that impact the spectral features of surface objects, including sensors, phenological characteristics, and environmental factors, as well as changes in the types of surface objects caused by man or sudden natural disasters. However, change detection aims to identify changed objects caused by man or such natural disasters. The texture features of changed objects have clear outlier characteristics, both in samples and change detection. Some scholars describe the concept of an outlier from different aspects [58][59][60]. Intuitively, an outlier is an observation that deviates so much from other observations that it arouses suspicion that it is generated by a different mechanism [61,62]. In this paper, the outlier data can be defined as data sets of low-density areas in the texture feature space (e.g., changed image objects). Consequently, the outlier detection idea is employed to detect outlier samples and changed objects.
Some researchers have proposed the method of calculating density outlier according to the spatial distribution characteristics of outlier data [63,64]. However, for outlier image objects that need to be detected, there may be a large number of outlier objects with the same or similar texture features. In order to detect outlier data more accurately, a feature space outlier index (FSOI) is defined to detect outlier samples and changed objects based on the local reachable density and global characteristics of image objects. In addition, this paper designs an iteration procedure (described in Figure 1) to refine unchanged samples. The FSOI can be calculated through three steps as follows.
The first step is to calculate the reachability distance of an object in texture feature space. Let Rdis k ob j , ob i denote the reachability k_distance of object ob i with respect to object ob j , and it is defined as: where k is a natural number, and denotes the least number of objects that should be included in the neighborhood of an object. The k_distance denotes the maximum value of Euclidean distance from an object to its neighborhood objects. Let N k (ob j ) be the number of objects in the k_distance neighborhood of object ob j , k ≤ N k (ob j ). d ob j , ob i is the Euclidean distance from object ob i to ob j , and k_dis(ob i ) denotes the k_distance of object ob i . The reachability k_distance denotes the maximum value of the k_distance and Euclidean distance from an object to its neighborhood objects. The principle of the reachability 10_distance in three-dimensional texture feature space is shown in Figure 3, where the reachability 10_distance denotes the reachable distance of an object when k value is 10. From Figure 3, the 10_distance of object ob 1 is d 1 , and the Euclidean distance from object ob 1 to ob j is d 1 . Because d 1 is greater than d 1 , the reachability 10_distance of object ob 1 with respect to object ob j is d 1 . By the same reason, the reachability 10_distance of object ob 2 with respect to object ob j is d 2 .
Remote Sens. 2021, 13, 3857 8 of 25 ability 10_distance in three-dimensional texture feature space is shown in Figure 3, where the reachability 10_distance denotes the reachable distance of an object when k value is 10. From Figure 3, the 10_distance of object 1 ob is 1 ′ d , and the Euclidean distance from object 1 ob to j ob is 1 . Because 1 is greater than 1 ′ d , the reachability 10_distance of object 1 ob with respect to object j ob is 1 . By the same reason, the reachability 10_distance of object 2 ob with respect to object j ob is 2 ′ d . The second step is to calculate local reachability density (LRD) of an object according to the reachability distance. Let LRD( ) be the local reachability density of object j ob .
LRD( ) is defined as: LRD( ) is the inverse of the average reachability distance. Note that LRD( ) can be ∞ if all the reachability distances in the summation are 0.
The last step is to calculate FSOI based on LRD. Let FSOI( ) be the FSOI of object j ob ; FSOI( ) is defined as: where D is the set of objects used for outlier detection. The FSOI value is between 0 and 100%, and the higher its value, the greater the probability that an object deviates from the typical normal objects. Outlier samples and changed objects can be identified according to the size of the FSOI value.
F e a tu r e 1 The second step is to calculate local reachability density (LRD) of an object according to the reachability distance. Let LRD ob j be the local reachability density of object ob j . LRD ob j is defined as: LRD ob j is the inverse of the average reachability distance. Note that LRD ob j can be ∞ if all the reachability distances in the summation are 0.
The last step is to calculate FSOI based on LRD. Let FSOI ob j be the FSOI of object ob j ; FSOI ob j is defined as: where D is the set of objects used for outlier detection. The FSOI value is between 0 and 100%, and the higher its value, the greater the probability that an object deviates from the typical normal objects. Outlier samples and changed objects can be identified according to the size of the FSOI value.

Refining Samples and Selecting the Optimal Texture Features for Each Category
Based on the results of sampling design, changed sample objects can be described as outlier samples in each category. Outlier samples can be identified and eliminated by the iteration of texture feature selection and outlier sample elimination. The iteration procedure can be described as follows: 1.
Calculate the TFCI values using the a priori categories of the initial samples based on Equation (4), and establish the first TFSV by texture feature selection.

2.
Calculate the FSOI values of the initial samples in the TFSV established in step (1) based on Equation (8 Calculate TFCI values using the updated samples in step (2) based on Equation (4), and establish the second TFSV by texture feature selection.

4.
Calculate the FSOI values of samples in the TFSV established in step (3) based on Equation (8). Detect and eliminate outlier samples, and update sample sets.

5.
Repeat steps (3) and (4) until the results of texture feature selection are the same for each category in the last two iterations.
After the iteration, the optimal texture features of each category can be determined, and the samples with unchanged categories can be obtained. Refined samples can be applied to detect changed objects and classify resegmented changed image objects.

Changed Object Detection Based on the FSOI
In the proposed texture outlier detection method, changed image objects are considered as outlier data according to texture homogeneity of the refined sample image objects with the same a priori categories. Accordingly, changed objects can be identified with the refined samples by calculating the FSOI values of image objects. Figure 4 presents the process of changed object detection using a texture feature space outlier index. The steps are described in detail as follows.
2. Calculate the FSOI values of the initial samples in the TFSV established in step (1) based on Equation (8). Compared with unchanged samples, outlier samples (i.e., the changed samples in the initial sample sets) have higher FSOI values. Thus, outlier samples can be identified by setting an appropriate FSOI threshold. In general, a higher FSOI threshold may misjudge outlier samples as unchanged samples. On the contrary, a lower FSOI threshold may misjudge unchanged samples as outlier samples. In outlier sample detection, it is crucial that all outlier samples must be able to be identified. Accordingly, it is reasonable that each outlier sample can be identified by setting a relatively lower FSOI threshold. Then, eliminate outlier samples by comparing the size of FSOI values with the FSOI threshold, and update sample sets. 3. Calculate TFCI values using the updated samples in step (2) based on Equation (4) (3) and (4) until the results of texture feature selection are the same for each category in the last two iterations.
After the iteration, the optimal texture features of each category can be determined, and the samples with unchanged categories can be obtained. Refined samples can be applied to detect changed objects and classify resegmented changed image objects.

Changed Object Detection Based on the FSOI
In the proposed texture outlier detection method, changed image objects are considered as outlier data according to texture homogeneity of the refined sample image objects with the same a priori categories. Accordingly, changed objects can be identified with the refined samples by calculating the FSOI values of image objects. Figure 4 presents the process of changed object detection using a texture feature space outlier index. The steps are described in detail as follows.

1.
First, according to the a priori category c j of an image object to be detected, the data set used for outlier detection with the samples Sam j and the object ob i is established, and the TFSV j is determined by the optimal texture features. Let S be the data set used for outlier detection. S can be written as: where #{ } denotes the set of objects used for outlier detection, and t is the number of samples with the same categories c j .

2.
Second, the reachability distance between image objects in S is calculated in the TFSV j based on Equation (6).

3.
Third, the local reachability density of the image objects in S is calculated by Equation (7) Finally, a determination is made whether the object ob i has changed or not by comparing the FSOI value of the object ob i with FSOI threshold. If the FSOI value of the object ob i is greater than FSOI threshold, the object ob i should be identified as changed objects. On the contrary, if the FSOI value of the object ob i is smaller than FSOI threshold, the object ob i . should be identified as unchanged objects.
It should be noted that it is necessary and different from outlier sample detection to evaluate results according to overall accuracies for change detection. Both higher and lower FSOI thresholds can reduce the overall accuracy of change detection results. Accordingly, it is very important to set an appropriate FSOI threshold for change detection. In addition, due to partly changing or changing to multiple different objects, the changed image objects must be resegmented to extract change information. Multi-resolution segmentation technology [46,47] is employed to resegment the changed image objects. After resegmenting the changed image objects, the resegmented changed image objects can be classified with the refined samples based on the proposed outlier detection method.

Experiments and Results
Since temporal and spatial resolutions, remote sensing sensors, and environmental characteristics have a significant impact on spectral characteristics of surface objects, two study areas are selected to validate the effectiveness and the adaptability of the proposed change detection method, including three experiments using vector data and remote sensing images acquired from different sensors at different times. In addition, the change detection methods based on two-temporal images are also selected to compare with the proposed method.

Study Area B
To evaluate the effectiveness of the proposed method in the other study area, another study area B was also selected for experiment three. The study area B is located in Pingchang county, Sichuan province, China (31 • 30 N, 106 • 24 E). It is a very mountainous region, and its highest and lowest elevations are 712 m and 652 m, respectively ( Figure 5(b3)). QuickBird images and vector data were also used in this experiment. The vector data and DEM were both acquired by digital surveying and mapping in April 2014. The vector data contain 1954 objects and 6 types of surface objects (i.e., forest, water bodies, buildings, cultivated land, roads, and bare land ( Figure 5(b1)). The QuickBird images were acquired on 14 August 2016 ( Figure 5(b2)). The size of the QuickBird images is 2334 × 2334 pixels with red, green, and blue bands selected for the experiment, and the spatial resolution of the images is 0.61 m.
( Figure 5(a1)). QuickBird images were acquired on 18 September 2017 ( Figure 5(a2)) and 20 April 2009 ( Figure 5(a5)), respectively. The size of the QuickBird images is 2920 × 2920 pixels with red, green, and blue bands selected for the experiment, and the spatial resolution of the images is 0.61 m. The size of the aerial images acquired on 8 February 2016 with DOM sensor is 2227 × 2227 pixels with red, green, and blue bands selected for the experiment, and its spatial resolution is 0.8 m ( Figure 5

Study Area B
To evaluate the effectiveness of the proposed method in the other study area, another study area B was also selected for experiment three. The study area B is located in Pingchang county, Sichuan province, China (31°30′ N, 106°24′ E). It is a very mountainous region, and its highest and lowest elevations are 712 m and 652 m, respectively ( Figure  5(b3)). QuickBird images and vector data were also used in this experiment. The vector data and DEM were both acquired by digital surveying and mapping in April 2014. The vector data contain 1954 objects and 6 types of surface objects (i.e., forest, water bodies, buildings, cultivated land, roads, and bare land ( Figure 5(b1)). The QuickBird images were acquired on 14 August 2016 ( Figure 5(b2)). The size of the QuickBird images is 2334 × 2334 pixels with red, green, and blue bands selected for the experiment, and the spatial resolution of the images is 0.61 m.

Results
In the experiments, image objects are first extracted by segmenting images with the vector map. Second, texture features of image objects are calculated according to GLCM. To obtain GLCM of image objects, gray value of each pixel should be calculated by the forest buildings water bodies bare land roads cultivated land

Results
In the experiments, image objects are first extracted by segmenting images with the vector map. Second, texture features of image objects are calculated according to GLCM. To obtain GLCM of image objects, gray value of each pixel should be calculated by the equal-weighted average of red, green, and blue bands. Third, sampling design is conducted. Then, changed samples are refined by the iteration procedure of texture feature selection and outlier sample detection. Finally, change detection and validation are carried out. In this section, change detection results are thoroughly analyzed, including sampling design, texture feature selection and outlier sample detection, change detection, and validation.

Results of Sampling Design
Sampling design needs to be conducted in the study area A and B. The results of sampling design in the study area A are used for the experiments one and two, and the results of sampling design in the study area B are used for the experiment three. According to the proposed sampling design approach, a priori information in the vector map (e.g., spatial distribution of the surface objects and topographic properties in the study area) is employed to allocate samples. First, the sampling area is divided into a uniform grid whose interval is 100 m × 100 m based on horizontal distance. The results of the uniform grids in the study area A and B are shown in Figure 6(a1,b1), respectively. Second, the sampling area is divided into different sampling levels by using the 10 m contour interval as the standard according to topographic properties based on the DEM. The study area A and B is divided into four and six sampling levels, respectively. The results are shown in Figure 6(a2,b2). Then, the number of sampling for six types of surface objects is calculated in each cell according to Equation (1). Finally, sample objects in each cell are distributed in a purely random fashion. The results of the sampling design in the two study areas are shown in Figure 7. sampling area is divided into different sampling levels by using the 10 m contour interval as the standard according to topographic properties based on the DEM. The study area A and B is divided into four and six sampling levels, respectively. The results are shown in Figure 6(a2,b2). Then, the number of sampling for six types of surface objects is calculated in each cell according to Equation (1). Finally, sample objects in each cell are distributed in a purely random fashion. The results of the sampling design in the two study areas are shown in Figure 7.   sampling area is divided into different sampling levels by using the 10 m contour interval as the standard according to topographic properties based on the DEM. The study area A and B is divided into four and six sampling levels, respectively. The results are shown in Figure 6(a2,b2). Then, the number of sampling for six types of surface objects is calculated in each cell according to Equation (1). Finally, sample objects in each cell are distributed in a purely random fashion. The results of the sampling design in the two study areas are shown in Figure 7.
(a2) (b1) (a1) (b2) Figure 6. The results of the uniform grid and the terrain levels in the two study areas: (a1) the uniform grid in the study area A; (a2) the terrain levels in the study area A; (b1) the uniform grid in the study area B; and (b2) the terrain levels in the study area B.    Figure 7(a2,a3) are the sample image objects from the QuickBird images in 2017 and the aerial images in 2016 in the study area A, respectively. It is noted that the sample image objects in the study area B are not shown in Figure 7. Because the sample objects are taken based on a priori information in the vector map, the image objects that have changed in a posteriori category are inevitably sampled. For example, as shown in Figure 7(a2,a3), some changed objects are contained in the sample image objects, and the same results of the sampling design contain a different number of changed samples. However, the number of changed sample objects is smaller than the number of unchanged sample objects. Therefore, the results of sampling design can meet requirements for outlier data.

Texture Feature Selection and Outlier Sample Detection
After obtaining the results of sampling design in the two study areas, the sample image objects need to be refined to eliminate outlier samples and select the optimal features for six types of surface objects in the three experiments. To achieve omission errors of zero in the outlier sample detection, the FSOI threshold and the k value are set as 70% and 1/5 of total number of outlier detection data, respectively, and only the texture features with high and very high contribution levels are selected in the iterations. The sizes of the optimal FSOI threshold and the k value for outlier detection will both be discussed in detail in the discussion section. After the iterations are completed, the results of texture feature selection for six types of surface objects in the three experiments are shown in Table 3, and the results of outlier sample detection in the three experiments are shown in Figure 8. Forest Cultivated land from the QuickBird images in 2017 and the aerial images in 2016 in the study area A, respectively. It is noted that the sample image objects in the study area B are not shown in Figure 7. Because the sample objects are taken based on a priori information in the vector map, the image objects that have changed in a posteriori category are inevitably sampled. For example, as shown in Figure 7(a2,a3), some changed objects are contained in the sample image objects, and the same results of the sampling design contain a different number of changed samples. However, the number of changed sample objects is smaller than the number of unchanged sample objects. Therefore, the results of sampling design can meet requirements for outlier data.

Texture Feature Selection and Outlier Sample Detection
After obtaining the results of sampling design in the two study areas, the sample image objects need to be refined to eliminate outlier samples and select the optimal features for six types of surface objects in the three experiments. To achieve omission errors of zero in the outlier sample detection, the FSOI threshold and the k value are set as 70% and 1/5 of total number of outlier detection data, respectively, and only the texture features with high and very high contribution levels are selected in the iterations. The sizes of the optimal FSOI threshold and the k value for outlier detection will both be discussed in detail in the discussion section. After the iterations are completed, the results of texture feature selection for six types of surface objects in the three experiments are shown in Table 3, and the results of outlier sample detection in the three experiments are shown in Figure 8.   From Table 3, it can be seen that the results of texture feature selection for roads and bare land are both the same or very similar in the three experiments, e.g., f 6 , f 8 , and f 9 for roads and bare land. Texture features of buildings and water bodies both have similar contribution levels in the same study areas. For example, f 1 and f 4 have high contribution levels on buildings in study area A. However, the results of texture feature selection for cultivated land and forest are both different in the three experiments, and this is mainly due to the different textures of forest and cultivated land caused by different phenological characteristics during different seasons. It follows that selecting the type of texture features is mainly related to textures of the surface objects themselves, but is not strongly related to time, remote sensors, and geographical regions of acquired images. Due to the different textures of the surface objects in different seasons and geographical regions, it is important to select the optimal features for different types of surface objects according to images.
An accuracy assessment is carried out to confirm the effect of outlier samples detection, including commission errors, omission errors, and overall accuracies. In this study, commission errors are defined as the proportion of unchanged objects being judged to be outlier objects in all objects, omission errors are defined as the proportion of changed objects being judged to be normal objects in all objects, and overall accuracies are defined as the proportion of sample objects being correctly identified in all objects. The results of accuracy assessment for six types of surface objects in the three experiments are shown in Table 4. It can be seen that omission errors of samples for all types are all 0 in the three experiments, and overall accuracies are all very high. This shows that the results of outlier sample detection can meet the requirements of sample objects used for change detection, and the outlier samples detection approach is effective for samples taken.

Change Detection and Validation
In the two study areas, three experiments were conducted to detect whether or not the objects have changed, respectively. First, image objects with a priori information are extracted from three images using a vector map, respectively. Second, the optimal texture features are selected to establish the TFSV according to a priori categories of image objects, and the data set used for outlier detection is constructed with image objects needed to be detection and sample image objects which have the same a priori categories. Then, the FSOI value of the image object needed to be detection is calculated by Equation (8). In order to obtain higher overall accuracies, FSOI threshold is set as 80% in the change detection experiment. After that, changed objects can be obtained according to the size of the FSOI values. Figure 9(a1,b1,c1) are the change detection results in the three experiments, respectively. In Figure 9(a1,b1,c1), the white areas denote changed areas. It can be seen that there are both clear changes in the two study areas, and there are greater changes in experiment one than in experiment two and three.
Due to partly changing or changing to multiple different objects, the changed image objects must be resegmented to extract change information. Multi-resolution segmentation technology is employed to resegment the changed image objects, and Figure 9(a2,b2,c2) show the results of resegmentation for the changed image objects in the three experiments, respectively. Then, the changed categories can be extracted according to the proposed outlier detection algorithm, i.e., the object can be identified as this type of surface object if the FSOI values of an object in sample objects of one type of surface object are less than the FSOI threshold. The results are shown in Figure 9(a3,b3,c3), respectively. The change extents and trajectories of each type can be calculated according to the results of the changed categories, and the results are shown in Tables 5-7, respectively. order to obtain higher overall accuracies, FSOI threshold is set as 80% in the change detection experiment. After that, changed objects can be obtained according to the size of the FSOI values. Figure 9(a1,b1,c1) are the change detection results in the three experiments, respectively. In Figure 9(a1,b1,c1), the white areas denote changed areas. It can be seen that there are both clear changes in the two study areas, and there are greater changes in experiment one than in experiment two and three. Due to partly changing or changing to multiple different objects, the changed image objects must be resegmented to extract change information. Multi-resolution segmentation technology is employed to resegment the changed image objects, and Figure  9(a2,b2,c2) show the results of resegmentation for the changed image objects in the three experiments, respectively. Then, the changed categories can be extracted according to the proposed outlier detection algorithm, i.e., the object can be identified as this type of surface object if the FSOI values of an object in sample objects of one type of surface object are less than the FSOI threshold. The results are shown in Figure 9(a3,b3,c3), respectively. The change extents and trajectories of each type can be calculated according to the results of the changed categories, and the results are shown in Tables 5-7, respectively.
From Table 5, it can be seen that six types of surface objects have shifted greatly over the period from 2009 to 2017 in the study area A. In this period, forest and cultivated land decreased by 28.07% and 38.17%, respectively. In contrast, roads, buildings, bare land, and water bodies increased by 268.98%, 146.33%, 90.77%, and 18.53%, respectively. In addition, we can explore the reason for internal conversions between different types from Table 5, e.g., the increase of bare land is mainly caused by the decrease of forest and cultivated land. From Table 6, it can also be seen that roads, buildings, and bare land all increased, and forest, water bodies, and cultivated land all decreased over the period from 2009 to 2016 in the study area A. From Table 7, it can be seen that six types of surface Figure 9. The results of change detection based on the proposed method. (a1-a3) are the results of changed object detection, resegmentation, and classification of changed image objects in experiment one, respectively; (b1-b3) are the results of changed object detection, resegmentation, and classification of changed image objects in experiment two, respectively; (c1-c3) are the results of changed object detection, resegmentation, and classification of changed image objects in experiment three, respectively.   From Table 5, it can be seen that six types of surface objects have shifted greatly over the period from 2009 to 2017 in the study area A. In this period, forest and cultivated land decreased by 28.07% and 38.17%, respectively. In contrast, roads, buildings, bare land, and water bodies increased by 268.98%, 146.33%, 90.77%, and 18.53%, respectively. In addition, we can explore the reason for internal conversions between different types from Table 5, e.g., the increase of bare land is mainly caused by the decrease of forest and cultivated land. From Table 6, it can also be seen that roads, buildings, and bare land all increased, and forest, water bodies, and cultivated land all decreased over the period from 2009 to 2016 in the study area A. From Table 7, it can be seen that six types of surface objects have also shifted over the period from 2014 to 2016 in the study area B. For example, water bodies and cultivated land decreased by 29.99% and 7.44%, respectively. In contrast, roads, forest, buildings, and bare land increased by 55.44%, 13.21%, 7.20%, and 7.03%, respectively.
Accuracy assessment is an important part of change detection. The most common accuracy assessment elements include overall accuracy, omission errors, commission errors, and the kappa coefficient. The error matrix is the most common method for accuracy assessment of the change detection results. In order to properly generate an error matrix, 468 objects from the change detection results are randomly selected in the three experiments, respectively. The actual types of objects are compared with the results of change detection, and the accuracies of the change detection results are evaluated by omission errors, commission errors, and overall accuracy. The results of accuracy evaluation are shown in Table 8. As shown in Table 8, change detection results have high accuracy. The overall accuracies in the three experiments are 95.94%, 96.36%, and 96.28%, respectively. Omission and commission errors of six types are all very low in the three experiments. Although the accuracies of bare land are relatively lower compared with other types of surface objects, their accuracies are still very high. This shows that the proposed change detection method is valid and can satisfy the accuracy requirement of change detection. The proposed change detection method can be well suited to a variety of study areas and images acquired from different sensors, which can be feasible for the automated change detection and updating land cover data at a large or global scale.

Comparison of the Proposed OTO-Based Method with Other Change Detection Methods
To validate the effectiveness of the proposed method, four other widely used methods based on two-temporal images, e.g., the object-based methods (OBMs) [20], the deeplearning-based methods (DLMs) [26], random forest (RF) [65], and support vector machine (SVM) [24], were selected for comparison. The two-temporal QuickBird images in the study areas A (Figure 5(a2,a5)) are used for experiments. These four change detection methods are all based on the classified images. First, two-temporal images are separately classified into two thematic maps, and then changed results are obtained by implementing comparison of classified images. In the object-based change detection method, remote sensing images are first segmented using the multi-resolution segmentation method from eCognition (v8.7) software, and then the image objects are classified based on the hierarchical classification method. DLM, RF, and SVM all use ENVI (5.3) software to classify two-temporal images and extract change information. The training samples of the four change detection methods required for the supervised classifiers are selected by visual interpretation of images. The change detection results are shown in Figure 10. By visual judgment, there are significant different results of change detection among the four methods. The ground truth data are compared with results of four change detection methods, and the accuracies of change detection results are achieved and are shown in Table 9.

Comparison of the Proposed OTO-Based Method with Other Change Detection Methods
To validate the effectiveness of the proposed method, four other widely used methods based on two-temporal images, e.g., the object-based methods (OBMs) [20], the deeplearning-based methods (DLMs) [26], random forest (RF) [65], and support vector machine (SVM) [24], were selected for comparison. The two-temporal QuickBird images in the study areas A (Figure 5(a2,a5)) are used for experiments. These four change detection methods are all based on the classified images. First, two-temporal images are separately classified into two thematic maps, and then changed results are obtained by implementing comparison of classified images. In the object-based change detection method, remote sensing images are first segmented using the multi-resolution segmentation method from eCognition (v8.7) software, and then the image objects are classified based on the hierarchical classification method. DLM, RF, and SVM all use ENVI (5.3) software to classify two-temporal images and extract change information. The training samples of the four change detection methods required for the supervised classifiers are selected by visual interpretation of images. The change detection results are shown in Figure 10. By visual judgment, there are significant different results of change detection among the four methods. The ground truth data are compared with results of four change detection methods, and the accuracies of change detection results are achieved and are shown in Table 9.   As shown in Table 9, the overall accuracies of OBMs, DLMs, RF, and SVM are 79.23%, 90.16%, 78.5%, and 80.5%, respectively. The overall accuracy of the proposed change detection method is higher than that of the four methods. The omission and commission errors of the four methods are all higher than those of the proposed change detection method. Compared with the proposed method, the shortfalls of the four methods mainly include: (1) it is difficult to choose training samples due to the lack of a priori information; (2) the results of change detection are sensitive to the training data quality and the number of training samples; and (3) unchanged areas need to also be classified. In conclusion, the proposed change detection method is outstanding. The main reasons include: (a) using existing vector data to segment images can reduce the search space and minimize false segmentation of objects from images, (b) the change detection error caused by the transmission of classification error is reduced to a great extent, and (c) samples for change detection are taken automatically.

Influence of Sample Proportions and Sizes on the Texture Feature Selection of Surface Objects
In the proposed change detection method, it is very important to select the optimal texture features for types of surface objects. However, the optimal texture features need to be identified by calculating TFCI values using samples. Therefore, to test the influence of sample proportions and sizes on the TFCI value, different sampling schemes will be executed in this section.
Two types of surface objects from the QuickBird images in the study area B (Figure 5(b2)), i.e., cultivated land and forest, are selected for the experiment. Two sets of experiments for each type of surface objects are designed to test the influence of samples on the TFCI value. The first set of experiments with different sample proportions are carried out to observe the difference of the TFCI value, and the results of TFCI values for cultivated land and forest are shown in Figure 11(a1,b1), respectively. As shown in Figure 11(a1), the size of cultivated land objects included in samples varies from 60 to 160, and the size of the other types of surface objects is fixed as 160. For example, in Figure 11(a1), 60/160 denotes 60 cultivated land objects and 160 other types of surface objects which are included in the samples. As shown in Figure 11(b1), the size of forest objects included in samples varies from 20 to 100, and the size of the other types of surface objects is fixed as 100. For example, in Figure 11(b1), 20/100 denotes 20 forest objects and 100 other types of surface objects which are included in the samples. The second set of experiments with the same sample proportions and different total sample sizes are carried out to observe the difference of the TFCI value, and the results of TFCI values for cultivated land and forest are shown in Figure 11(a2,b2), respectively. As shown in Figure 11(a2), the sample proportions of cultivated land objects are fixed as 50%, and the total sample sizes vary from 80 to 320. As shown in Figure 11 From Figure 11(a1), it can be seen that the contribution levels of texture features on cultivated land are all very similar when the number of cultivated land objects varies from 60 to 160. For example, the TFCI values of f5 and f13 are both lower than 40%, and it shows that f5 and f13 are both in low contribution levels. The TFCI values f6, f8 and f9 are all higher than 60%, and they are all in high contribution levels. The same conclusions can also be drawn in Figure 11(b1), e.g., f1, f2, f3, f4, f7, f10, f11 and f12 all have high or very high contribution levels on forest. From Figure 11(a2), it can also be seen that f6, f8 and f9 all have very From Figure 11(a1), it can be seen that the contribution levels of texture features on cultivated land are all very similar when the number of cultivated land objects varies from 60 to 160. For example, the TFCI values of f 5 and f 13 are both lower than 40%, and it shows that f 5 and f 13 are both in low contribution levels. The TFCI values f 6 , f 8 and f 9 are all higher than 60%, and they are all in high contribution levels. The same conclusions can also be drawn in Figure 11(b1), e.g., f 1 , f 2 , f 3 , f 4 , f 7 , f 10 , f 11 and f 12 all have high or very high contribution levels on forest. From Figure 11(a2), it can also be seen that f 6 , f 8 and f 9 all have very high contribution levels on cultivated land when the total sample sizes vary from 80 to 320. As shown in Figure 11(b2), f 1 , f 2 , f 3 , f 4 , f 10 , f 11 and f 12 all have very high contribution levels on forest when the total sample sizes vary from 40 to 200. The overall result indicates that contribution levels of texture features on types of surface objects will not be affected by sample proportions and sizes.

Influence of Image Data Source on the Texture Feature Selection of Surface Objects
To test the influence of different image data sources on the texture feature selection of surface objects, two study areas including four images are selected for the experiment. From Figure 12, it can be seen that the contribution levels of some texture features on bare land and roads are very similar in the four images. For example, f6, f8 and f9 all have very high contribution levels on bare land and roads. Texture features of buildings and water bodies both have similar contribution levels in the same study areas, and their contribution levels are different in the different study areas. For example, f6, f8, f9, f13 and f14 all have high contribution levels on buildings in the first study area. f1 and f4 have high contribution levels on buildings in the second study area. However, the contribution levels of texture features on cultivated land and forest are very different in the four images. Thus, it can be seen that the different contribution levels of texture features on types of surface objects are mainly caused by different textures of the surface objects themselves. For example, textures of building roofs are different in different study areas due to different architectural styles, and forest and cultivated land have different textures during different phenological periods. Therefore, it is very important to select the optimal features for different types of surface objects according to images acquired from different study areas and phenological periods because of the different textures of the surface objects in different seasons and geographical regions.

Role of Neighborhood Parameter k and FSOI Threshold in Outlier Detection
Calculating the FSOI values of image objects, the only parameter that needs to be set is the neighborhood parameter k. The FSOI value of an image object is affected by the size of k value, owing to the following: the greater the number of image objects included in the neighborhood, the smaller the probability that they belong to the same category. In addition, setting an appropriate FSOI threshold can also remarkably increase the accuracy of outlier detection. Therefore, it is very important to select an appropriate k value and FSOI threshold for outlier detection.
To evaluate the effect of different k values and FSOI threshold on outlier detection, four sets of outlier detection data from the QuickBird images acquired on 18 September 2017 in the study area A ( Figure 5(a2)), i.e., cultivated land (145 cultivated land objects and 65 outlier objects), forest (120 forest objects and 30 outlier objects), buildings (85 buildings objects and 35 outlier objects), and water bodies (135 water bodies objects and 45 outlier objects) are selected for experiment. It should be noted that these outlier detection data were randomly selected by visual interpretation, which does not affect the implementation of the proposed automatic change detection.
To effectively achieve outlier detection, it is necessary and important to construct a texture feature space vector for the outlier detection data by selecting the optimal texture features. The results of texture features selection for four sets of outlier detection data are shown in Table 3 (experiment one). Then, the FSOI values of each object are calculated, and the frequency distribution histograms of the FSOI values for outlier detection data with different k values are shown in Figure 13. As shown in Figure 13, it is clear that the number of objects at a low FSOI interval increases gradually with the increase of the k value, and the number at the high FSOI interval decreases gradually. When the k value changes during a certain range, e.g., 35-65 in Figure 13a, the number of objects at high FSOI interval tends to be stable. When the k value is too large (e.g., close to the total number of outlier detection data), the objects to be detected are almost all at a low outlier degree level, e.g., Figure 13c. Therefore, a k value that is set too large or too small decreases the accuracy of the outlier detection results, and it is very important to select an appropriate k value for outlier detection. From Figure 13, we can conclude that it is reasonable to set k value as 1/5-1/3 of the number of total outlier detection objects.
To quantitatively evaluate the effect of outlier detection, commission errors, omission errors, and overall accuracies of four sets of outlier data are calculated by different k values and FSOI threshold, the results of which are shown in Figure 14. As shown in Figure 14, the higher the FSOI threshold, the higher the omission errors and the lower the commission errors, On the contrary, the lower the FSOI threshold, the lower the omission errors, and the higher the commission errors. Omission errors and commission errors can both reach 0, and overall accuracies can all reach 100% when the FSOI threshold is set as 80% and an appropriate k value is selected (e.g., 50-90 in Figure 14(a1-a3), 35-65 in Figure 14(b1-b3), 20-50 in Figure 14(c1-c3), and 35-65 in Figure 14(d1-d3)). When the FSOI threshold is set as 70%, no matter what the value of k is, omission errors can all reach 0; however, that would lead to a high commission error and low overall accuracies. It is reasonable that omission errors can reach 0 at the cost of high commission errors in outlier sample detection, but it is necessary to evaluate the experimental results according to overall accuracies in change detection. Therefore, the results of outlier detection are valid and reliable when the k value is set as 1/5-1/3 of the number of total outlier detection objects and the FSOI threshold is set as 80%.
number of objects at a low FSOI interval increases gradually with the increase of the k value, and the number at the high FSOI interval decreases gradually. When the k value changes during a certain range, e.g., 35-65 in Figure 13a, the number of objects at high FSOI interval tends to be stable. When the k value is too large (e.g., close to the total number of outlier detection data), the objects to be detected are almost all at a low outlier degree level, e.g., Figure 13c. Therefore, a k value that is set too large or too small decreases the accuracy of the outlier detection results, and it is very important to select an appropriate k value for outlier detection. From Figure 13, we can conclude that it is reasonable to set k value as 1/5-1/3 of the number of total outlier detection objects. To quantitatively evaluate the effect of outlier detection, commission errors, omission errors, and overall accuracies of four sets of outlier data are calculated by different k values and FSOI threshold, the results of which are shown in Figure 14. As shown in Figure 14, the higher the FSOI threshold, the higher the omission errors and the lower the commission errors, On the contrary, the lower the FSOI threshold, the lower the omission errors, and the higher the commission errors. Omission errors and commission errors can both reach 0, and overall accuracies can all reach 100% when the FSOI threshold is set as 80% and an appropriate k value is selected (e.g., 50-90 in Figure 14(a1-a3), 35-65 in Figure  14(b1-b3), 20-50 in Figure 14(c1-c3), and 35-65 in Figure 14(d1-d3)). When the FSOI threshold is set as 70%, no matter what the value of k is, omission errors can all reach 0; however, that would lead to a high commission error and low overall accuracies. It is reasonable that omission errors can reach 0 at the cost of high commission errors in outlier sample detection, but it is necessary to evaluate the experimental results according to overall accuracies in change detection. Therefore, the results of outlier detection are valid and reliable when the k value is set as 1/5-1/3 of the number of total outlier detection objects and the FSOI threshold is set as 80%. (b1-b3) are commission errors, omission errors, and overall accuracy of forest, respectively; (c1-c3) are commission errors, omission errors, and overall accuracy of buildings, respectively; (d1-d3) are commission errors, omission errors, and overall accuracy of water bodies, respectively. Note: Transverse axis denotes k values, and T denotes FSOI threshold. CE: commission errors, OE: omission errors, and OA: overall accuracy.

Role of Texture Feature Selection in Outlier Detection
In the existing literature, only a few texture features are considered based on experience to describe the texture information of image objects, which lacks accurate quantitative evaluation. For example, Anniballe et al. [66] selected five texture features (contrast, correlation, energy, homogeneity, and entropy) to investigate the textural properties of buildings. However, Sofina and Ehlers et al. [38] utilized three other texture features (angular second moment, contrast, and inverse difference moment) to detect buildings damaged by an earthquake. To evaluate the performance of the optimal texture features on outlier detection, two experiments with and without texture feature selection are conducted. The QuickBird images acquired on September 18, 2017 in the study area A ( Figure  5(a2)) are used for two experiments. To compare the results of two experiments, 600 ob- Figure 14. Accuracy analysis of outlier detection by using different k values and FSOI threshold: (a1-a3) are commission errors, omission errors, and overall accuracy of cultivated land, respectively; (b1-b3) are commission errors, omission errors, and overall accuracy of forest, respectively; (c1-c3) are commission errors, omission errors, and overall accuracy of buildings, respectively; (d1-d3) are commission errors, omission errors, and overall accuracy of water bodies, respectively. Note: Transverse axis denotes k values, and T denotes FSOI threshold. CE: commission errors, OE: omission errors, and OA: overall accuracy.

Role of Texture Feature Selection in Outlier Detection
In the existing literature, only a few texture features are considered based on experience to describe the texture information of image objects, which lacks accurate quantitative evaluation. For example, Anniballe et al. [66] selected five texture features (contrast, correlation, energy, homogeneity, and entropy) to investigate the textural properties of buildings. However, Sofina and Ehlers et al. [38] utilized three other texture features (angular second moment, contrast, and inverse difference moment) to detect buildings damaged by an earthquake. To evaluate the performance of the optimal texture features on outlier detection, two experiments with and without texture feature selection are conducted. The QuickBird images acquired on 18 September 2017 in the study area A (Figure 5(a2)) are used for two experiments. To compare the results of two experiments, 600 objects are selected in each experiment, including 300 outlier objects (changed objects). The frequency distribution histograms of outlier detection with and without texture feature selection are shown in Figure 15a,b, respectively.

Role of Texture Feature Selection in Outlier Detection
In the existing literature, only a few texture features are considered based on experience to describe the texture information of image objects, which lacks accurate quantitative evaluation. For example, Anniballe et al. [66] selected five texture features (contrast, correlation, energy, homogeneity, and entropy) to investigate the textural properties of buildings. However, Sofina and Ehlers et al. [38] utilized three other texture features (angular second moment, contrast, and inverse difference moment) to detect buildings damaged by an earthquake. To evaluate the performance of the optimal texture features on outlier detection, two experiments with and without texture feature selection are conducted. The QuickBird images acquired on September 18, 2017 in the study area A ( Figure  5(a2)) are used for two experiments. To compare the results of two experiments, 600 objects are selected in each experiment, including 300 outlier objects (changed objects). The frequency distribution histograms of outlier detection with and without texture feature selection are shown in Figure 15a,b, respectively. From Figure 15a, it can be seen that the FSOI values of unchanged objects are smaller than 80%, while those of outlier objects (changed objects) are mostly larger than 80%. This indicates that the FSOI values of objects with the optimal texture feature selection can be used to distinguish changed and unchanged objects. However, the distributions of changed and unchanged objects both overlap considerably in Figure 15b. Thus, it is difficult to distinguish changed and unchanged objects based on the FSOI values of objects without optimal texture feature selection. When the FSOI threshold is set as 80%, the results of the quantitative accuracy analysis of the outlier detection with and without texture feature selection are shown in Table 10. Compared with the optimal texture features, the overall accuracy of outlier detection without texture feature selection, which reduced significantly, is only 57.78%. The omission and commission errors, which both significantly increased, reach 35.00% and 7.22%, respectively. Therefore, the best accuracy results of outlier detection depend on the results of the optimal texture features.

Conclusions
In this paper, we have proposed a change detection method using a texture feature space outlier index from mono-temporal remote sensing images and existing vector data. In the proposed method, the vector data are taken as a substitute for historic remote sensing images, and changed objects in the recent images are considered as outlier data according to texture homogeneity among objects belonging to the same category. The sampling design considering spatial distribution and topographic properties of image objects is devised to incorporate as few changed samples as possible while still having enough statistical power to detect changed objects. A TFCI is defined by information gain to select the optimal texture features for each category. An FSOI based on local reachability density is presented to automatically detect outlier samples and changed objects. Samples with changed categories are refined by the iteration procedure of texture feature selection and outlier sample elimination. Overall, the proposed method has the following advantages: (a) the proposed method can reduce the search space and minimize false segmentation of image objects by using existing vector data to segment images, (b) the change detection error caused by the transmission of classification error can be reduced to a great extent, and (c) samples for change detection can be automatically extracted.
The performance of the proposed method was tested by three experiments in the two study areas. In outlier samples detection, omission errors of zero can be achieved when the FSOI threshold is set as 70%. In change detection, overall accuracies of 95.94%, 96.36%, and 96.28% were achieved in the three experiments, respectively, while the omission errors and commission errors of every category were all very low. To validate the effectiveness of the proposed method, four other widely used methods (i.e., OBMs, DLMs, RF, and SVM) based on two-temporal images were used for comparison. The experiment results showed that the accuracy of the proposed method is higher than that of the four change detection methods.
The proposed method can be well suited to a variety of images and different study areas, can accurately detect a given geographical object, and can be applied for ecological environmental monitoring, spatial data updating, and post-disaster emergencies, etc. Despite the advantages in our method, much work remains to improve the effectiveness of change detection from mono-temporal images. For example, the FSOI threshold plays an important role in detecting changed objects by the proposed outlier detection technique, but it is set though many experiments in this paper. Therefore, future work will investigate how to set the FSOI threshold with a more reasonable approach. In addition, our proposed method may not be efficient and accurate for change detection of high-rise buildings in city areas, because it is often inaccurate in identifying high-rise building roofs from an image by using a vector map.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.