An Object-Based Change Detection Approach Using Uncertainty Analysis for VHR Images

This paper proposes an object-based approach to supervised change detection using uncertainty analysis for very high resolution (VHR) images. First, two temporal images are combined into one image by band stacking. Then, on the one hand, the stacked image is segmented by the statistical region merging (SRM) to generate segmentation maps; on the other hand, the stacked image is classified by the support vector machine (SVM) to produce a pixel-wise change detection map. Finally, the uncertainty analysis for segmented objects is implemented to integrate the segmentation map and pixel-wise change map at the appropriate scale and generate the final change map. Experiments were carried out with SPOT 5 and QuickBird data sets to evaluate the effectiveness of proposedapproach.Theresultsindicatethattheproposedapproachoftengeneratesmoreaccuratechangedetectionmapscomparedwithsomemethodsandreducestheeffectsofclassificationandsegmentscaleonthechangedetectionaccuracy.TheproposedmethodsuppliesaneffectiveapproachforthesupervisedchangedetectionforVHRimages.


Introduction
In recent years, change detection has been one of the most important issues in the remote sensing and plays an important role in many practical applications, such as environment monitoring [1], disaster detection [2,3], urban growing [4,5], and forest monitoring [6,7].
Since change detection identifies changes by analyzing multitemporal images acquired in the same geographical area at different times [8], many factors affect its accuracy, such as sensor calibration, sunlight and atmospheric conditions, spectral characteristics of vegetation due to seasonal effects, and registration strategy [9].Hence, to reduce these impacts on change detection accuracy, some preprocessing steps need implementing, such as noise reduction, sensor calibration, and radiometric and geometric corrections [10].But different factors should be considered in different change detection strategies.In the past decades, two change detection strategies were developed according to the nature of data processing: unsupervised and supervised [11].The former partitions pixels in unchanged and changed parts by comparing two multitemporal images directly.The latter implements a supervised classification to two multitemporal images, respectively, and detects changes by postcomparisons between classification maps, namely, the postclassification method.The supervised strategy not only supplies "from-to" information, but also behaves more robust to different sunlight and atmospheric conditions compared to the unsupervised strategy [12].
This study adopts the supervised strategy to detect changes.In an early stage, pixel-wise classification methods were widely used to obtain "from-to" change information.These methods were performed to detect land cover changes, and it was indicated that the postclassification method is effective for multitemporal images acquired by different sensors or with different resolution [13,14].The postclassification method was also implemented for Landsat TM and SRTM-DEM data to detect habitat changes, and it was found that this method is capable of combining data from multiple sources [15].Additionally, damage induced by earthquake also can be detected using postclassification method [16,17].Many classification algorithms were utilized in the postclassification method, such as maximum-likelihood classification (MLC) [18], decision tree [15,16], transfer learning [19], and support vector machine (SVM) [20].
However, traditionally pixel-wise classification methods only consider gray value of pixels, and the contextual information is not taken into count.Additionally, with the development of space technology, more very high resolution (VHR) multispectral images are available, acquired by satellite sensors (e.g., SPOT-5, QuickBird, WorldView-2, GeoEye-1, and Ikonos).To improve change detection accuracy, the contextual information should be considered in the postclassification process.Therefore, the object-based classification for change detection was proposed and discussed in detail using spatial and spectral information [21,22].In the objectbased change detection, pixels of the multitemporal images were segmented into objects, a classifier was then performed to classify these objects, and changes were detected by comparing classified objects of multitemporal images.In addition, a change detection model based on neighborhood correlation image computed from contextual information and decision tree classification was proposed, and it was found that this model yielded superior results than pixels-wise and postclassification methods [23].However, the traditionally postclassification change detection methods classify multitemporal images, respectively, and compare multiple classification results to find changes, regardless of pixel-based or objectbased classification.Thus, change detection results were significantly impacted by the classification of multitemporal images.To reduce the impact of separate classification, onepass classification [24,25] was used to detect changes, in which "from-to" changes were directly detected by performing a classifier to stacked multitemporal images.But for most one-pass and object-based change detection methods, it is very important to select the appropriate segment scale to produce segmented objects, which affects change detection results seriously.
In this paper, a novel object-based approach to change detection using uncertainty analysis (OBCDUA) is proposed, and Figure 1 shows the detailed process of proposed approach.First, two multitemporal images with respect to  1 and  2 bands are stacked into one image of  1 +  2 bands.Second, the statistical region merging method (SRM) is adopted to segment the stacked image into objects with similar characteristics.Then samples of all the types including unchanged and changed classes are selected, and the pixelwise SVM classification is performed to classify the stacked image.Finally, the segmented maps and pixel-wise classification result are incorporated through uncertainty analysis for segmented objects.Experiments were carried out on SPOT 5 and QuickBird data sets to evaluate the effectiveness of proposed approach.

Proposed Supervised Change Detection Approach
Suppose that two multispectral images of size  ×  and bands  (assuming equivalent bands are contained in the two images) were acquired from the same geographical area at two different times  1 and  2 .

Stack of Two Temporal
Images.Actually, the traditional postclassification approach reduces the impacts of sunlight and atmospheric conditions on change detection results, but the accuracy of separate classification significantly affects the quality of change maps.Hence, a one-pass classification is adopted in this paper, which just performs classification once.After obtaining two temporal images X 1 and X 2 , they are stacked into one image X = {  (, ) | 1 ≤  ≤ , 1 ≤  ≤ , 1 ≤  ≤ 2} by simple band stacking.

Segmentation of the Stacked Image.
As known to us, some traditional algorithms (e.g., -means, ISODATA) segment images into clusters, but the decision of initialization model often affects segment results.In order to generate robust segment results, the SRM is adopted to segment the stacked image, which has the ability of coping with significant noise, handling occlusions, and performs scale-sensitive segmentations fast [26].
In SRM, the stacked image X is the observed image and contains × pixels, each containing 2 values, each of the 2 channels belonging to the set {0, 1, . . ., } (we have  = 255 in this paper).Let X * denote the perfect segment scene of observed image X, and each colour channel of X is obtained by sampling each statistical pixel of X * from a set of exactly  independent random variables (taking values on [0, /]) for observed 2 channels.The tuning  controls the scale of segmentation: the larger it is, the more regions exist in the final segmentation.
The realization of SRM relies on an interaction between a merging predicate and an order in merging.The merging predicate (,   ) can be expressed as where  and   represent a fixed couple of regions of X,   and    denote the observed average for colour channel  in region  and   , respectively, and (,   ) = √(1/2)(1/|| + 1/|  |) ln(2/) (0 <  < 1).If (,   ) = true,  and   are merged.As for the merging order, the function  can be used to sort pixel pairs in X, and it can be written as where  and   are the pixels of X and   and    are the pixel values of channel .The SRM is then performed to segment the stacked image, where we let  = 2  and the values of scale  belonging to [0, 1, 2, . . ., 12].

Pixel-Wise Classification Using SVM. As shown in
Figure 1, on the one hand, the stacked image is segmented by SRM; on the other hand, the pixel-wise classification is performed on the stacked image using the robust classifier SVM, which prepares input data for the following uncertainty analysis.
The SVM is a nonparametric supervised classifier based on statistical learning theory [27], which is robust to high dimensional data sets and to ill-posed problems and has been widely used for classification [28,29].The linearly separable binary classification is considered first.Assume that a training data set with  sample is given, and it can be represented as {x  ,   },  = 1, 2, . . ., , where x  represents the spectral response of the case, and   ∈ {1, −1} is the class label.The SVM aims to find the optimal separating hyperplane that positions the samples of a class in one side of it and makes the distance between it and the closest training samples in both classes as large as possible.A hyperplane in feature space is given by the equation w ⋅ x +  = 0, where vector w is normal to the hyperplane, x is a point on the hyperplane, and the scalar  is the bias of the hyperplane from the origin.Then a separating hyperplane can be defined () = w ⋅ x + , and the optimal hyperplane can be obtained by maximizing the margin using the constrained optimization problem: If the data set is not linearly separable, the constraints of (3) cannot be satisfied in practice.Thus, slack variables   ( = 1, 2, . . ., ) are introduced to relax the constraints, so that the problem of unsatisfied constraints is solved [30], namely, soft margin.Considering the introduced slack variables, (3) can be written as where the constant  is a penalty parameter associated with training samples that lie on the wrong side of the hyperplane and must be determined by user carefully to avoid problems such as a higher penalty to errors due to its large value.This classifier finds an optimal separating hyperplane as a decision function in a high dimensional space to solving a nonlinear separation in the original input space.Hence, the input data are mapped into a high dimensional space through a nonlinear vector mapping function, which can be replaced by valid kernel function (⋅, ⋅) [31].Therefore, the classification decision function in the high dimensional space is given by where   ( = 1, 2, . . ., ) is Lagrange multipliers for looking for the optimal separating hyperplane and (x, x  ) is a kernel function.
As known, so many kernel functions exist, such as polynomial, Gaussian radial basis function (RBF), and hyperbolic tangent, and the Gaussian RBF is adopted in this paper due to its interpretability and positive performances [25].Additionally, the one-against-one approach [32] is adopted to solve the problem of multiclass classification.Finally, the optimal hyperplanes are obtained for classification after training processing.

Object-Based Change Detection Using Uncertainty Analysis.
After the stacked image is segmented by SRM and classified by SVM, the object-based change detection using uncertainty analysis can be performed.In fact, a spectralspectral classification method (SSCM) has been proposed by Tarabalka et al. [33,34]; however, the uncertainty of segment scale was not considered, which cannot obtain results at optimal scale for different objects and decrease the accuracy of results.Therefore, a change detection approach using uncertainty analysis for segment scale is proposed to make full use of spectral and spatial information as in Figure 2.
Step 1.A moderate scale segmentation map   is selected and integrated with pixel-wise classification map, where  is the segment scale.For a segmented object   , the number of pixels   for the th class is counted and sorted in all classes Final change map of the object   .The percentage of class with largest pixel number is calculated: where   is the percentage of class  with largest pixel number,  is the pixel number of class , and  is the class number in the object   .A threshold  is set and compared with   to analyze the uncertainty of current segment scale for the object   .If   > , the current scale  can be seen as the appropriate segment scale for the object   , and the object   is then identified as class .On the contrary, the current scale  is too coarse to combine the segmented object   with the pixel-wise classification result, and the object   remains original state and is then labeled as an uncertainty one.As can be seen from the first row of Figure 2, the classes with largest pixel number in the objects A and B of the segmentation map are dark and white classes, respectively.Supposing the both percentages of dark and white classes are larger than the threshold , the objects A and B are then identified as dark and white as shown in the second row of Figure 2.For the object C, the percentage of the class grey with largest pixel number is smaller than the threshold , so the current segment scale is too coarse for the object C.Moreover, it remains original state and is labeled as an uncertainty one.
Step 2. A further uncertainty analysis for the labeled uncertain object above is performed using a more detailed segmentation map.In the SRM of Section 2.2, the larger the  value is, the more detailed the segmentation map is.The uncertain objects in the last step can be segmented into more objects in the more detailed segmentation map.For these new objects, Step 1 is implemented to analyze their uncertainties under the current segment scale.If   > , the new object can be labeled as the class  with largest pixel number.As can be seen from the second row of Figure 2, the object C of the segmentation map is divided into objects C and D in the more detailed segmentation map.Therefore, the objects C and D are identified as grey and dark classes through the uncertainty analysis, respectively.Contrarily, it is still seen as an uncertain one and analyzed using a more detailed segmentation map.
Step 3. The uncertainty analyses for all objects are performed until the most detailed segmentation map has been used for uncertainty analysis.Though these objects are refined by the detailed segmentation map, some still cannot meet the requirements and are labeled uncertain ones.Give that, a majority voting is implemented in uncertain objects, and they are labeled the corresponding class having maximum number of pixels.Finally, the change map is obtained by integrating the segmentation maps and pixel-wise change detection result through the uncertainty analysis.
The implementation of proposed OBCDUA includes four steps.
Step 1 (stacking of two temporal images).To reduce the impact of twice classification on change detection results, two temporal images are combined into one image simply by band stacking, so that input data is prepared.
Step 2 (segmentation of the stacked image).The stacked image is segmented into homogenous objects using SRM, and the segmentation maps provide spatial information in the following integration approach.
Step 3 (pixel-wise classification of the stacked image).All kinds of training samples are selected, such as road, grass, bare soil to grass, and water to grass, and the SVM is then performed to classify the stacked image, so the pixel-wise change map is generated.
Step 4 (integration of the segmentation maps and pixel-wise change map using uncertainty analysis).The segmentation maps and pixel-wise change map are integrated through the uncertainty analysis approach, and the final change map is obtained by making full use of spectral and spatial information.where the   and   are the accuracy of methods A and B, respectively.When the accuracy reaches a relatively great value, we assume that any increases becomes valuable.With this in mind, the index termed RRE is used to emphasize the increases in accuracy.

Results of the Proposed Approach.
The stacked image was segmented using SRM into homogenous objects, in which a parameter  tunes the tradeoff between the segment scale and computational complexity.In the experiments, we let  = 2  and the values of scale  belonging to [0, 1, 2, . . ., 12] were used to obtain segmentation maps.Some segmentation maps were shown in Figure 4 (e.g., scale  = 5, 7, and 9, resp.).As can be seen, a larger  generates more numerous and smaller regions in the segmentation map, but some large homogenous regions are remained.Additionally, smaller regions often correspond to smaller perceptual regions at different scales, and larger regions are often displayed as a whole in the stacked image.It is indicated that SRM performs segmentation reasonably.Moreover, the stacked image was then classified by SVM, in which Gaussian radial basis function (RBF) was adopted and two parameters  and  were set as 100 and 0.167, respectively.The pixel-wise change map using SVM classification is shown in Figure 5(a).As can be seen, much "salt and pepper" noise exists in the classification map because only spectral information was used without spatial information.
Figure 5 shows the change maps generated by the proposed approach, where the scale  value of initial segmentation map was 8 and the threshold  was set to 0.8.It can been seen that about half objects are identified as uncertain when the value of segmentation scale  is 8.With the increasing of  values, some uncertain objects are labeled in a more detailed segmentation map.Few uncertain objects exist in the change map after analyzing with the segmentation map of  value 12 as shown in Figure 5(d).Finally, the majority voting method was implemented for the uncertain objects and labeled them as the class having the maximum pixel number in the corresponding objects as shown in Figure 5(e).Both homogenous and detailed regions exist in the final change map, because the optimal segmentation scale is found for different objects through uncertainty analysis and spectral and spatial information is integrated properly.
Two parameters affect the accuracy of proposed approach, namely, the threshold  for uncertainty analysis and the initial segment scale .increasing of threshold until the value 0.8 and then decrease, but the overall accuracy only changes between 93.0% and 93.5% and the Kappa coefficient slightly ranges from 0.925 to 0.930.Besides, the missed detections first increase and then decrease with the increasing of threshold; the false alarms first decrease and then slightly increase with the increasing of threshold.However, the total errors always keep at around 2.9%.As can be seen from above, the proposed approach is robust for the threshold . 8 and then decrease, but the overall accuracy and Kappa coefficient always remain at around 93.5% and 0.926, respectively.The missed detections generally and slightly decrease with the increasing of scale ; the false alarms always remain at around 2.55% with the increasing of scale .Moreover, the total errors keep at around 2.95%.In a word, the proposed approach is also robust for the initial segment scale.

Comparison with Other Change Detection Methods.
In order to verify the effectiveness of the proposed change detection approach, other methods were implemented and compared with the proposed one, namely, the traditional postclassification method (TPCM), the pixel-wise classification method (PWCM), and SSCM.
In the TPCM, the SVM was implemented to the  1 and  2 images and classified the two images into road, grass, water, bright buildings, dark buildings, and bare soil, respectively.The classification maps of  1 and  2 images were then compared pixel by pixel, and the change map was obtained as shown in Figure 8(a).Since the postclassification change  map included more change classes than the reference data, the excess classes were recorded as "other classes" and presented using white.For the grass, it is easily recognized and classified as homogenous regions; however, much "salt and pepper" noise exists for some other classes.Figure 8(b) presents the change map generated by the PWCM.For the grass and water, it can obtain homogenous regions, but "salt and pepper" noise exists for many classes as marked in the change map, which especially occurs around edge pixels.
In the SSCM, the change map of pixel-wise classification was combined with segmentation maps at different scale using the majority voting method.Hence, the spectral-spatial change map of segment scale 12 was adopted and compared with the proposed one as shown in Figure 8(c).The SSCM mostly contains homogenous regions, which seems better than TPCM and PWCM visually as marked in Figure 8(c).However, the integrated change map using the coarse segmentation map may contain more errors and the accuracy is affected by the segment scale seriously.Figure 8(d) shows the change map generated by the proposed approach with the initial segment scale value of 8 and the threshold value of 0.8.As can be seen, the proposed approach generates more homogenous regions and removes more noise than other three methods as marked in the change detection maps.Additionally, the detailed change information can be also accurately identified.The reason is that the proposed approach finds the optimal scales for different objects through uncertainty analysis, which appropriately integrates segmented objects with pixel-wise classification results.
Table 1 gives the accuracy indices of overall accuracy, Kappa coefficient, missed detections, false alarms, total errors, and RRE for the comparisons between the proposed OBCDUA and other three methods.As can be seen from Table 1, the overall accuracy and Kappa coefficient of change detection map generated by the proposed OBCDUA are 93.55% and 0.9283, respectively.Compared with other methods, the values of RRE for overall accuracy are 75.6%,29.0%, and 17.5%, respectively.The OBCDUA reduces the missed detections, false alarms, and total errors when compared with TPCM, PWCM, and SSCM.The value of total errors for OBCDUA is 2.93%, and the RRE values are 74.2%,32.2%, and 18.2%, respectively.It can be seen that many objects are labeled as uncertain under current scale.More and more uncertain objects are labeled in a more detailed segmentation map with the increasing of  values, and most objects were identified after the segmentation map of scale  value 12 as shown in Figure 12(d).The final change map was created by implementing the majority voting for the uncertain objects as shown in Figure 12(e).Because the optimal segmentation scale is found for different objects in the proposed approach, both homogenous and detailed regions can be detected in the final change map. Figure 13(a) presents the change patterns of accuracy indices for different thresholds ranging from 0.7 to 0.9 with steps 0.5 under the initial segment scale value 8.Both change patterns of overall accuracy and Kappa coefficient increase with the increasing of threshold until the value 0.85 and then decrease, but the overall accuracy only changes between 93.5% and 94.2% and the Kappa coefficient slightly ranges from 0.923 to 0.931.Besides, both the false alarms and the total errors change slightly, and the missed change detection always keeps at around 12%.Therefore, the proposed approach is robust for the threshold  to a certain extent.

Experiments of
Figure 14 shows the change patterns of accuracy indices for different initial segment scale  values ranging from 6 to 10 with the threshold value 0.8.The change patterns of overall accuracy and Kappa coefficient are similar, and they both first increase with the increasing of scale  until 8 and then decrease slightly, but the overall accuracy and Kappa coefficient always remain at around 94.0% and 0.925, respectively.Additionally, all the missed detections, false alarms, and total errors change slightly the increasing of scale .So the proposed approach is also robust for the initial segment scale in the second experiments.

Comparison with Other Change Detection Methods.
Some experiments were implemented to verify the effectiveness of the proposed change detection approach compared with TPCM, PWCM, and SSCM, and change maps were shown in Figure 15.
In the TPCM, the  1 image was classified into road, vegetation, water, and buildings, and  2 image was classified into road, vegetation, water, buildings, and workshops using SVM.The change map was obtained by comparing the classification maps pixel by pixel as shown in Figure 15(a).The excess classes excluded in the reference data were recorded as "other classes" and presented using white.The vegetation was easily confused with water, and much "salt and pepper" noise exists in the change detection map. Figure 15(b) presents the change map generated by the PWCM.Compared with TPCM, it can obtain more accurate change detection map, but "salt and pepper" noise still exists the same as TPCM.
For the SSCM, the majority voting method was used to obtain the change map by combining the pixel-wise classification map with segmentation maps at a specific scale.Figure 16 presents the change patterns of accuracy indices for different segment scale of SSCM.The overall accuracy and kappa coefficient generally grow with the increasing of segment scale.The false alarms always grow with the increasing of segments scale.The missed detections drop circuitously, and total errors first drop then increase with the increasing scale.As can be seen the segment scale is very important for obtaining the optimal change detection results.Finally, the segment scale 12 was adopted and compared with the proposed one as shown in Figure 15(c).Figure 15(d) shows the change map generated by OBCDUA with the initial segment scale value of 8 and the threshold value of 0.8.Both OBCDUA and SSCM mostly generate homogenous regions than TPCM and PWCM as marked in Figure 15, but OBCDUA retains more detailed change information.As can be seen, the proposed approach generates more homogenous regions and removes more noise than other three methods as marked in the change detection maps.Additionally, the   with SPOT 5 and QuickBird data sets to evaluate the effectiveness of proposed approach.It is confirmed that the OBC-DUA not only improves the accuracy of change detection results compared with TPCM, PWCM, and SSCM, but also enhances the robustness of results for the segments scales.The proposed approach supplies an effective approach to supervised change detection for VHR images.

Figure 1 :
Figure 1: Flowchart of the proposed supervised change detection approach.

Figure 2 :
Figure 2: Integration of the segmentation map and pixel-wise change detection results.

3. 1 .
Experiments of SPOT Images.A data set including two VHR images acquired from a same geographical area of China is used in the experiments to evaluate the effectiveness of the proposed change detection approach.The images were acquired by SPOT 5 on April 2008 ( 1 ) and February 2009 ( 2 ), respectively, and they both were generated by fusing panchromatic and multispectral images, which had three
Figure 6 presents the change patterns of accuracy indices for different thresholds ranging from 0.7 to 0.9 with the steps 0.5 under the initial segment scale value 8.The change patterns of overall accuracy and Kappa coefficient are similar.They both increase with the

Figure 5 :
Figure 5: Results of experiments of SPOT 5 images: (a) pixel-wise change map using SVM; semifinished change maps generated by uncertainty analysis under segment scale value of (b) 8, (c) 10, and (d) 12, respectively, where white regions are uncertain objects.(e) The final change map under the threshold value 0.8.

Figure 7 Figure 6 :Figure 7 :
Figure 6: Change patterns of (a) overall accuracy and Kappa coefficient and (b) missed detections, false alarms, and total errors for different thresholds under the initial segment scale  value 8 in experiments of SPOT 5 images.

Figure 9 :
Figure 9: Change patterns of the accuracy indices for different segment scale  values of SSCM in experiments of SPOT 5 images.

Figure 11 :
Figure 11: Segmentation map of the stacked image using SRM with different values (a) 5, (b) 7, and (c) 9 of  in experiments of QuickBird images.

Figure 13 :Figure 14 :
Figure 13: Change patterns of (a) overall accuracy and Kappa coefficient and (b) missed detections, false alarms, and total errors for different thresholds under the initial segment scale  value 8 in experiments of QuickBird images.

Figure 16 :
Figure 16: Change patterns of the accuracy indices for different segment scale  values of SSCM in experiments of QuickBird images.

Table 1 :
Accuracy comparison between traditional methods and the proposed approach in experiments of SPOT 5 images.

Table 2 :
Accuracy comparison between traditional methods and the proposed approach in experiments of QuickBird images.