THE change detection of remote sensing images plays an

Transcription

1 1822 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 Change Detection in Heterogenous Remote Sensing Images via Homogeneous Pixel Transformation Zhunga Liu, Gang Li, Gregoire Mercier, You He, and Quan Pan Abstract The change detection in heterogeneous remote sensing images remains an important and open problem for damage assessment. We propose a new change detection method for heterogeneous images (i.e., SAR and optical images) based on homogeneous pixel transformation (HPT). HPT transfers one image from its original feature space (e.g., gray space) to another space (e.g., spectral space) in pixel-level to make the pre-event and post-event images represented in a common space for the convenience of change detection. HPT consists of two operations, i.e., the forward transformation and the backward transformation. In forward transformation, for each pixel of pre-event image in the first feature space, we will estimate its mapping pixel in the second space corresponding to post-event image based on the known unchanged pixels. A multi-value estimation method with noise tolerance is introduced to determine the mapping pixel using K-nearest neighbors technique. Once the mapping pixels of pre-event image are available, the difference values between the mapping image and the post-event image can be directly calculated. After that, we will similarly do the backward transformation to associate the post-event image with the first space, and one more difference value for each pixel will be obtained. Then, the two difference values are combined to improve the robustness of detection with respect to the noise and heterogeneousness (modality difference) of images. Fuzzy-c means clustering algorithm is employed to divide the integrated difference values into two clusters: changed pixels and unchanged pixels. This detection results may contain some noisy regions (i.e., small error detections), and we develop a spatial-neighborbased noise filter to further reduce the false alarms and missing detections using belief functions theory. The experiments for change detection with real images (e.g., SPOT, ERS, and NDVI) during a flood in U.K. are given to validate the effectiveness of the proposed method. Manuscript received March 29, 2017; revised October 15, 2017 and December 1, 2017; accepted December 11, Date of publication December 8, 2017; date of current version January 12, This work was supported in part by the National Natural Science Foundation of China under Grant , Grant , Grant , and Grant , in part by the Civil Space Advance Research Program of China under Grant D010305, and in part by the Fundamental Research Funds for the Central Universities-China under Grant zy020. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Peter Tay. (Corresponding author: Gang Li.) Z. Liu is with the School of Automation, Northwestern Polytechnical University, Xi an , China, and also with the Department of Electronic Engineering, Tsinghua University, Beijing 10084, China ( liuzhunga@nwpu.edu.cn). G. Li and Y. He are with the Department of Electronic Engineering, Tsinghua University, Beijing 10084, China ( gangli@mail. tsinghua.edu.cn). G. Mercier is with Télécom Bretagne, Technopôle Brest-Iroise, Brest, France. Q. Pan is with the School of Automation, Northwestern Polytechnical University, Xi an , China. Color versions of one or more of the figures in this paper are available online at Digital Object Identifier /TIP Index Terms Change detection, remote sensing, heterogeneous images, mapping image, belief functions theory. I. INTRODUCTION THE change detection of remote sensing images plays an important role in the rapid damage assessment after natural disasters (e.g. flood, earthquake, etc) [1] [3]. The remote sensing images before (pre-) and after (post-) the event may be obtained by heterogeneous sensors (e.g. optics & radar) [4]. To quickly obtain the knowledge about damage, there is a need to investigate the change detection among heterogeneous remote sensing images before and after the disaster. Heterogeneous images reflect the different characteristics of object, and they are usually obtained by different types of sensors (e.g. one SAR image and one optical image). There have already existed many literatures dedicated to change detection of remote sensing images, and they can be broadly divided into three levels: pixel level, feature level and object level. For the detection methods in feature level, the features (e.g. texture, edge, statistic measure) are extracted from the original pixel information for comparison between pre-event and post-event images [3], [5] [9]. The deep neural networks have been recently employed for the unsupervised feature learning to capture the relationships of the pair of images in change detection [10] [12]. In object level, the image contents are usually classified using unsupervised or supervised methods, and the classification results of different images are compared/combined to detect the changes [13] [15], [21]. The image segmentation is often involved with object-level change detection to extract and separate the objects in the image [17]. A number of image segmentation methods have been developed for dealing with different cases [18], such as region based methods (e.g. fuzzy clustering, region growing), edge or boundary based methods, and so on. For example, a separate segmentation strategy is introduced in [19] for the object-level change detection from high-resolution remote sensing images, and three separate segmentations are employed to establish spatial correspondence of changed objects at different phases. The change detection methods in feature level and object level are often applied for dealing with the images in different modalities. An interesting similarity measurement between heterogeneous images is introduced in [3], and it takes into account the physical properties of sensor, the associated measurement noise models and local joint distributions. In [1], the optical image and the SAR image are used to detect IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission. See for more information.

2 LIU et al.: CHANGE DETECTION IN HETEROGENOUS REMOTE SENSING IMAGES VIA HPT 1823 the damages of buildings after earthquake. The signature of building in the post-event SAR scene is predicated according to the 3-D building parameters derived from the pre-event optical image and the acquisition parameters of the post-event SAR data. Then the changes are detected by comparing the actual post-event SAR image with the predicted SAR image. An unsupervised nonparametric method is developed in [22] for detecting changes among the multi-temporal SAR images. This method relies on an interesting feature which captures the structural change between two SAR images, and it is robust to the statistical change caused by the speckle and coregistration inaccuracies. A Bayesian network is introduced in [23] for the fusion of remote sensing data, i.e. multi-temporal SAR intensity and interferometric SAR (InSAR) coherence data, with the ancillary information (e.g. geomorphic and other ground information) for flood detection. This method can effectively reduce the false alarms and well recognize the flooded areas in the complex land cover ground conditions. In [4], a change detection method for heterogeneous images is presented based on the change measure, which is defined by the local statistics estimated according to the dependence of the pair of images before and after the events. In [16], it transfers the multi-source remote sensing data represented in low-dimension observation spaces into a high-dimension feature space (joint of the low-dimension spaces), and an iterative coupled dictionary learning (CDL) model is employed for unsupervised change detection from multi-source images in the high-dimension feature space. In [20], a Bayesian model coupled with a Markov random field is introduced for detecting changes from homogeneous or heterogeneous remote sensing images, and this method mainly consists of two steps, i.e. the image segmentation via a region based approach and building a similarity measure between the images based on the joint statistical properties of the objects. We have developed a dynamic evidential reasoning (DER) fusion method [21] for change detection of heterogeneous images. Each image is classified at first, and then DER is used to combine the classification results of different images taking into account some available prior knowledge. DER is able to deal with multi-temporal (more than two) images. DER has been further extended to a more general framework called multi-dimensional evidential reasoning (MDER) in [29] to handle the images acquired by different sensors. In the feature and object levels, different images are compared using the features or target classification results that are derived according to the pixel values. Nevertheless, some original pixel information may be lost during the process of feature selection and classification. In the pixel level methods, the normalized pixel values in different images can be compared for change detection between the homogeneous 1 images [24] [27], and the pixel information can be fully utilized in these methods to produce good results. The contents of heterogeneous images reflect the different characteristics of object, and they are generally described in distinct feature spaces like the gray space of SAR image and spectral space of optical image. Thus, the change detection cannot be carried out by directly comparing heterogeneous images. In this work, we mainly consider the change detection between SAR image and multi-spectral image. A new method is proposed to transfer one image from its original feature space (e.g. gray space with one dimension) to another space (e.g. spectral space with three even more dimensions) assuming it is not affected by the event, and the transferred image is named mapping image here. By doing this, the pre-event image and post-event image are represented in a common feature space so that their pixels values can be easily compared for change detection. This process is called homogeneous pixel transformation (HPT) consisting of forward and backward transformations. It is expected to keep the sufficient pixel information via HPT for pursuing as good as possible detection performance. In the image transformation between different feature spaces, some unchanged regions in the pair of images will be selected as prior knowledge 2 to estimate the mapping image. Because of the noisy influence and the heterogeneousness of images, some pixels with very close values 3 in one feature space may have more or less different values in another space even if they are not affected by the event. Such uncertainty often causes false alarms, and this is a big challenge in the actual estimation of mapping image. We propose a multi-value estimation strategy using the K -nearest neighbors (K-NN) technique to cope with this problem. In the forward transformation, for each pixel say x in pre-event image, its K-NN are selected from the given unchanged data according to the pixel value, and the K corresponding pixels in the postevent image are all considered as the possible estimations of the mapping of x. So the mapping pixel is calculated by the weighted average of the K corresponding pixels in the post-event image based on a new weight determination rule. Once the mapping pixel is obtained, it is directly compared with the actual pixel in the post-event image to get a difference value. After that, we also similarly do the backward transformation to associate the post-event image with the feature space of the pre-event image, and calculate one more difference value. Then the two difference values are combined to further improve the robustness of detection with respect to the noise and the modality difference of the images. The multivalue estimation strategy joint with the combination of forward and backward pixel transformation is able to efficiently reduce false alarms in change detection of heterogeneous images. Fuzzy c-means (FCM) clustering method is employed to divide the integrated difference values (i.e. the sum of the two difference values) of all pixels into two clusters: the changed pixels and the unchanged pixels. In the detection results, it may still contain some noisy regions, e.g. very small regions of false alarms and missing detections. A new noise filter is 1 Homogeneous images represent the similar characteristics of object, and they are usually acquired by the sensors of the same kind (e.g. two SAR images or two optical images). 2 This is very weak prior knowledge, because we just know that these regions are not changed during the event and nothing else. 3 The texture information can be also taken into account.

3 1824 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 introduced here to further improve the detection performance based on belief functions theory [31], [32], which is good at representing and combining the uncertain and ignorant information. It is considered that the pixels located together (close to each other in the space location) generally have the similar (changed or non-changed) status. So the change detection knowledge about the spatial neighbors around one pixel will be taken into account to modify (improve) the detection result of this pixel using Dempster s combination rule with a proper discounting technique. Three pairs of real images (e.g. ERS, SPT and NDVI images) during a flood in UK are used to evaluate the performance of the proposed change detection method. This paper is organized as follows. The detailed homogeneous pixel transformation (HPT) method for change detection from a pair of heterogeneous remote sensing images is presented in Section II, and the fusion of the pixel transformation is introduced in Section III. The noise filter for the improvement of change detection performance is developed in section IV. The experimental results of the proposed method will be analyzed in section V by comparing with other methods based on real heterogeneous remote sensing images. The concluding remarks are given in section VI. II. HOMOGENEOUS PIXEL TRANSFORMATION Let us consider a pair of heterogenous images before (pre-) and after (post-) an event respectively denoted by X (the 1 st image) and Y (the 2 nd image). Because the images X and Y reflect the different object characteristics that are represented in different feature spaces X and Y, e.g. gray space of SAR image and spectral space of optical image, it is impossible to directly compare their pixels for change detection. We want to transfer the image X from its original feature space X to another space Y assuming it is not affected by the event. Then the transferred image Ŷ (called mapping image) will be described in the same feature space as the post-event image Y. So the images Ŷ and Y become homogeneous, and they can be directly compared for change detection. How to efficiently estimate the mapping image plays a crucial role in this change detection method. A new homogeneous pixel transformation (HPT) method is introduced here to carry out the estimation of mapping image. Some unchanged regions in the pair of images X and Y are selected at first as prior knowledge for HPT, and the selected unchanged pixel pairs are denoted by T ={(x n, y n ), n = 1,...,N}. It is worth noting that we just know that these selected pixels are not seriously affected by the event, but we have no idea what the content of each pixel is. So this is very weak prior knowledge, and it cannot be used to train the supervised classifier for image classification. The unchanged regions are usually easy to obtain, and this is convenient for the applications. 4 The other pixels in the image will be 4 In certain cases, the sufficient prior knowledge about various change occurrences may be hard to obtain, but the unchanged regions could be easier to acquire. If the knowledge on some changed regions becomes available, it can be taken into account as the prior constraints to improve the performance of change detection, and it can be also used as validation data to optimize the method. transferred from one feature space to another space based on these selected unchanged pixel pairs. In HPT, we can do the forward transformation to transfer the pre-event image X to the feature space Y in which the post-event image Y is represented, and we can also do the backward transformation to associate the post-event image Y with the space X corresponding to the pre-event image X in the similar way. Let us consider the forward transformation at first, and it is assumed the images with accurate registration. 5 For each pixel x i in the image X, its actual corresponding pixel located at the same position as x i in the post-event image Y is given by y i, and the estimation of its mapping pixel described in the space of Y is denoted by ŷ i. In heterogeneous images, some pixels have very close values in the pre-event image (e.g. SAR image), but their corresponding pixel values are more or less different in the post-event image (e.g. SPOT image) even when they are not affected by the event. Such uncertainty is mainly caused by noisy influence and difference of modalities of images, and it often yields false alarms in change detection. This brings a big challenge for the accurate transformation of pixels. In this work, we propose a multi-value estimation strategy using K -nearest neighbors (K-NN) technique to deal with the uncertainty of pixel transformation. We find the K-NN of x i from the prior unchanged pixels in the preevent image as ẋ i, i = 1,...,K with the corresponding pixels in the post-event image as ẏ k, k = 1,...,K. Each of ẏ k, k = 1,...,K can be considered as a potential estimation of the mapping pixel ŷ i. Thus, the K pixels ẏ k, k = 1,...,K provide multiple estimations (i.e. potential range) for ŷ i. Hence, the value of mapping pixel ŷ i can be approximated by the weighted sum of ẏ i, i = 1,...,K,and it is given by eq. (1). 6 ŷ i = K w k ẏ k (1) k=1 The determination of the weighting factors w k, k = 1,...,K in (1) is a key point in the calculation of the mapping pixel ŷ i. There exist some related methods to calculate the weighting factors w k, k = 1,...,K in field of pattern classification. For example, in the incomplete pattern classification problem, the missing attributes values can be imputed based on the known attributes using the K-NN technique [37], [38]. It is considered that if the known attribute values of one pattern is quite close to another pattern (training data), its missing part should be also very close to the corresponding part of 5 In this work, we mainly focus on the change detection method for heterogeneous images on the basis of accurate registration. The image registration remains an important research topic, and there have been many methods developed for image registration. For example, the resampling techniques (e.g. Nearest-Neighbor resampling, Bilinear resampling) are usually employed in the registration of images with different resolutions and scales, and the cross correlation and mutual information are often used for the image geometrical registration. The Bilinear resampling and mutual-information-based method are applied here for image registration in the pre-processing step, and it can be implemented with ENVI software. 6 The linear model is often used for data estimation, like the K-NN based missing data imputation [37], [38], sparse representation, etc. It is simple, but it works well.

4 LIU et al.: CHANGE DETECTION IN HETEROGENOUS REMOTE SENSING IMAGES VIA HPT 1825 Fig. 1. Illustration of the pixel mapping without change. Fig. 2. ERS and SPOT images of Gloucester UK: (a) ERS image acquired before a flood; (b) SPOT image acquired after a flood. this training pattern. So the K-NN of the incomplete pattern are found according to the known attributes, and the missing attributes of this pattern will be filled by the weighted average of selected K neighbors. The weighting factors are usually calculated according to the distance between the pattern and the selected neighbors in the known attributes. The bigger distance leads to the smaller weighting factor. In the change detection of heterogeneous images, the realistic situation is very complicated. Some pixels are closer to x i than other pixels in the pre-event image, but their corresponding pixels may be not so close to y i as these other pixels in the post-event image because of the noisy influence and the heterogeneousness of observations. This can be explicitly shown by the Fig. 1. One can see from Fig.1 that ẋ 1 is closer to x 0 than ẋ 2 in the 1 st feature space (i.e. gray space of ERS image), but its corresponding pixel ẏ 1 is not so close to y 0 as ẏ 2 in the 2 nd feature space (i.e. three spectral bands of SPOT image). Such phenomenon can be encountered in the multi-temporal heterogeneous images. Let us consider a pair of real images (i.e. ERS and SPOT) shown by Fig.2. ERS image and SPOT were acquired before and after the flood respectively, but this area in the image was not seriously affected by the flood. We can see that the pixels of the selected small region (up) in ERS image are all in black color, but their corresponding pixels in SPOT image are with different colors (e.g. black and red). The selected pixels of SPOT image (down) are in green, but their corresponding pixels in ERS image have different values (e.g. black and gray). This real example shows that the pixels with close values in one image may have more or less different values in another image even if the event to be detected does t happen. In such case, if we calculate the weighting factors w k in eq. (1) according to the distances between the pixel x i and its neighbors ẋ k, k = 1,...,K in the 1 st image as done in the traditional way, the estimated mapping pixel value ŷ i must be the closest to the pixel (say ẏ 1 ) whose corresponding pixel (say ẋ 1 )inthe1 st space is the nearest neighbor of x i.however, the pixel ẏ 1 may be not very close to the actual pixel y i in the selected K neighbors ẏ k, k = 1,...,K, and this is very likely to cause false alarm when we perform the comparison between the mapping image Ŷ and the actual 2 nd image Y for change detection. Thus, we have to develop a new method to calculate the weighting factors. In the K pixels {ẏ k, k = 1,...,K }, there usually exist several ones close to ŷ i if there is no change occurrence. So we propose to calculate the weighting factors w k according to the distances between actual pixel value y i and the K selected pixels ẏ k, i = 1,...,K in the post-event image. The smaller distance of ẏ k to y i, the bigger weight of ẏ k (i.e. w k ). The pixels close to y i will play an important role in the determination of mapping pixel ŷ i, and the estimated ŷ i will be close to truth (i.e. y i ) if this pixel is not seriously affected by the event. As shown in Fig. 1, the pixel ẏ 2 will be assigned much bigger weight than the others in the estimation of the mapping pixel say ŷ 0. So the estimated ŷ 0 is very close to y 0. If there are several noisy pixels included in the set {ẏ k, k = 1,...,K }, the noisy pixels usually are far from y i due to the influence of noise. Hence, the noisy pixels will be given small weights and they generally have little influence on the determination of ŷ i. The estimation of ŷ i mainly depends on the pixels close to y i. The range of the K pixels (i.e.ẏ k, k = 1,...,K ) in fact provides a certain tolerance to the noisy changes. So this multi-value estimation method is robust to the noisy influence, and it is very helpful to reduce false alarms in change detection. In the estimation of the mapping pixel value ŷ i by eq. (1), the exponential function often used in the weighted K-NN classifier [39] is employed here to calculate the weighting factor of each selected pixel ẏ k, k = 1,...,K. w k = e γ d k (2) where γ is a tuning parameter to control the distance influence in the calculation of weighting factor, and determination of the parameter will be explained later. For convenience of applications, d k is defined by the normalized (relative) distance measure as d k = y i ẏ k (3) max k y i ẏ k where represents the normal Euclidean distance. The estimated mapping pixel value ŷ i will be close to the selected pixels that are very near to y i. If the pixel y i is seriously affected by the event, the actual pixel y i generally will become far from all the K selected pixels ẏ k, k = 1,...,K. Because the mapping pixel ŷ i defined by the weighted sum of ẏ k, k = 1,...,K as eq. (1) and (2) always lies around these K selected pixels, the distance between ŷ i and y i will be also very large. This is clearly illustrated by Fig. 3. One can see that the actual pixel y 0 is quite far from the three selected pixels ẏ 1, ẏ 2, ẏ 3, and the

5 1826 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 Fig. 3. Illustration of the pixel mapping with change occurence. mapping pixel ŷ 0 determined by the weighted average of ẏ 1, ẏ 2, ẏ 3 is also very far from y 0. In general, when the weights of ẏ k, k = 1,...,K are determined according to the distance between y i and ẏ k as eq. (2), the estimated mapping pixel ŷ i will be very close to y i if the pixel is not affected by the event, whereas ŷ i will be far from y i if the change happens. Thus, the changed and unchanged pixels can be identified based on the difference value between y i and ŷ i. d Y i =ŷ i y i (4) For the other pixels in the pre-event image, the difference values of their mapping pixels and the actual pixels in the post-event image can be similarly calculated. Thus, one gets the difference image (DI) between Ŷ and Y. III. FUSION OF PIXEL TRANSFORMATION In the heterogeneous images, the noisy influence and the difference of modalities of images could be very large for some pixels in certain case. Then the K selected pixels with close values to x i in the pre-event image could be all far from y i (corresponding to x i ) in the post-event image even if there is no change occurrence. In such case, it is very likely to cause false detection only based on the pixel transformation in one direction (i.e. froward transformation). If we do the opposite transformation say backward transformation to associate y i with the feature space X of the pre-event image, some pixels with close values to y i in the post-event image may be also with close values to the x i in the pre-event image. Hence, the fusion of forward and backward pixel transformation will further improve the robustness of change detection. The backward transformation to associate the post-event image Y with the feature space X can be similarly done as the forward transformation. Then, we can get one more difference value between the mapping pixel ˆx i and the actual one x i. d X i =ˆx i x i (5) For the pixel index i, the integrated difference value for change detection is given by d i = d Y i + d X i (6) If the pixel is affected by the event, both values of d Y i and di X will be big, and the sum of d Y i and di X in eq. (6) will become bigger. If there is no change and the noisy influence is low, both values of d Y i and di X should be small. So the combination (sum) of d Y i and di X as eq.(6) will make the gap of difference values between the changed and unchanged pixels become bigger, and this is more convenient for change detection. If the change doesn t happen but the noisy influence (or the heterogeneousness of images) is quite large, it usually has that one of the values say d Y i is big. This indicates that the K selected neighbors have close values to x i, but their corresponding pixels are quite different from y i in the post-event image. Nevertheless, in the opposite pixel transformation, there may exist some pixels from the K nearest neighbors of y i also with close values to x i in the pre-event image, and then the difference value say di X will be small. In such case, the sum of d Y i and di X will not be so big. This fusion procedure can efficiently make use of the complementary information from the forward and backward pixel transformations, and it is very helpful to reduce the false alarms caused by the noisy influence (or heterogeneousness of images). Fuzzy c-means (FCM) clustering method [30] is employed to divided the pixels into two clusters (i.e. the changed pixels and unchanged pixels) according to the integrated difference values. The output of FCM is the soft membership/probability of the pixel belonging to each cluster. Due to the complex variety of the heterogeneous images, the detection results directly produced by FCM may still contain some noisy regions (e.g. small regions of false alarms and miss detections). The proper modification of this clustering results seems necessary to improve the detection performance. A new noise filter method will be introduced in next section. IV. NOISE FILTER TO IMPROVE THE DETECTION RESULTS In real situations, if one pixel x i is seriously affected by the event, its spatial neighbors located in a small window around x i are also likely affected by the event, and many changed pixels are usually located together. So we want to modify the detection results obtained by FCM for each pixel according to its spatial neighbors. If one pixel is detected as the changed (unchanged) point but its neighbors are mostly unchanged (changed), this pixel is likely considered as noisy point, and its neighborhood information will be used to update the original detection results produced by FCM. We define a small s s square window to determine the spatial neighbors of the pixel x i. Belief functions theory [31], [32] also called Dempster-Shafer theory (DST) or evidence theory provides an efficient tool to deal with the uncertain and ignorant information [34], [35], and it has been well applied in the information fusion [28], [40] [42], pattern recognition [21], [43], parameter estimation [36], and so on. It is employed here to combine the clustering results of the pixel and its neighbors. Some background knowledge about DST is briefly introduced here. A. Basic Knowledge on DST DST works with a framework of discernment = {θ 1,θ 2,...,θ c }, which consists of c mutually exclusive and exhaustive hypotheses. The power-set of denoted by 2 is composed by all the subsets of, and the power-set generally

6 LIU et al.: CHANGE DETECTION IN HETEROGENOUS REMOTE SENSING IMAGES VIA HPT 1827 contains 2 elements. 7 The basic belief assignments (BBA) is a mapping function m(.) from the power-set 2 to [0, 1], and it satisfies m(a) = 1andm( ) = 0. The quantity m(a) A 2 is interpreted as a measure of the belief committed exactly to A. The subsets A of such that m(a) >0 are called the focal elements of m(.). m() denotes the degree of total ignorance. In applications, the multiple sources of evidence represented by different BBA s can be combined using Dempster s rule [31]. Mathematically, Dempster s rule for the combination of two BBA s m 1 (.) and m 2 (.) is defined by m( ) = 0and for A =, A, B, C, X, Y 2 by m(a) = m 1 m 2 m 1 (B)m 2 (C) B C=A = 1 m 1 (X)m 2 (Y ). (7) X Y = Dempster s rule allows to commit the product of the consistent information from two BBA s to their intersection in the combination result. Because Dempster s rule is associative, the combination order has no influence on the final result for combining multiple (more than three) sources of evidence. B. Elimination of Noisy Detections Based on DST Clustering results of these neighbors in the s s window located around the pixel x i are firstly combined by Dempster s rule. This combination result provides one piece of evidence m with a certain weight to indicate the possibility of change happening for the pixel x i according to the neighbors, and it will be further combined with the clustering result (i.e. m i )of the pixel x i to improve the detection performance. In this change detection method, the framework of discernment is defined by = {θ 1 change,θ 2 nonchange}. The clustering result for change detection of one pixel x i can be represented by a basic belief assignment (BBA) m i. m i (θ 1 ) denotes the probability of change happening, whereas, m i (θ 2 ) denotes the probability of nonchange. The BBA s for the s s 1 spatial neighbors located around x i is given by m i,1, m i,2,...,m i,s 2 1. We just consider two elements θ 1 and θ 2 in the framework of discernment here. So Dempster s rule can be simplified in the combination of these N = s 2 1 BBA s corresponding to the N = s s 1 neighbors, and the combination results are given by: g = 1, 2 Nn=1 m i,n (θ g ) m i (θ g ) =. (8) 2 Nn=1 m i,n (θ l ) l=1 Then combination result m i will be fused with the prior detection result m i of the pixel x i. Because m i is an external information source derived from the neighborhoods, it is generally considered with a smaller weight than the prior detection result m i in the fusion. The classical discounting technique introduced by Shafer in [31] will be operated, and the discounted BBA with the given weight number α [0, 1] 7 represents the number of elements (hypotheses) in. is defined by {α m i (θ i ) = α m i (θ i ) α (9) m i () = α m i () + 1 α. In eq. (9), the masses of belief committed to the hypothesizes θ 1 and θ 2 have been discounted to the ignorant element by the weight number α. In fact, m() plays a neutral role in the evidence combination. So this discounting operation has reduced the influence of the evidence m i in the combination with m i. The smaller weight α, the higher ignorance degree of α m i () and the lower influence of m i to m i.ifα = 0, one gets α m i () = 1, which has no influence in the combination with other evidence as α m i m i = m i. The combination of the discounted evidence α m i and m i by Dempster s rule is given by: g = 1, 2 ˆm(θ g ) = α m i m i = α m i (θ g )m i (θ g ) + α m i ()m i (θ g ) 1 α. (10) m i (X)m i (Y ) X Y = The combination result ˆm will be regraded as the updated change detection result for the pixel x i. 1) Discussion: In this work, we mainly focus on the presentation of the new change detection method for heterogeneous images under the assumption that the images are with good registration and the same resolution. In fact, it remains a big challenge for change detection from images with different resolutions and geometry errors. There have been many methods (e.g. geometric rectification techniques, resampling techniques, etc) developed for image registration, and these techniques can be employed in the pre-processing step to make the images suitable for the application of the proposed change detection method. After the pre-processing procedure, there may still exist some registration errors. Of course, the registration errors are harmful for change detection, and they may cause false alarms. Our method is robust to such errors in certain degree. In HPT, a pixel may be linked with its nearby (spatial) neighbor due to the registration error. When the pixel and its neighbors represent the similar contents of land cover in the pre-event image, these pixel values could be quite close, and their corresponding pixel values in the post-event images are usually also close if there is no change happening. In such case, the registration errors will not have big influence on the change detection results, since the pixel and its neighbors have the similar property. If the pixel lies in the border of different contents, it quite likely causes false alarms in change detection. If the registration error is small, the false alarms are usually like the slim edges of the different contents, and these false alarms could be reduced by the proposed spatial-neighbor-based noise filter in general. The computational burden of HPT mainly depends on the number of selected unchanged pixels (i.e. training data) that are used to estimate the mapping image. If there is a big number of training pixels, the estimation accuracy of mapping pixel can be high, but the computational burden will become heavy, because it is time consuming for seeking the K-nearest neighbors from the big training data to calculate

7 1828 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 the mapping pixel. When the high computational speed is necessary in some applications, we can reduce the number of training data in the pre-processing step, e.g. removing the redundant (similar) pixels. In the object-level change detection method (e.g. MDER), the changes are detected based on the comparison (combination) of the classification results of images. The computational speed of object-level method like MDER [29] is usually faster than HPT. However, some useful information could be lost in the image classification process, and this is not good for pursing the good detection performance. The unsupervised CDL method [16] has the relatively high computational complexity, and it is very time consuming for sample selection with the iterative scheme and the dictionary learning in change detection. The computational speed of CDL generally is lower than HPT, since some supervised knowledge (i.e. unchanged pixels) is taken into account in HPT. HPT provides a proper compromise between computational burden and detection accuracy. 2) Guideline of Parameter Tuning: There are several important parameters involved in this change detection method, i.e. the number of K for selecting the close pixels from training data, the distance penalized coefficient γ and the discounting factor α. The bigger K value as well as γ value will make the estimated mapping pixel closer to the actual pixel. So the big values of K and γ can efficiently reduce false alarms, but it may increase the missing detections. The big K value also leads to heavy computational burden. However, if the values of K and γ are too small, it will cause many errors. The K value mainly depends on the roughness of images. If the similar contents in the pair of images have the close pixel values, then a small K value should be good to produce the mapping image. Otherwise, one must take a big K value to ensure that the suitable pixels can be found from the K neighbors to well estimate the mapping image. α is mainly used for eliminating the noisy pixels. If α is rather big, it can efficiently remove the noisy pixels, but it may also erode the edge between the changed and unchanged regions, which will increase the missing detections. The value of α is also related with the neighborhood window size in the noise filter. When the window size is big, one should take a small α value to control the influence of neighbors in the modification of the original detection results. The proper value of α (0, 1) should produce an acceptable compromise between the elimination of noise and increasement of missing detections. The cross validation technique can be applied to optimize the parameters using training data. A part of training data is considered as the validation data that is treated by proposed HPT method, and the proper parameter value should correspond to the good result. V. EXPERIMENT APPLICATIONS A. Experiment 1: Change Detection With ERS&SPOT Images A pair of heterogenous images, i.e. an ERS and a SPOT image of size , is considered for change detection here. ERS image was acquired over Gloucester, UK before a flood occurred on Oct. 21, 1999, and SPOT image was obtained after the flood in For ERS image, the ground humidity induced a lack of backscattering and a strong wind increased surface roughness. The ERS image and SPOT image as shown in Fig. 4-(a)-(b) are with good registration. The ERS radar image is despeckled by a refined Lee filter [44] with a 7 7 sliding window. The SPOT image is represented by three spectral bands, and the texture information is also considered using the variance of the near infra red band through a 3 3 sliding window. The binary image of ground truth for changes is shown in Fig. 4-(c). This ground truth is generated by manual mapping taking into account the expert knowledge and prior information (i.e. on-the-spot investigation). In the experiments, several methods will be applied for change detection. The first one is change detection with the mapping image estimated by the traditional method as done in the incomplete pattern classification [38], and weighting factors in eq. (2) are determined based on the distances between the original pixel (e.g. x i ) and its K nearest neighbors x k. This can be called traditional estimation method for mapping image denoted by TEMI for short. The second one is our previously developed multi-dimensional evidential reasoning (MDER) method [29] for change detection of heterogeneous remote sensing images in object level. Each image is unsupervised/supervised classified, and then the classification results will be combined by MDER to detect the changes. The supervised image classification highly relies on the selected training data, which is not convenient for the application. The unsupervised clustering method FCM is adopted here as similarly done in [29]. The recent unsupervised coupled dictionary learning (CDL) method [16] is also included here to be compared with the proposed HPT method. Five frequently used measures are considered here as the evaluation criteria, such as the accuracy rate R a = (n a +n c )/T (n a being the number of changed pixels correctly detected, n c being the number of unchanged pixels correctly recognized, and T being the total number of test pixels), precision rate R p = n a /N d (N d being the total number of changed pixels detected by the method), the missing rate R m = n m /N c (n m being the number of non-detected pixels of changes and N c being the total number of changed pixels in ground truth), the false alarm rate R f = n f /N d (n f being the number of false alarm pixels) and the Kappa index K a, which is commonly used to comprehensively characterize the quality of classification results with respect to the change detections. The selected unchanged regions in ERS and SPOT are shown in Fig. 5-(a)-(b), and these pixels are used as training data to estimate the mapping images, i.e. the transformation of ERS image to SPOT feature space and the transformation of SPOT image to ERS feature space. These pixels are manually selected. There are 2177 training pixels and test pixels. A part of training data can be used as the validation data set to optimize the parameters in HPT, and the proper parameter value should correspond to the high estimation accuracy of mapping pixels. The good results can be obtained here with admissible computational burden when one has the distance penalized factor γ = 100 and the number of selected nearest neighbors K = 300. The detection performance curves of HPT with different discounting factors α [0, 1] and different

8 LIU et al.: CHANGE DETECTION IN HETEROGENOUS REMOTE SENSING IMAGES VIA HPT 1829 Fig. 4. ERS and SPOT Images of Gloucester UK: (a) ERS image acquired before the flood; (b) SPOT image acquired after the flood; (c) Ground truth of changes. Fig. 5. Selected unchanged regions in ERS and SPOT images: (a) Selected pixels in ERS; (b) Selected pixels in SPOT. Fig. 7. Change detection results of ERS & SPOT with the methods TEMI(-1) and HPT(-2): (a-1/2) Combined difference image by TEMI/HPT; (b-1/2) Comparison of detection result by TEMI/HPT with ground truth (white: change occurrences, red: missing detections, green: false alarms, black: unchanged regions.). Fig. 6. Detection performance of HPT for ERS & SPOT image with different discounting factors α: (a) Missing rate and false alarm rate with s = 3; (b) Missing rate and false alarm rate with s = 7; (c) Missing rate and false alarm rate with s = 11; (d) Kappa index with different window sizes. window sizes s {3, 7, 11} in the noise filter are shown by Fig. 6. When the discounting factor α becomes bigger, the spatial neighbors play a more important role in the noise filter, and this is helpful to reduce false alarms. So the rate of false alarms decreases with the increasing of α. Nevertheless, the bigger α causes more missing detections as shown in Fig. 6. Moreover, when the window size s becomes bigger, the missing rate increases faster, and the Kappa index decreases when α is close to one. This is harmful for the change detection especially when the changed regions are very important for us. We have to find a balance between the missing detections and the false alarms according to the actual applications. So we should choose a small value of α if the size of window s is big. It seems that HPT produces good performance with the value of s = 3andα = 0.65, and the corresponding experimental results are reported in the sequel. In order to explicitly show the superiority of the proposed method HPT over the traditional estimation method as TEMI, we present the combined difference image (DI) and detection results of both methods in Fig. 7. The combined DI (i.e. the integration of DI between the actual SPOT image and the estimated mapping images of ERS and DI between the actual ESR image and the mapping images of SPOT) produced by TEMI and HPT are respectively shown in Figs. 7-(a-1) and 7-(a-2). For a good visibility, the difference value is normalized by d i = d i max j d j 255. The changes can be derived from the difference image using FCM and noise filter, and the comparison of the detection result of TEMI and HPT with the ground truth are respectively shown in Figs. 7-(b-1) and 7-(b-2). The quantitative performance evaluation (i.e. accuracy rate R a, precision rate R p, missing rate R m, false alarm

9 1830 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 TABLE I QUANTITATIVE PERFORMANCE EVALUATION FOR CHANGE DETECTION OF ERS & SPOT IMAGES Fig. 8. NDVI image of Gloucester UK: (a) NDVI image acquired before the flood; (b) Unchanged pixels selected in NDVI image. rate R f and Kappa index K a ) of the different methods is illustrated in table I. In order to show the use of fusion of pixel transformation in HPT, the detection results only with forward pixel transformation (FPT) and backward pixel transformation (BPT) are presented. Several different values of K are used here to test its influence on detection results. We can see that the proposed HPT method produces much higher accuracy/precision rate and lower false alarms rate than other methods including TEMI, MDER and CDL. This is mainly thanks to the new KNN-based multi-value estimation strategy and the fusion of the forward and backward pixel transformations. In the traditional estimation method of mapping image TEMI, the mapping image is estimated based on the distances of a pixel value of the ERS image to its K selected neighbors in the transformation of ERS to SPOT space. However, for one pixel closer to the objective pixel than other pixels in the ERS image, its corresponding pixel in SPOT image may be not so close to the objective pixel as other pixels any more even if they are not affected by the event. It is similar in the transformation of SPOT image to ERS space. As a result, this traditional estimation causes too many false alarms between this pair of heterogeneous images. In the object-level change detection method MDER, its detection performance mainly depends on the image classification, which is also a very challenging problem in the processing of remote sensing images. Unfortunately, in the classification procedure, some useful knowledge (for the change detection) about the pixel details may be lost. CDL is an unsupervised method, and it doesn t take into account the training information. Hence, the detection performances of MDER and CDL are not so good as HPT. In HPT, the missing detection rate is the lowest compared with the other methods, and it indicates that the change occurrences have been almost correctly detected by HPT. The Kappa index of HPT is much higher than the other methods, and this means that HPT generally obtains the best detection results. Moreover, HPT as the fusion of FPT and BPT produces better performance than the only FPT or BPT, because HPT efficiently takes advantage of the complementary information between FPT and BPT via the fusion procedure. The different values of K are tested here. We find if K is too big or small, it will causes many false alarms and missing detections. A proper K value should be tuned according to the actual application. This experimental results demonstrate the effectiveness of HPT as well as the belief-based noise filter on overcoming the influence of noise and heterogeneousness of images in change detection. Nevertheless, there still exist some false alarms in HPT, and these false alarms could be reduced if the prior knowledge about location of changed areas or other constraint is available. It is worth noting that one region in the middle bottom of SPOT image is covered by cloud, and this region is considered as changes. If the cloud elimination technique is applied before the change detection, such false alarms will be reduced. B. Experiment 2: Change Detection With NDVI & SPOT Images In this experiment, we use the pre-event NDVI (Normalized Difference Vegetation Index) image and the post-event SPOT image shown in previous subsection for change detection. This NDVI image in Fig. 8-(a) was obtained before the flood in Gloudcester area, and it is defined by the infrared band and near infrared band. The corresponding selected unchanged regions (i.e. training data) in this NDVI image are presented in Fig. 8-(b), and these regions are with the same locations as that in Fig. 5. The parameters of HPT can be optimized in the training data space, and the proper values of K = 300 and γ = 100 are adopted here. The detection performance curves of HPT with the tuning of discounting factors α [0, 1] are shown in Fig. 9. In Fig.9, we find that the rate of false alarm decreases but the missing rate increases when the discounting factor α becomes bigger. Moreover, the missing rate increases faster when the window size s is big, and the Kappa index decreases when α approaches to one. So a proper α value should be chosen to produce a good compromise between false alarms and missing detections. It seems that HPT has good performance with the value of α = 0.65 and s = 3, and the corresponding detection results are given here. The normalized combined difference images produced by TEMI and HPT are shown in Figs. 10-(a-1) and (a-2). The detection results of HPT and TEMI by comparisons with the ground truth are shown in Fig. 10-(b-1) and (b-2), respectively.

10 LIU et al.: CHANGE DETECTION IN HETEROGENOUS REMOTE SENSING IMAGES VIA HPT 1831 TABLE II Q UANTITATIVE P ERFORMANCE E VALUATION FOR C HANGE D ETECTION OF NDVI& SPOT I MAGES ( IN %) Fig. 9. Detection performance of HPT for NDVI & SPOT image with different discounting factors α: (a) Missing rate and false alarm rate with s = 3; (b) Missing rate and false alarm rate with s = 7; (c) Missing rate and false alarm rate with s = 11; (d) Kappa index with different window sizes. Fig. 11. Images of Gloucester UK: (a) SPOT image acquired before the flood; (b) NDVI image acquired after flood. find that the missing rate in TEMI is not very high, since the estimated mapping image in the changed regions are quite different from the actual image. The Kappa index value of HPT is much higher than the other methods, and it means that the detection result of HPT is very consistent with the ground truth. The performance of HPT generally is better than FPT and BPT, and this validates the effectiveness of the fusion of pixel transformation in HPT. Meanwhile, the proper tuning of K value seems necessary for pursuing the best detection performance of HPT. So this experiment shows again the interest of the proposed method for change detection from heterogenous images. C. Experiment 3: Change Detection With SPOT & NDVI Images Fig. 10. Change detection results of NDVI & SPOT with the methods TEMI(-1) and HPT(-2): (a-1/2) Combined difference image by TEMI/HPT; (b-1/2) Comparison of detection result by TEMI/HPT with ground truth (white: change occurrences, red: missing detections, green: false alarms, black: unchanged regions.). The quantitative detection results including accuracy rate Ra, precision rate R p, missing rate Rm, false alarm rate R f and Kappa index K a are given in table II. In table II, it indicates that the accuracy rate and precision rate of HPT is still higher than the other methods. We also The pre-event SPOT image acquired in 1999 and the postevent NDVI image acquired in 2000 over the same region (i.e. Gloudcester area, UK) are used to further test the performance of the proposed method. The SPOT image and NDVI image are shown in Fig. 11. Three spectral bands of SPOT image are considered here. The selected unchanged regions (training data) are still located in the same region as that in Fig. 5. The proper values of parameters can be determined using the training data, and it is set by K = 50, γ = 100 and α = The normalized combined difference images

11 1832 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 a common feature space for the convenience of change detection. Nevertheless, the missing rates of FPT, BPT and HPT are a bit high. The pixel values (before and after the flood) of several small regions along the river are similar to the selected unchanged pixels (i.e. training data), and these changed regions are really difficult to detect. In this experiment, we find that HPT yields good results with the value of K = 50. This value is much smaller that that used in Experiments 1 and 2, since the roughness of the SPOT and NDVI images in this experiment seems much smaller than the images in Experiments 1 and 2. Compared with the other methods, HPT obtains the highest Kappa index. HPT generally produces the best performance thanks to the fusion of FPT and BPT, which can efficiently improve the detection results. Fig. 12. Change detection results of SPOT & NDVI with the methods TEMI(-1) and HPT(-2): (a-1/2) Combined difference image by TEMI/HPT; (b-1/2) Comparison of detection result by TEMI/HPT with ground truth (white: change occurrences, red: missing detections, green: false alarms, black: unchanged regions.). TABLE III QUANTITATIVE PERFORMANCE EVALUATION FOR CHANGE DETECTION OF SPOT& NDVI IMAGES (IN %) produced by TEMI and HPT are presented in Figs. 12-(a-1) and (a-2). The comparisons between the detection results of HPT/TEMI and the ground truth are shown in Fig. 12-(b-1) and (b-2), respectively. The quantitative detection results of different methods are reported in table III, such as accuracy rate R a, precision rate R p, missing rate R m, false alarm rate R f and Kappa index K a. One can see that the proposed pixel transformation methods including FPT, BPT and HPT obtain better results than the other three methods. This is mainly because the proposed method can well transfer the NDVI and SPOT images into VI. CONCLUSION A new change detection method for the heterogeneous remote sensing images has been proposed via homogeneous pixel transformation (HPT). HPT consisting of the forward and backward operations is to associate one image (e.g. SAR image) with the feature space (e.g. spectral space) of another image (e.g. optical image) based on the prior known unchanged pixel pairs. By doing this, the pre-event and postevent images are represented in a common feature space for the convenience of change detection. In heterogeneous images, the pixels with close values in one feature space may have more or less different values in another space due to noisy influence and modality difference, and such uncertainty often causes false detections. A new multi-value estimation method is introduced using K-nearest neighbors (K-NN) technique to cope with the uncertainty in pixel transformation. In forward HPT, for each pixel x in the pre-event image, its K-NN are selected from the prior unchanged pixels according to the pixel value. The K corresponding pixels (i.e. ẏ k, k = 1,...,K ) in the post-event image are all considered as the potential estimations of the mapping of x (i.e. ŷ). So the mapping pixel ŷ is determined by the weighted sum of ẏ k, k = 1,...,K, and the weighting factor of each pixel ẏ k is calculated depending on the distance between ẏ k and the actual pixel value y (corresponding to x) in post-event image. The smaller distance, the bigger weight. Hence, the estimated mapping pixel ŷ will be very close to y if it is not affected by the event. If the change happens, the actual pixel y generally becomes quite far from all the K selected pixels ẏ k, k = 1,...,K, and the estimated value of ŷ is also far from y. So the change is identified according to the difference value between the estimated mapping pixel ŷ and the actual pixel y. Meanwhile, the backward HPT is similarly done to transfer the post-image into the feature space of pre-event image, and one more difference value for each pixel can be obtained. The two difference values are combined in order to further improve the robustness of the detection method against noise and heterogeneousness of images. FCM algorithm is employed for clustering the integrated difference values of all pixels, and the changes are recognized by the clustering results. Nevertheless, it may still contain some noisy points (the small regions of false alarms and missing detections) in this clustering results. A new noise filter is developed based on DST to suppress

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13 1834 IEEE TRANSACTIONS ON IMAGE PROCESSING, VOL. 27, NO. 4, APRIL 2018 [42] N. B. Abdallah, N. Mouhous-Voyneau, and T. Denæux, Combining statistical and expert evidence using belief functions: Application to centennial sea level estimation taking into account climate change, Int. J. Approx. Reasoning, vol. 55, no. 1, pp , [43] Z.-G. Liu, Q. Pan, J. Dezert, and G. Mercier, Hybrid classification system for uncertain data, IEEE Trans. Syst., Man, Cybern., Syst., vol. 47, no. 10, pp , Oct [44] J.-S. Lee, Refined filtering of image noise using local statistics, Comput. Graph. Image Process., vol. 15, no. 4, pp , You He was born in Jilin, China in He received the Ph.D. degree from Tsinghua University, Beijing, China, in He is currently a Professor with the Department of Electronic Engineering, Tsinghua University. He was elected as the Chinese Academy of Engineering Academician in His main research interests focus on information fusion and signal processing. Zhunga Liu was born in Luoyang, China in He received the bachelor s, master s, and Ph.D. degrees from Northwestern Polytechnical University (NPU), Xi an, China, in 2007, 2010, and 2013, respectively, and the Ph.D. degree from Télécom Bretagne, France, in He has been a full-time Professor with the School of Automation, NPU, since His research interest mainly focuses on pattern recognition and information fusion. Gang Li received the B.S. and Ph.D. degrees in electronic engineering from Tsinghua University, Beijing, China, in 2002 and 2007, respectively. Since 2007, he has been with the Faculty of Tsinghua University, where he is currently an Associate Professor with the Department of Electronic Engineering. From 2012 to 2014, he visited Ohio State University, Columbus, OH, USA, and Syracuse University, Syracuse, NY, USA. His research interests include radar imaging and compressed sensing. Gregoire Mercier was born in Paris, France in He received the Engineering degree from Institut National des Telecommunications, France, in 1993, and the Ph.D. degree from the University of Rennes, France, in Since 1999, he has been with Télécom Bretagne, where he is a Professor with the Image and Information Processing Department. His research interests are remote sensing image processing and information fusion. Quan Pan was born in Shanghai, China in He received the bachelor s degree from the Huazhong University of Science and Technology, Wuhan, China, and the master s and Ph.D. degrees from Northwestern Polytechnical University (NPU), Xi an, China, in 1991 and 1997, respectively. He has been a Professor with NPU since 1998, where he has been the Dean of the School of Automation since His main research interests are information fusion and pattern recognition.