Image change detection using Gaussian mixture model and genetic algorithm

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Abstract

In this paper, we propose a novel method for unsupervised change detection in multi-temporal satellite images of the same scene using Gaussian mixture model (GMM) and genetic algorithm (GA). The difference image data computed from multi-temporal satellite images of the same scene is modelled by using N components GMM. GA is used to estimate the parameters of the GMM. Then, the GMM of the difference image data is partitioned into two sets of distributions representing data distributions of “changed” and “unchanged” pixels by minimizing a cost function using GA. Bayesian inference is exploited together with the estimated data distributions of “changed” and “unchanged” pixels to achieve the final change detection result. The proposed method does not need any parameter tuning process, and is completely automatic. As a case study for the unsupervised change detection, multi-temporal advanced synthetic aperture radar (ASAR) images acquired by ESA Envisat on the recent flooding area in Bangladesh and parts of India brought on by two weeks of persistent rain and multi-temporal optical images acquired by Landsat 5 TM on a part of Alaska are considered. Change detection results are shown on real data and comparisons with the state-of-the-art techniques are provided.

Research highlights

► Unsupervised change detection in temporal images. ► Automated difference image data modelling using Gaussian mixture modelling. ► Parameter estimation using genetic algorithm.

Introduction

Climate change is now widely recognized as the major environmental problem facing the globe. Rising global temperature will bring changes in weather patterns, increased frequency and intensity of extreme weather and rising sea levels. Land changes due to the effects caused from the climate change could be automatically detected using multi-temporal satellite images. Automatically addressing the land changes due to climate change is central to the work of unsupervised change detection methods. Unsupervised change detection is a process that makes a direct comparison of a pair of remote sensing images acquired on the same geographical area at different time instances in order to identify changes that may have occurred.

Remote sensing imagery generally requires certain corrections due to undesirable sensor characteristics and other disturbing effects before performing data analysis. Typical corrections include noise reduction, radiometric calibration, sensor calibration, atmospheric correction, solar correction, topographic correction, and geometric correction [1], [2], [3]. In this paper, we assume that the changes between two images are only caused from the physical changes incurred in the geographical area, and those typical corrections mentioned previously are either playing no issue or having been done on the images before applying the proposed change detection method.

Unsupervised change detection techniques can be categorized into two major classes according to the domain they are applied in: (1) image-domain; and (2) transform-domain. The techniques in image-domain [4], [5], [6] use the statistical data directly extracted from the input images themselves, meanwhile transform-domain techniques [7], [8], [9] use transformations on the input images such as undecimated discrete wavelet transform [7], [9] or dual-tree complex wavelet transform [8] to achieve the unsupervised change detection.

In [4], two automatic techniques based on the Bayes theory for the analysis of the difference image are proposed. One allows an automatic selection of the decision threshold for minimizing the overall change detection error under the assumption that the pixels of the difference image are spatially independent (referred in this paper as expectation maximization (EM)-based method). The other which is based on the Markov random fields (MRFs) analyzes the difference image by considering the spatial-contextual information included in the neighborhood of each pixel (referred in this paper as MRF-based method). The EM-based thresholding is free of parameters, while the MRF-based thresholding depends on the parameter β which influences the spatial-contextual information on the change detection process. In [5], the observed multi-temporal images are modelled as MRFs in order to search for an optimal change image by means of the maximum a posteriori (MAP) probability decision criterion and the simulated annealing (SA) energy minimization procedure. The SA algorithm is used to generate a random sequence of binary change images from which a new configuration is established that depends only on the previous change image and observed images by using the Gibbs sampling procedure [5]. These algorithms are applied in raw-data domain and provide impressive results, but they highly depend on the assumptions employed in modelling the difference image. Furthermore, the iterative solutions for model parameter estimations have the problem of tackling to the local optimum points, which might lead to unexpected results.

Recently, computationally efficient yet effective method for unsupervised change detection is proposed in [6] (referred in this paper as PCA-based method). The method analyzes the difference image by using principal component analysis (PCA) and k-means clustering with k = 2. The k-means clustering is employed on feature vectors to compute the final change detection result. A feature vector for each pixel is extracted by projecting the local change data onto the eigenvector space. The number of eigenvectors determines the dimensionality of the feature vector. The eigenvector space is created by PCA of h × h non-overlapping blocks collected from the entire difference image. The algorithm produces promising results with a low computational cost. It employs PCA for dimension reduction and feature extraction, which is a canonical technique to find useful data representations in compressed space. It finds a set of eigenvectors which are uncorrelated and Gaussian. PCA can only separate pair-wise linear dependencies between data points, because of this reason PCA-based methods may fail in some situations. Besides, it does not consider the multi-scale data fusion for the difference image, so that it is prone to produce false detections due to the noise contaminations.

Transform-domain techniques are applied to reduce the effect of the noise contamination and to analyze the difference image using a multiresolution structure. In [7], undecimated discrete wavelet transform (UDWT)-based multi-scale decomposition of the difference image (log-ratio image which is obtained by taking the logarithm of the pixel ratio of two images) for generating different scales (levels) of representation of the difference image is used. Each scale is characterized by a trade off between speckle noise reduction and preservation of image details. The final change detection result is obtained according to an adaptive scale-driven fusion algorithm. The method achieves good results but has the major disadvantage of the selection of appropriate detection thresholds.

In [8] (referred in this paper as DT-CWT-based method), dual-tree complex wavelet transform (DT-CWT) is used to individually decompose each input image into one low-pass subband and six directional high-pass subbands at each scale. DT-CWT coefficient difference resulted from the six high-pass subbands of the two satellite images under comparison are analyzed in order to decide whether each pixel position belongs to “changed” or “unchanged” class for each subband. Then, the binary change detection mask is formed for each subband, and all the produced subband masks are merged by using both the inter-scale and the intra-scale fusion to yield the final change detection mask. The method is free of parameter selection except the number of decomposition scales used in DT-CWT. Similar to [4], [5], the iterative solution for model parameter estimation may tackle to the local optimum, and may lead the algorithm to produce incorrect results.

Recently, in [9], the difference image is decomposed using S-scales undecimated discrete wavelet transform (UDWT) (referred in this paper as Multiresolution-based method). Then, for each pixel in the difference image a multi-scale feature vector is extracted using the subbands of the UDWT decomposition and the difference image itself. The final change detection mask is achieved by clustering the multi-scale feature vectors using k-means algorithm into two disjoint classes: “changed” and “unchanged”. The method performs very good in detecting adequate changes even in high-level noise contamination cases, but it has problems in detecting accurate region boundaries between “changed” and “unchanged” regions caused from the direct use of subbands from the UDWT decompositions.

All the above mentioned unsupervised change detection methods depend on the parameter selection and/or assumptions in the modelling the difference image computed from the multi-temporal images. Even though, they produce satisfactory results with default parameter selections, they still need handling proper parameter setting scheme and validated assumptions for modelling the difference image. It is well known that the can be used to model any data distribution using an adequate number of Gaussian distributions. In change detection, the main aim is to partition the data from the difference image into two groups “changed” and “unchanged”. The GMM of the difference image data is assumed to be mixture of two distributions modelling “changed” and “unchanged” data. Then each pixel in the difference image is categorized into one of the classes “changed” or “unchanged” according to it’s fit to “changed” or “unchanged” models. The parameters of the GMM is estimated using expectation–maximization and genetic algorithm (GA) [10] and GMM is separated into two distributions representing the data distributions of “changed” or “unchanged” pixels by minimizing a cost function through a simple GA [11]. Recent advances in computing technology makes it possible to perform high-load computations very fast by employing parallel computing with high-powered processors. This motivates us to solve the parameter estimation problem using the evolutionary method rather than using iterative parameter estimation. It is well known that iterative solutions might converge to local optimum and highly dependent on the initialization, but the better solution is guaranteed in the GA.

The paper is organized as follows. Section 2 introduces the unsupervised change detection problem and describes the proposed unsupervised change detection algorithm. Section 3 provides some experimental results of the proposed method and compares with the state-of-the-art methods presented in [4], [6], [8], [9]. Finally, the Section 4 concludes the paper.

Section snippets

Problem definition

Let us consider two satellite images, X1 = {x1(i, j) ∣1  i  H, 1  j  W} and X2 = {x2(i, j) ∣1  i  H, 1  j  W}, of size H × W pixels acquired at the same geographical area but at two different time instances, namely t1 and t2, respectively. Let us further assume that such images have been registered with respect to each other [2]. The main objective of the unsupervised change detection techniques is to generate a binary change detection mask, CM = {cm(i, j) ∣1  i  H, 1  j  W}, where cm(i, j)  {0, 1}, using the difference

Description of dataset

In order to assess the effectiveness of the different change detection methods for the analysis of the difference image, we considered real multi-temporal data sets corresponding to the geographical area of the flooding in Bangladesh and parts of India brought on by two weeks of persistent rain and Alaska.

The first dataset1 contains a set of ASAR images (7503 × 4371 pixels) collected on Bangladesh and parts of

Conclusions

In this paper, we proposed a novel method for unsupervised change detection in multi-temporal satellite images of the same scene using Gaussian mixture model (GMM) and genetic algorithm (GA). The difference image data computed from multi-temporal satellite images of the same scene is modelled by using N components GMM. GA is used to estimate the parameters of the GMM. Then, the GMM of the difference image data is partitioned into two sets of distributions representing data distributions of

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This work was supported by the Singapore Ministry of Education under Grant R-143-000-358-112.

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