آناليز خودكار آشكارسازي تغييرات بر مبناي تصوير اختلاف با استفاده از تركيب مدل آميخته‌ي گاوسي و ميدان‌هاي تصادفي ماركوف

Automatic Change Detection Analysis of the Difference Image Using Gaussian Mixture Model and Markov Random Fields

نبود يك روش خودكار مناسب براي جداكردن پيكسل­هاي تغييريافته و تغييرنيافته، از اصلي­ترين مشكلات مربوط به آشكارسازي تغييرات بر مبناي تصاوير اختلاف است. اين جدايي معمولا به وسيله روش­هاي مبتني بر آزمون و خطا صورت مي­گيرد كه بر روي دقت و درجه اعتمادپذيري فرآيند آشكارسازي تغييرات تاثير گذار است. براي فائق آمدن بر اين مشكل، در اين تحقيق، در ابتدا بر مبناي قضيه بيز و با استفاده از مدل آميخته­ي گاوسي روشي خودكار براي آناليز تصوير اختلاف ارائه شده است كه مي­تواند به انتخاب نقطه­ ي تغيير (حد آستانه) دو كلاس تغييريافته و تغييرنيافته، كمك كند. در اين روش حد آستانه­اي انتخاب مي­شود كه احتمال خطاي كلي آشكارسازي تغييرات را با فرض اينكه پيكسل ­هاي موجود در تصوير اختلاف از يكديگر مستقل هستند، كمينه كند. در گام بعد بر مبناي استفاده از اطلاعات مكاني و همسايگي، از ميدان­هاي تصادفي ماركوف براي بررسي وابستگي بين پيكسل­ها استفاده شده است. روش پيشنهادي بر روي تصاوير ماهواره­اي لندست 8 از شهر حلب سوريه اعمال شده است. نتايج حاصل از اين تحقيق نشان داده است كه استفاده از اطلاعات مكاني به عنوان منبع اطلاعاتي مكمل، سبب بهبود نتايج شناسايي تغييرات مي­شود. همچنين بر اساس نتايج تجربي به­دست آمده، تكنيك پيشنهادي در مقايسه با روش مدل آميخته گاوسي و استفاده از حد آستانه تجربي (كه نتايج نسبتا مشابه ي داشتند) از كارايي و دقت بالاتري برخوردار اس

One of the main problems related to unsupervised change detection methods based on difference image lies in the lack of efficient automatic techniques for discriminating between changed and unchanged pixels in the difference image. Such discrimination is usually performed by manual trial-and-error procedures, which affect both accuracy and the reliability of the change detection process. To overcome such drawbacks, this study proposes two automatic techniques for analysis of the difference image based on Gaussian Mixture model (GMM). The first technique allows an automatic selection of the decision threshold that minimizes the overall change detection error probability under the assumption that pixels in the difference image are independent of one another. The second one analyzes the difference image by considering the spatial-contextual information included in the neighborhood of each pixel. In particular, this study presents an approach based on Markov Random Fields (MRFs) that exploits inter-pixel class dependency contexts. In this study, we define the problem of the analysis of the difference image for unsupervised change detection in terms of the Bayes decision theory. The application of this theory requires the estimations of the a priori probabilities and of the conditional density functions for the classes associated with the unchanged and changed pixels in the difference image. To this end, we present an approach based on Expectation-Maximization (EM) algorithm that allows such estimations to be performed in an unsupervised way. Within this framework, two automatic techniques for the analysis of the difference image are presented that overcome the main problems inherent in classical techniques. One assumes that the gray-level values of the pixels in the difference image are independent of one another. Under this assumption, the Bayes rule for minimum error is applied in order to select the decision threshold that minimizes the overall error probability in the change detection process. The other technique considers the spatial-contextual information contained in the difference image in order to increase the accuracy of the final change detection map. In particular, an approach based on Markov Random Fields (namely GMM-MRF) is proposed that exploits the inter-pixel class dependence to model the prior probabilities of classes. In order to assess the effectiveness of both proposed techniques, we carried out experiments on two different data sets. One was a real multi-temporal data set composed of two multispectral images acquired by the Landsat 8 satellite from Aleppo city. The other was a synthetic data set generated to evaluate the robustness of the proposed techniques against different levels of noise. Three different experiments were carried out to test the validity of the proposed techniques. The first experiment allowed an evaluation of the accuracy and stability of the proposed approach based on the GMM algorithm and the EM algorithm for the estimation of the statistical terms of the a priori probabilities. To this end, the true values of the a priori probabilities were compared by with the estimates obtained by the GMM approach. The second experiment aimed at assessing the effectiveness of the technique for the analysis of the difference image under the assumption of the independent pixel values. The third experiment made it possible to assess the capability of the GMM-MRF that exploits the spatial-contextual information to improve the change detection accuracies provided by the classical thresholding approach. Analytical evaluations of the final maps show the superiority of the GMM-MRF technique on both the simulated data and the real Landsat 8 data set of Aleppo city in terms of the kappa coefficient and the overall accuracy measures. Experimental results obtained on the simulated data show an improvement of about 0.8 and 82% in terms of the kappa coefficient and the overall accuracy, respectively. Also, the results obtained on the real Landsat 8 data set show an improvement of 8% and 4% in terms of the kappa coefficient and the overall accuracy, respectively.