New statistical modeling of multi-sensor images with application to change detection Jorge PRENDES Supervisors: Marie CHABERT, Fr´ ed´ eric PASCAL, Alain GIROS, Jean-Yves TOURNERET October 22, 2015
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Outline 1 Introduction 2 Image model 3 Similarity measure 4 Expectation maximization 5 Bayesian non parametric 6 Conclusions J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 2 / 46
Section 1 Introduction
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Introduction Change Detection for Remote Sensing Remote sensing images are images of the Earth surface captured from a satellite or an airplane. Multitemporal datasets are groups of images acquired at different times. We can detect changes on them! J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 3 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Introduction Heterogeneous Sensors Optical images are not the only kind of images captured. For instance, SAR images can be captured during the night, or with bad weather conditions. J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 4 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Introduction Difference Image J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 5 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Introduction Sliding window Images Sliding Window: W Using several windows . . . W Opt W SAR Optical SAR Decision Result H 0 : Absence of change Similarity Measure H 1 : Presence of change d = f ( W Opt , W SAR ) H 0 d ≷ τ H 1 J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 6 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Introduction Similarity measures Statistical similarity measures Estimation of the joint pdf Measure the dependency Non parametric computation between pixel intensities Histogram Correlation Parzen windows Coefficient Based on a parametric modeling Mutual Information Bivariate gamma distribution [1] Others Pearson distribution [2] KL-Divergence Copulas modeling [3] [1] F. Chatelain et al. “Bivariate Gamma Distributions for Image Registration and Change Detection”. In: IEEE Trans. Image Process. 16.7 (2007), pp. 1796–1806. [2] M. Chabert and J.-Y. Tourneret. “Bivariate Pearson distributions for remote sensing images”. In: Proc. IEEE Int. Geosci. Remote Sens. Symp. (IGARSS). Vancouver, Canada, July 2011, pp. 4038–4041. [3] G. Mercier, G. Moser, and S. B. Serpico. “Conditional Copulas for Change Detection in Heterogeneous Remote Sensing Images”. In: IEEE Trans. Geosci. Remote Sens. 46.5 (May 2008), pp. 1428–1441. J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 7 / 46
Section 2 Image model
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model Optical image Affected by additive Gaussian noise I Opt = T Opt ( P ) + ν N (0 ,σ 2 ) 10 � T Opt ( P ) , σ 2 � I Opt | P ∼ N where 5 T Opt ( P ) is how an object with physical properties P would be ideally seen by an optical sensor σ 2 is associated with the noise variance 0 0 1 I Opt Histogram of the normalized image [1] J. Prendes, M. Chabert, F. Pascal, A. Giros, and J.-Y. Tourneret, “A new multivariate statistical model for change detection in images acquired by homogeneous and heterogeneous sensors,” IEEE Trans. Image Process., vol. 24, no. 3, pp. 799–812, March 2015. J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 8 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model SAR image Affected by multiplicative speckle noise (with gamma distribution) I SAR = T SAR ( P ) × ν Γ ( L , 1 L ) 4 � � L , T SAR ( P ) I SAR | P ∼ Γ L 2 where T SAR ( P ) is how an object with physical properties P would be ideally seen by a SAR 0 sensor 0 1 I SAR L is the number of looks of the SAR sensor Histogram of the normalized image J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 9 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model Joint distribution Independence assumption for the sensor noises p( I Opt , I SAR | P ) = p( I Opt | P ) × p( I SAR | P ) 1 I SAR Conclusion Statistical dependency (CC, MI) is not always an 0 0 1 I Opt appropriate similarity measure J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 10 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model Sliding window Usually includes a finite number of objects, K Different values of P for each object Pr( P = P k | W ) = w k 1 p( I Opt , I SAR | W ) = I SAR K � w k p( I Opt , I SAR | P k ) 0 0 1 I Opt k =1 Mixture distribution! J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 11 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model Resulting improvement Goodness of fit of the Performance for image model change detection 1 3 Mixture 0 PD 3 Histogram 20 × 20 Hist. 20x20 Hist. 5x5 0 Mixture 0 1 KS test p-value 0 0 PFA 1 J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 12 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Image model Limitation of dependency based measures Correct detection Incorrect detection J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 13 / 46
Section 3 Similarity measure
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Similarity measure Motivation Parameters of the mixture distribution 1 Can be used to derive I SAR [ T Opt ( P ) , T SAR ( P )] for each object 0 0 1 I Opt � T Opt ( P ) , σ 2 � I Opt | P ∼ N � � L , T SAR ( P ) 1 I SAR | P ∼ Γ P 3 P 4 L P 2 T SAR ( P ) P 1 Related to P 0 0 1 T Opt ( P ) They are all related J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 14 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Similarity measure Distance measure Unchanged regions Changed regions Pixels belong to the same Pixels belong to different object objects P is the same for both P changes from one image images to another � � � � T Opt ( P 1 ) , ˆ ˆ T Opt ( P ) , ˆ ˆ v = ˆ T SAR ( P 2 ) v = ˆ T SAR ( P ) 0 . 3 0 . 3 T SAR ( P ) T SAR ( P ) ✗ ✓ 0 0 0 1 0 1 T Opt ( P ) T Opt ( P ) J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 15 / 46
Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions Similarity measure Manifold For each unchanged window, Several unchanged windows v ( P ) = [ T Opt ( P ) , T SAR ( P )] can be considered as a point . . . on a manifold The manifold is parametric 0 . 3 on P T SAR ( P ) Estimating v ( P ) from pixels with different values of P 0 0 1 will build the manifold T Opt ( P ) [1] J. Prendes, M. Chabert, F. Pascal, A. Giros, and J.-Y. Tourneret, “A new multivariate statistical model for change detection in images acquired by homogeneous and heterogeneous sensors,” IEEE Trans. Image Process., vol. 24, no. 3, pp. 799–812, March 2015. J. Prendes T´ eSA – Sup´ elec-SONDRA – INP/ENSEEIHT – CNES New statistical modeling of multi-sensor images with application to change detection 16 / 46
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