Jorge Prendes

(IRIT, University of Toulouse and SONDRA, CentraleSupelec, FR)

https://s3-seminar.github.io/seminars/jorge-prendes

Title — Analysis of remote sensing multi-sensor heterogeneous images

Abstract — Remote sensing images are images of the Earth acquired from planes or satellites. In recent years the technology enabling this kind of images has been evolving really fast. Many different sensors have been developed to measure different properties of the earth surface, including optical images, SAR images and hyperspectral images. One of the interest of this images is the detection of changes on datasets of multitemporal images. Change detection has been thoroughly studied on the case where the dataset consist of images acquired by the same sensor. However, having to deal with datasets containing images acquired from different sensors (heterogeneous images) is becoming very common nowadays. In order to deal with heterogeneous images, we proposed a statistical model which describe the joint distribution of the pixel intensity of the images, more precisely a mixture model. On unchanged areas, we expect the parameter vector of the model to belong to a manifold related to the physical properties of the objects present on the image, while on areas presenting changes this constraint is relaxed. The distance of the model parameter to the manifold can be thus be used as a similarity measure, and the manifold can be learned using ground truth images where no changes are present. The model parameters are estimated through a collapsed Gibbs sampler using a Bayesian non parametric approach combined with a Markov random field. In this talk I will present the proposed statistical model, its parameter estimation, and the manifold learning approach. The results obtained with this method will be compared with those of other classical similarity measures.

Biography — Jorge Prendes was born in Santa Fe, Argentina in 1987. He received the 5 years Eng. degree in Electronics Engineering with honours from the Buenos Aires Institute of Technology (ITBA), Buenos Aires, Argentina in July 2010. He worked on Signal Processing at ITBA within the Applied Digital Electronics Group (GEDA) from July 2010 to September 2012. Currently he is a Ph.D. student in Signal Processing in SONDRA laboratory at Supélec, within the cooperative laboratory TéSA and the Signal and Communication Group of the Institut de Recherche en Informatique de Toulouse (IRIT). His main research interest include image processing, applied mathematics and pattern recognition.

Transcript

1. Analysis of remote sensing multi-sensor
   heterogeneous images
   Jorge PRENDES
   Marie CHABERT, Fr´
   ed´
   eric PASCAL,
   Alain GIROS, Jean-Yves TOURNERET
   March 20, 2015 – S3 Seminar, Sup´
   elec
   

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2. 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
   Analysis of remote sensing multi-sensor heterogeneous images 2 / 41
   

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3. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Remote Sensing Images
   Remote sensing images are images of the Earth surface captured
   from a satellite or an airplane.
   J. Prendes T´
   eSA – Sup´
   elec-SONDRA – INP/ENSEEIHT – CNES
   Analysis of remote sensing multi-sensor heterogeneous images 3 / 41
   

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4. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Change Detection
   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
   Analysis of remote sensing multi-sensor heterogeneous images 4 / 41
   

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5. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Heterogeneous Sensors
   Optical images are not the only kind of images captured.
   J. Prendes T´
   eSA – Sup´
   elec-SONDRA – INP/ENSEEIHT – CNES
   Analysis of remote sensing multi-sensor heterogeneous images 5 / 41
   

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6. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Heterogeneous Sensors
   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
   Analysis of remote sensing multi-sensor heterogeneous images 6 / 41
   

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7. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Difference Image
   J. Prendes T´
   eSA – Sup´
   elec-SONDRA – INP/ENSEEIHT – CNES
   Analysis of remote sensing multi-sensor heterogeneous images 7 / 41
   

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8. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Difference Image
   J. Prendes T´
   eSA – Sup´
   elec-SONDRA – INP/ENSEEIHT – CNES
   Analysis of remote sensing multi-sensor heterogeneous images 7 / 41
   

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9. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
   Introduction
   Sliding window
   Optical SAR
   Images
   WOpt
   WSAR
   Sliding Window: W
   d = f(WOpt
   , WSAR
   )
   Similarity Measure
   H0
   : Absence of change
   H1
   : Presence of change
   d
   H0
   ≷
   H1
   τ
   Decision
   . . .
   Using several
   windows
   Result
   J. Prendes T´
   eSA – Sup´
   elec-SONDRA – INP/ENSEEIHT – CNES
   Analysis of remote sensing multi-sensor heterogeneous images 8 / 41
   

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10. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Correlation coefficient
    d = f (W1
    , W2) =
    E[(W1 − µW1
    )(W2 − µW2
    )]
    E (W1 − µW1
    )2 E (W2 − µW2
    )2
    no change
    change
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 9 / 41
    

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11. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Correlation coefficient
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 10 / 41
    

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12. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Correlation coefficient
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 10 / 41
    

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13. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Mutual information
    d = f (W1
    , W2) =
    w1∈W1 w2∈W2
    p(w1
    , w2) log
    p(w1
    , w2)
    p(w1)p(w2)
    no change
    change
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 11 / 41
    

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14. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Mutual information
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 12 / 41
    

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15. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Introduction
    Mutual information
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 12 / 41
    

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16. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Image model
    Optical image
    Affected by additive
    Gaussian noise
    IOpt = TOpt(P) + νN(0,σ2)
    IOpt|P ∼ N TOpt(P), σ2
    where
    TOpt(P) is how an object with physical
    properties P would be ideally seen by an
    optical sensor
    σ2 is associated with the noise variance
    0 1
    0
    5
    10
    IOpt
    Histogram of the normalized image
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 13 / 41
    

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17. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Image model
    SAR image
    Affected by multiplicative
    speckle noise (with gamma
    distribution)
    ISAR = TSAR(P) × ν
    Γ(L, 1
    L
    )
    ISAR|P ∼ Γ L,
    TSAR(P)
    L
    where
    TSAR(P) is how an object with physical
    properties P would be ideally seen by a SAR
    sensor
    L is the number of looks of the SAR sensor
    0 1
    0
    2
    4
    ISAR
    Histogram of the normalized image
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 14 / 41
    

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18. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Image model
    Joint distribution
    Independence assumption
    for the sensor noises
    p(IOpt
    , ISAR|P) =
    p(IOpt|P) × p(ISAR|P)
    Conclusion
    Statistical dependency
    (CC, MI) is not always an
    appropriate similarity
    measure
    0 1
    0
    1
    IOpt
    ISAR
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 15 / 41
    

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19. 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 = Pk|W ) = wk
    p(IOpt
    , ISAR|W ) =
    K
    k=1
    wkp(IOpt
    , ISAR|Pk)
    Mixture distribution!
    0 1
    0
    1
    IOpt
    ISAR
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 16 / 41
    

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20. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Motivation
    Parameters of the mixture distribution
    Can be used to derive
    [TOpt(P), TSAR(P)] for each
    object
    IOpt P ∼ N TOpt(P), σ2
    ISAR|P ∼ Γ L,
    TSAR(P)
    L
    Related to P
    They are not independent
    0 1
    0
    1
    IOpt
    ISAR
    0 1
    0
    1
    P1
    P2
    P3 P4
    TOpt (P)
    TSAR (P)
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 17 / 41
    

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21. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Manifold
    For each unchanged window,
    v(P) = [TOpt(P), TSAR(P)]
    can be considered as a point
    on a manifold
    The manifold is parametric
    on P
    Estimating v(P) from pixels
    with different values of P
    will trace the manifold
    Several
    unchanged windows
    . . .
    0 1
    0
    0.3
    TOpt (P)
    TSAR (P)
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 18 / 41
    

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22. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Distance to the manifold
    Unchanged regions
    Pixels belong to the same
    object
    P is the same for both
    images
    ˆ
    v = ˆ
    TOpt(P), ˆ
    TSAR(P)
    0 1
    0
    0.3
    TOpt
    (P)
    TSAR
    (P)
    
    Changed regions
    Pixels belong to different
    objects
    P changes from one image
    to another
    ˆ
    v = ˆ
    TOpt(P1), ˆ
    TSAR(P2)
    0 1
    0
    0.3
    TOpt
    (P)
    TSAR
    (P)
    
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 19 / 41
    

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23. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Manifold estimation
    The manifold is a priori
    unknown
    We must estimating the
    distance to the manifold
    PDF of v(P)
    Good distance measure
    Learned using training
    data from unchanged
    images
    0 1
    0
    0.3
    TOpt
    (P)
    TSAR
    (P)
    →
    0 1
    0
    0.3
    TOpt (P)
    TSAR (P)
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 20 / 41
    

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24. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Manifold estimation
    The manifold is a priori
    unknown
    We must estimating the
    distance to the manifold
    PDF of v(P)
    Good distance measure
    Learned using training
    data from unchanged
    images
    0 1
    0
    0.3
    TOpt
    (P)
    TSAR
    (P)
    →
    0 1
    0
    0.3
    TOpt (P)
    TSAR (P)
    H0 : Absence of change
    H1 : Presence of change
    ˆ
    pv (ˆ
    v)−1
    H1
    ≷
    H0
    τ
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 20 / 41
    

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25. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Similarity measure
    Summary
    WOpt WSAR
    Sliding Window: W
    Mixture
    µ1
    , σ2
    1
    , k1
    , α1
    θ1
    :
    TS1
    (P1), TS2
    (P1)
    vP1
    :
    µ4
    , σ2
    4
    , k4
    , α4
    θ4
    :
    TS1
    (P4), TS2
    (P4)
    vP4
    :
    . . .
    . . .
    0 1
    0
    0.3
    P1
    P2
    P3 P4
    TS1 (P)
    TS2 (P)
    Manifold Samples
    . . .
    0 1
    0
    0.3
    TOpt (P)
    TSAR (P)
    Using several
    windows
    0 1
    0
    0.3
    TOpt (P)
    TSAR (P)
    Manifold Estimation
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 21 / 41
    

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26. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Expectation maximization
    Motivation
    To estimate v(P) we must estimate the mixture parameters θ
    We can use a maximum likelihood estimator
    θ = arg max
    θ
    p(IOpt
    , ISAR|θ)
    Two pixels iOpt,n and iSAR,m are not independent
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 22 / 41
    

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27. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Expectation maximization
    Algorithm
    The class labels Z make the pixels independent
    p(IOpt
    , ISAR|θ, Z) =
    N
    n=1
    p(iOpt,n
    , iSAR,n|θ, zn)
    where we have N pixels in the window
    Now we also have to estimate Z
    θ = arg max
    θ
    p(IOpt
    , ISAR|θ, Z)
    =
    N
    n=1
    log [p(iOpt,n
    , iSAR,n|θ, zn)]
    Z can take NK different values
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 23 / 41
    

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28. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Expectation maximization
    Algorithm
    Iterative algorithm, estimate θ(i) using θ(i−1)
    p z(i)
    n
    = k =
    p iOpt,n, iSAR,n θ(i−1), zn = k
    K
    j=1
    p iOpt,n, iSAR,n θ(i−1), zn = j
    θ(i) =
    N
    n=1
    log
    
    
    K
    j=1
    p iOpt,n, iSAR,n θ(i−1), zn = j × p z(i)
    n
    = j
    
    
    The value of K is fixed
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 24 / 41
    

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29. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Synthetic Optical and SAR Images
    Synthetic optical image Synthetic SAR image
    Change mask
    Mutual
    Information
    Correlation
    Coefficient
    Proposed Method
    0 1
    0
    1
    PFA
    PD
    Proposed
    Correlation
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 25 / 41
    

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30. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Real Optical and SAR Images
    Optical image
    before the
    flooding
    SAR image during
    the flooding
    Change mask
    [1] G. Mercier, G. Moser, and S. B. Serpico, “Conditional copulas
    for change detection in heterogeneous remote sensing images,”
    IEEE Trans. Geosci. and Remote Sensing, vol. 46, no. 5, pp.
    1428–1441, May 2008.
    Mutual
    Information
    Conditional
    Copulas [1]
    Proposed Method
    0 1
    0
    1
    PFA
    PD
    Proposed
    Copulas
    Correlation
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 26 / 41
    

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31. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Pl´
    eiades Images
    Pl´
    eiades – May 2012 Pl´
    eiades – Sept. 2013
    Change mask
    Special thanks to CNES for providing the Pl´
    eiades images
    Change map
    0 1
    0
    1
    PFA
    PD
    Proposed
    Correlation
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 27 / 41
    

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32. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Pl´
    eiades and Google Earth Images
    Pl´
    eiades – May 2012 Google Earth – July 2013
    Change mask
    Change map
    0 1
    0
    1
    PFA
    PD
    Proposed
    Correlation
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 28 / 41
    

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33. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results
    Homogeneous images
    Pl´
    eiades – Pl´
    eiades
    0 1
    0
    1
    PFA
    PD
    Proposed
    Correlation
    Mutual Inf.
    CC and MI
    Similar performance
    Proposed method
    Improved performance
    Heterogeneous images
    Pl´
    eiades – Google Earth
    0 1
    0
    1
    PFA
    PD
    Proposed
    Correlation
    Mutual Inf.
    CC
    Reduced Performance
    Proposed method and MI
    Performance not affected
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 29 / 41
    

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34. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Motivation
    Introduce a Bayesian framework into the labels: K is not fixed
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 30 / 41
    

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35. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Motivation
    Introduce a Bayesian framework into the labels: K is not fixed
    Classic mixture model
    in|vn ∼ F(vn)
    vn V ∼
    K
    k=1
    wk
    δ vn − vk
    in = iOpt,n, iSAR,n , and F is a distribution family which is application dependent, i.e., a bivariate
    Normal-Gamma distribution.
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 30 / 41
    

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36. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Motivation
    Prior in the mixture parameters
    vk
    ∼ V0
    w ∼ Dir αK−1uK
    Now make K → ∞
    vn
    will still present clustering behavior
    There are infinite parameters for the prior of vn
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 31 / 41
    

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37. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Bayesian non parametric
    Dirichlet Process
    in|vn ∼ F(vn)
    vn ∼ V
    V ∼ DP(V0
    , α).
    in|zn ∼ F vzn
    z ∼ CRP(α)
    vk
    ∼ V0
    .
    Algorithm
    For n ≥ 1
    u ∼ Uniform(1, α + n)
    If u < n
    vn ← v u
    Else
    vn ∼ V0
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 32 / 41
    

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38. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Markov random fields
    Markov random fields are a common tool to capture spatial
    correlation
    We would like to define
    p zn z\n
    = p zn zδ(n)
    MRF define the constraints to define a joint distribution p(Z)
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 33 / 41
    

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39. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Bayesian non parametric
    Markov random fields
    We will define out joint distribution as
    p zn z\n
    ∝ exp H zn z\n
    H zn z\n
    = Hn(zn) +
    m∈δ(n)
    ωnm 1zn
    (zm)
    = Hn(zn) +
    m∈δ(n)
    zn=zm
    ωnm
    The trick is to take Hn(zn) = log p(zn|In
    , V )
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 34 / 41
    

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40. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Synthetic Optical and SAR Images
    Synthetic optical image Synthetic SAR image
    Change mask
    Mutual
    Information
    EM BNP
    0 1
    0
    1
    PFA
    PD
    BNP-MRF
    EM
    Correlaton
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 35 / 41
    

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41. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Real Optical and SAR Images
    Optical image
    before the
    flooding
    SAR image during
    the flooding
    Change mask
    Mutual
    Information
    EM BNP
    0 1
    0
    1
    PFA
    PD
    BNP-MRF
    EM
    Copulas
    Correlaton
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 36 / 41
    

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42. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Pl´
    eiades Images
    Pl´
    eiades – May 2012 Pl´
    eiades – Sept. 2013
    Change mask
    Special thanks to CNES for providing the Pl´
    eiades images
    EM BNP
    0 1
    0
    1
    PFA
    PD
    BNP-MRF
    EM
    Correlaton
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 37 / 41
    

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43. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Results
    Results – Pl´
    eiades and Google Earth Images
    Pl´
    eiades – May 2012 Google Earth – July 2013
    Change mask
    EM BNP
    0 1
    0
    1
    PFA
    PD
    BNP-MRF
    EM
    Correlaton
    Mutual Inf.
    Performance – ROC
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 38 / 41
    

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44. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Conclusions
    Conclusions and Future Work
    Conclusions
    New statistical model to describe multi-channel images
    Analyze the joint behavior of the channels to detect changes,
    in contrast with channel by channel analysis
    e.g., Pl´
    eiades multi-spectral and panchromatic images
    New similarity measure showing encouraging results for
    homogeneous and heterogeneous sensors
    Pl´
    eiades–Pl´
    eiades
    Pl´
    eiades – SAR
    Pl´
    eiades – Other VHR instument
    Interesting for many applications
    Change detection
    Registration
    Segmentation
    Classification
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 39 / 41
    

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45. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Conclusions
    Conclusions and Future Work
    Future Work
    Study the method performance for different image features
    Texture coefficients: Haralick, Gabor, QMF
    Wavelet coefficients
    Gradients
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 40 / 41
    

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46. Introduction Image model Similarity measure Expectation maximization Bayesian non parametric Conclusions
    Conclusions
    Thank you for your attention
    Jorge Prendes
    jorge.prendes@tesa.prd.fr
    J. Prendes T´
    eSA – Sup´
    elec-SONDRA – INP/ENSEEIHT – CNES
    Analysis of remote sensing multi-sensor heterogeneous images 41 / 41
    

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