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A COMPUTATIONALLY EFFICIENT METHOD FOR
SEQUENTIAL MAP-MRF CLOUD DETECTION




     Paolo Addesso, Roberto Conte, Maurizio Longo,
           Rocco Restaino and Gemine Vivone

          University of Salerno, D.I.E.I.I., Fisciano, Italy;
       e-mail {paddesso,rconte,longo,restaino,gvivone}@ unisa.it
OUTLINE

   Introduction

   Cloud detection
       Penalty 3D Model


   Cloud tracking
       Region matching


   Experimental results

   Conclusions and future developments   2
PROBLEM TACKLED
   The classification consists in separating entities in a
    given knowledge domain into knowledge classes.

   Classification: cloud / clear sky

   Sensor used: SEVIRI




                                                              3
WHY CLOUD DETECTION ?


   The presence of clouds              drastically   affects
    measures of optical signals

   International Satellite Cloud Climatology Project
    ISCCP-FD data set give a cloud cover around 66%

   Many applications need a cloud masking phase
       Example: fire detection, ocean color



                                                                4
STATE OF ART


   Static thresholds

   Methods based on spatial coherence
       Markov Random Fields


   Adaptive thresholds
       A series of threshold tests depending on the variation
        of the surface type and of the solar illumination


   Machine learning tools
       Fuzzy logic, artificial neural networks or kernel        5
        methods
OUTLINE

   Introduction

   Cloud detection
       Penalty 3D Model


   Cloud tracking
       Region matching


   Experimental results

   Conclusions and future developments   6
RANDOM FIELD AND MAP ESTIMATION


   We define a random field F = {F1, … , Fm} as a
    family of random variables defined on a set of
    sites S in which each component Fi assumes a
    value fi in the label set L

   Estimator:
           ˆ
           f MAP  arg max       p f |d ( f | d )
                         f

                             pd,f (d,f )
            arg max   log
                  f           pd (d )
                                                     7
            arg max {log p(d | f )  log p( f )}
                  f
MARKOV RANDOM FIELD (MRF)

   F is a Markov Random Field if:                    P( f i | f S {i} )  P( f i | f Ni )
    Note: Ni is the neighbourhood of the pixel “i”.




                                                                                       8
CLASSIFICATION WITH MRF

   Given     the    Markovian      hypothesis, the
    Hammersley-Clifford theorem states that for the
    a priori probability can be expressed as:
                           1
                   p( f )  exp[  U ( f )]
                           Z
 A similar likelihood form is commonly used:

                     p(d | f )  exp[ U (d | f )]

   Hence the a posteriori density is:
       p( f | d )  exp[U ( f | d )]  exp[U (d | f )  U ( f )]
                                                                     9
MRF AND MAP CRITERIA

   The minimum error probability is given by the
    MAP estimator:
             ˆ
             f  arg max [ p( f | d )]  arg min [U ( f | d )]
                      f                        f

   Under    the   hypothesis      of   conditional
    independence among pixels, we have:

       U ( f | d )  U (d | f )  U ( f ) 
              U (d (i ) | f i )   V1 ( f i )    V2 ( f i , f j )
               iS                  iS            iS jN i


    where Ni is the neighbourhood of the pixel “i”.                       10
ISING MODEL
   The potential function defined on 4-neighbors1:
                  V2 ( f i , f j )   2   ( f i  f j )
    with
                                  1 if f i  f j
                 ( fi  f j )  
                                  0 otherwise




                                                             11
3D - PENALIZED ISING MODEL


   Penalty function approach:

        The potential function is defined as follows:

        V1 ( f i ( k ) )  t  [1  λ(i)]   ( f i ( k ) )  t  λ(i)  [1   ( f i ( k ) )]

         where       i    is a penalty function and



                           1 if                  f i ( k )  0  " clear sky"
                 ( fi )  
                      (k )

                           0 if                  f i ( k )  1  " cloud"                         12
BOUNDING BOX PENALTY FUNCTION
EXAMPLE




                                13
OUTLINE

   Introduction

   Cloud detection
       Penalty 3D Model


   Cloud tracking
       Region matching


   Experimental results

   Conclusions and future developments   14
MULTI-TARGET TRACKING


   Goal
       Estimation of the features of an unknown number of
        clouds



   Typical issues
       Multi-target involves at each temporal step the joint
        estimation of the target number and the state vectors

       The correct association between measures and
        targets is needed (Data Association)
                                                                15
TRACKING REGION MATCHING




   (x,y)


           X(k|k-1)        ( x + dx , y + dy )




                       Z(k)


                                                 16
OUTLINE

   Introduction

   Cloud detection
       Penalty 3D Model


   Cloud tracking
       Region matching


   Experimental results

   Conclusions and future developments   17
GLOSSARY


Abbreviation               Description
    2DI                          2D Ising
    3DI        3D-Ising-like (also named Extended MRF)
    3DP                       3D-Penalized




                                                     18
PENALTY FUNCTIONS:
SIMULATED DATA




         Abbreviation         Pe         Pfa        1-Pd

              2DI           0.018      0.0012       0.16
              3DI           0.038      0.0070       0.29
              3DP           0.012      0.0026      0.094
 Note
 3DP has a lower Pe w.r.t. the 2DI and 3DI in all the test cases.
                                                                    19
BOUNDING BOX PENALTY FUNCTION:
REAL IMAGES (SARDINIA ISLAND)




                                Note: Cloud pixel detected
                                   by 3DP and not by 2DI (cyan),
                                   by 3DP and not by 3DI (magenta)
                                   by 3DP and by neither 2DI/ 3DI (red)
                                   by 2DI and not by 3DP (blue),
                                   by 3DI and not by 3DP (green)

                                                                      20
OUTLINE

   Introduction

   Cloud detection
       Penalty 3D Model


   Cloud tracking
       Region matching


   Experimental results

   Conclusions and future developments   21
CONCLUSIONS
   The use of the penalty function is advantageous to detect
    cloud pixels (both inside cloud masses and on the edges)


FUTURE DEVELOPMENTS
   A more detailed penalty map should be fruitful in the
    presence of very rugged clouds

   Include the   multispectral   analysis   in   the   MAP-MRF
    framework

   Fusion of data collected by heterogeneous sensors
                                                                  22

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A computationally efficient method for sequential MAP-MRF cloud detection

  • 1. A COMPUTATIONALLY EFFICIENT METHOD FOR SEQUENTIAL MAP-MRF CLOUD DETECTION Paolo Addesso, Roberto Conte, Maurizio Longo, Rocco Restaino and Gemine Vivone University of Salerno, D.I.E.I.I., Fisciano, Italy; e-mail {paddesso,rconte,longo,restaino,gvivone}@ unisa.it
  • 2. OUTLINE  Introduction  Cloud detection  Penalty 3D Model  Cloud tracking  Region matching  Experimental results  Conclusions and future developments 2
  • 3. PROBLEM TACKLED  The classification consists in separating entities in a given knowledge domain into knowledge classes.  Classification: cloud / clear sky  Sensor used: SEVIRI 3
  • 4. WHY CLOUD DETECTION ?  The presence of clouds drastically affects measures of optical signals  International Satellite Cloud Climatology Project ISCCP-FD data set give a cloud cover around 66%  Many applications need a cloud masking phase  Example: fire detection, ocean color 4
  • 5. STATE OF ART  Static thresholds  Methods based on spatial coherence  Markov Random Fields  Adaptive thresholds  A series of threshold tests depending on the variation of the surface type and of the solar illumination  Machine learning tools  Fuzzy logic, artificial neural networks or kernel 5 methods
  • 6. OUTLINE  Introduction  Cloud detection  Penalty 3D Model  Cloud tracking  Region matching  Experimental results  Conclusions and future developments 6
  • 7. RANDOM FIELD AND MAP ESTIMATION  We define a random field F = {F1, … , Fm} as a family of random variables defined on a set of sites S in which each component Fi assumes a value fi in the label set L  Estimator: ˆ f MAP  arg max p f |d ( f | d ) f pd,f (d,f )  arg max log f pd (d ) 7  arg max {log p(d | f )  log p( f )} f
  • 8. MARKOV RANDOM FIELD (MRF)  F is a Markov Random Field if: P( f i | f S {i} )  P( f i | f Ni ) Note: Ni is the neighbourhood of the pixel “i”. 8
  • 9. CLASSIFICATION WITH MRF  Given the Markovian hypothesis, the Hammersley-Clifford theorem states that for the a priori probability can be expressed as: 1 p( f )  exp[  U ( f )] Z  A similar likelihood form is commonly used: p(d | f )  exp[ U (d | f )]  Hence the a posteriori density is: p( f | d )  exp[U ( f | d )]  exp[U (d | f )  U ( f )] 9
  • 10. MRF AND MAP CRITERIA  The minimum error probability is given by the MAP estimator: ˆ f  arg max [ p( f | d )]  arg min [U ( f | d )] f f  Under the hypothesis of conditional independence among pixels, we have: U ( f | d )  U (d | f )  U ( f )    U (d (i ) | f i )   V1 ( f i )    V2 ( f i , f j ) iS iS iS jN i where Ni is the neighbourhood of the pixel “i”. 10
  • 11. ISING MODEL  The potential function defined on 4-neighbors1: V2 ( f i , f j )   2   ( f i  f j ) with  1 if f i  f j  ( fi  f j )    0 otherwise 11
  • 12. 3D - PENALIZED ISING MODEL  Penalty function approach:  The potential function is defined as follows: V1 ( f i ( k ) )  t  [1  λ(i)]   ( f i ( k ) )  t  λ(i)  [1   ( f i ( k ) )] where  i  is a penalty function and 1 if f i ( k )  0  " clear sky"  ( fi )   (k ) 0 if f i ( k )  1  " cloud" 12
  • 13. BOUNDING BOX PENALTY FUNCTION EXAMPLE 13
  • 14. OUTLINE  Introduction  Cloud detection  Penalty 3D Model  Cloud tracking  Region matching  Experimental results  Conclusions and future developments 14
  • 15. MULTI-TARGET TRACKING  Goal  Estimation of the features of an unknown number of clouds  Typical issues  Multi-target involves at each temporal step the joint estimation of the target number and the state vectors  The correct association between measures and targets is needed (Data Association) 15
  • 16. TRACKING REGION MATCHING (x,y) X(k|k-1) ( x + dx , y + dy ) Z(k) 16
  • 17. OUTLINE  Introduction  Cloud detection  Penalty 3D Model  Cloud tracking  Region matching  Experimental results  Conclusions and future developments 17
  • 18. GLOSSARY Abbreviation Description 2DI 2D Ising 3DI 3D-Ising-like (also named Extended MRF) 3DP 3D-Penalized 18
  • 19. PENALTY FUNCTIONS: SIMULATED DATA Abbreviation Pe Pfa 1-Pd 2DI 0.018 0.0012 0.16 3DI 0.038 0.0070 0.29 3DP 0.012 0.0026 0.094 Note 3DP has a lower Pe w.r.t. the 2DI and 3DI in all the test cases. 19
  • 20. BOUNDING BOX PENALTY FUNCTION: REAL IMAGES (SARDINIA ISLAND) Note: Cloud pixel detected  by 3DP and not by 2DI (cyan),  by 3DP and not by 3DI (magenta)  by 3DP and by neither 2DI/ 3DI (red)  by 2DI and not by 3DP (blue),  by 3DI and not by 3DP (green) 20
  • 21. OUTLINE  Introduction  Cloud detection  Penalty 3D Model  Cloud tracking  Region matching  Experimental results  Conclusions and future developments 21
  • 22. CONCLUSIONS  The use of the penalty function is advantageous to detect cloud pixels (both inside cloud masses and on the edges) FUTURE DEVELOPMENTS  A more detailed penalty map should be fruitful in the presence of very rugged clouds  Include the multispectral analysis in the MAP-MRF framework  Fusion of data collected by heterogeneous sensors 22