A computationally efficient method for sequential MAP-MRF cloud detection Paolo Addesso, Roberto Conte, Maurizio Longo, Rocco Restaino, Gemine Vivone - University of Salerno

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
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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
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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 )
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 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”.
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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 )]
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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
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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)
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16. TRACKING REGION MATCHING
(x,y)
X(k|k-1) ( x + dx , y + dy )
Z(k)
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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
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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.
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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)
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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
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