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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
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OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments2
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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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WHY CLOUD DETECTION ?
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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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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
methods5
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OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments6
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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:
)}(log)|({logmaxarg
)(
)(logmaxarg
)|(maxargˆ|
fpfdp
dp
d,fp
dfpf
f
d
d,f
f
dff
MAP
7
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MARKOV RANDOM FIELD (MRF)
F is a Markov Random Field if:Note: Ni is the neighbourhood of the pixel “i”.
)|()|( i}i{i iNS ffPffP
8
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CLASSIFICATION WITH MRF
Given the Markovian hypothesis, the
Hammersley-Clifford theorem states that for the
a priori probability can be expressed as:
A similar likelihood form is commonly used:
Hence the a posteriori density is:
)]( exp[1
)( fUZ
fp
9
)]|(exp[)|( fdUfdp
)]()|(exp[)]|(exp[)|( fUfdUdfUdfp
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MRF AND MAP CRITERIA
The minimum error probability is given by the
MAP estimator:
Under the hypothesis of conditional
independence among pixels, we have:
where Ni is the neighbourhood of the pixel “i”.10
)]|([ minarg)]|([ maxargˆ dfUdfpfff
Si NjSiSi
ffVfVfidU
fUfdUdfU
i
),( )( )|)((
)()|()|(
ji2i1i
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ISING MODEL
The potential function defined on 4-neighbors1:
with
)(),( ji2ji2 ffffV
otherwise0
if1 )(
ji
ji
ffff
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3D - PENALIZED ISING MODEL
Penalty function approach:
The potential function is defined as follows:
where is a penalty function and
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)](1[)( )()](1[)( )(
i
)()(
i1
k
t
k
it
k fiλfiλfV
cloud"" 1 if0
sky"clear " 0 if1)(
)(
)(
)(
k
i
k
ik
if
ff
i
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BOUNDING BOX PENALTY FUNCTION
EXAMPLE
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OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments14
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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
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TRACKING REGION MATCHING
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X(k|k-1)
Z(k)
( x , y )
( x + dx , y + dy )
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OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments17
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GLOSSARY
Abbreviation Description
2DI 2D Ising
3DI 3D-Ising-like (also named Extended MRF)
3DP 3D-Penalized
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PENALTY FUNCTIONS:SIMULATED DATA
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Note
3DP has a lower Pe w.r.t. the 2DI and 3DI in all the test cases.
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
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BOUNDING BOX PENALTY FUNCTION: REAL IMAGES (SARDINIA ISLAND)
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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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OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments21
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CONCLUSIONS
The use of the penalty function is advantageous to detect
cloud pixels (both inside cloud masses and on the edges)
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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