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A computationally efficient method for sequential MAP-MRF cloud detectionPaolo Addesso, Roberto Conte, Maurizio Longo, Rocco Restaino, Gemine Vivone- University of Salerno
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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 developments2
3
PROBLEM TACKLED
The classification consists in separating entities in a
given knowledge domain into knowledge classes.
Classification: cloud / clear sky
Sensor used: SEVIRI
WHY CLOUD DETECTION ?
4
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
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
OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments6
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
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
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
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
ISING MODEL
The potential function defined on 4-neighbors1:
with
)(),( ji2ji2 ffffV
otherwise0
if1 )(
ji
ji
ffff
11
3D - PENALIZED ISING MODEL
Penalty function approach:
The potential function is defined as follows:
where is a penalty function and
12
)](1[)( )()](1[)( )(
i
)()(
i1
k
t
k
it
k fiλfiλfV
cloud"" 1 if0
sky"clear " 0 if1)(
)(
)(
)(
k
i
k
ik
if
ff
i
BOUNDING BOX PENALTY FUNCTION
EXAMPLE
13
OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments14
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
16
X(k|k-1)
Z(k)
( x , y )
( x + dx , y + dy )
OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments17
GLOSSARY
Abbreviation Description
2DI 2D Ising
3DI 3D-Ising-like (also named Extended MRF)
3DP 3D-Penalized
18
PENALTY FUNCTIONS:SIMULATED DATA
19
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
BOUNDING BOX PENALTY FUNCTION: REAL IMAGES (SARDINIA ISLAND)
20
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)
OUTLINE
Introduction
Cloud detection
Penalty 3D Model
Cloud tracking
Region matching
Experimental results
Conclusions and future developments21
CONCLUSIONS
The use of the penalty function is advantageous to detect
cloud pixels (both inside cloud masses and on the edges)
22
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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