A computationally efficient method for sequential MAP-MRF cloud detection

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