- The Institution of Engineers of Kenya

```Presentation in
Aircraft Satellite Image Identification
Using Bayesian Decision Theory And
Moment Invariants Feature Extraction
Dickson Gichaga Wambaa
Supervised By Professor Elijah Mwangi
University Of Nairobi
Electrical And Information Engineering Dept.
• 9th May 2012
IEK Presentation
OUTLINE
Introduction
Statistical Classification
Satellite images Denoising
Results
Conclusion
References
All aircraft are built with the
same basic elements:
Wings
Engine(s)
Fuselage
Mechanical Controls
 Tail assembly.
The differences of these elements distinguish
one aircraft type from another and therefore its
identification.
STAGES OF STATISTICAL
PATTERN RECOGNITION
• PROBLEM
FORMULATION
• DATA
COLLECTION AND
EXAMINATION
• FEATURE
SELECTION OR
EXTRACTION
• CLUSTERING
• DISCRIMINATION
• ASSESSMENT OF
RESULTS
• INTERPRETATION
Classification ONE
• There are two main
divisions of classification:
• Supervised
• unsupervised
SUPERVISED
CLASSIFICATION
• BAYES CLASSIFICATION IS
SELECTED SINCE IT IS
POSSIBLE
TO
HAVE
EXTREMELY HIGH VALUES IN
ITS OPTIMISATION.
A decision rule partitions
the measurement space
into C regions.
Preprocessing
PREPROCESSING
IMAGE
ACQUISITION
IMAGE
ENHANCEMENT
IMAGE
BINARIZATION
AND
THRESHOLDING
FEATURES
EXTRACTION
NOISE
IMAGES ARE CONTAMINATED
BY NOISE THROUGH
–
–
–
–
IMPERFECT INSTRUMENTS
PROBLEMS WITH DATA ACQUISITION PROCESS
NATURAL PHENOMENA INTERFERENCE
TRANSMISSION ERRORS
SPECKLE NOISE(SPKN)
• THE TYPE OF NOISE FOUND
IN SATELLITE IMAGES IS
SPECKLE NOISE AND THIS
DETERMINES
THE
ALGORITHM
USED
IN
DENOISING.
Speckle Noise (SPKN) 2
• This is a multiplicative noise. The
distribution noise can be expressed
by:
J = I + n*I
• Where, J is the distribution speckle
noise image, I is the input image and
n is the uniform noise image.
CHOICE OF FILTER
FILTERING
CONSISTS
OF
MOVING A WINDOW OVER
EACH PIXEL OF AN IMAGE
AND
TO
APPLY
A
MATHEMATICAL FUNCTION
TO ACHIEVE A SMOOTHING
EFFECT.
CHOICE OF FILTER II
• THE MATHEMATICAL FUNCTION
DETERMINES THE FILTER TYPE.
• MEAN FILTER-AVERAGES THE
WINDOW PIXELS
• MEDIAN FILTER-CALCULATES THE
MEDIAN PIXEL
CHOICE OF FILTER II
• LEE-SIGMA
AND
LEE
FILTERS-USE
STATISTICAL DISTRIBUTION OF PIXELS IN
THE WINDOW
• LOCAL REGION FILTER-COMPARES THE
VARIANCES OF WINDOW REGIONS.
• THE FROST FILTER REPLACES THE PIXEL
OF INTEREST WITH A WEIGHTED SUM OF
THE VALUES WITHIN THE NxN MOVING
WINDOW
AND
ASSUMES
A
MULTIPLICATIVE NOISE AND STATIONARY
NOISE STATISTICS.
LEE FILTER
the multiplicative model
It preserves edges and detail.
BINARIZATION AND THRESHOLDING
TRAINING DATA SET
RESULTS:
FEATURE EXTRACTION ORIGINAL
IMAGES
Aircraf
ts
Classe
s
Ø1
Ø2
Ø3
Ø4
Ø5
Ø6
Ø7
B2
(Class
1)
6.6132
14.053
8
15.246
2
17.452
1
33.946
9
24.679
8
39.264
8
AH64
(Class
2)
7.1729
16.672
3
19.741
3
21.878
4
42.803
8
30.214
6
47.133
6
C5
(Class
3)
7.1487
20.279
3
22.412
9
24.496
2
48.061
4
34.640
1
50.198
0
•Noise
with
Probabilities of 0.1,
0.2, 0.3 and 0.4 was
used for simulation.
FEATURE EXTRACTION:
SAMPLE IMAGES
Ø1
Ø2
B2 Class 1
6.6132
Test Image
Ø3
Ø4
Ø5
Ø6
Ø7
14.0538 15.2462
17.4521
33.9469
24.6798
39.2648
6.6001
13.9810 15.1678
17.4434
33.8456
24.6578
40.9765
6.5579
13.9115
15.0382
17.2442
33.5329
24.4031
41.0169
6.5406
13.8898
14.9673
17.1737
33.3923
24.3223
38.6145
6.4703
13.7136
14.6351
16.8403
32.7292
23.9045
38.4642
6.4124
13.5763
14.2593
16.4614
31.9765
23.4609
36.7216
NOISE
FILTERED
Test Image
( 0.1 Noise
Prob)
Test Image
(0.2 Noise
Prob)
Test Image
(0.3 Noise
Prob)
Test Image
WHY BAYES
CLASSIFICATION 1
Bayes statistical method is
the classification of choice
because of its minimum error
rate.
WHY BAYES
CLASSIFICATION 2
• Probabilistic learning: among the
most practical approaches to certain
types of learning problems
• Incremental: Each training example
can incrementally increase/decrease
the probability that a hypothesis is
correct
WHY BAYES
CLASSIFICATION 3
• Probabilistic prediction:
Predict multiple hypotheses
• Benchmark: Provide a
benchmark for other
algorithms
Bayesian Classification
• For a minimum error rate
classifier the choice is on the
class with maximum posterior
probability.
Probabilities
• Let λ be set of 3 classes C1,C2 ,C3.
• x be an unknown feature vector of
dimension 7.
• Calculate the conditional posterior
probabilities of every class Ci and
choose the class with maximum
posteriori probability.
Prior Probabilities
• 3 classes of Data which are all
likely to happen therefore
P(Ci)= 0.333
Posterior Probability 1
• Posterior = likelihood x prior
evidence
• P(Ci\x) = P(x\Ci)P(Ci)
P(x)
POSTERIOR PROBABILITY 2
• Posterior(AH 64)=P(AH 64)P(x/ AH 64)
p(evidence)
• Posterior(C5)=P(C5)P(x/ C5)
p(evidence)
• Posterior(B2)=P(B2)P(x/ B2)
p(evidence)
POSTERIOR PROBABILITY 3
Posterior
Test Image
probability NOISE
FILTERED
Test Image
( 0.1 Noise
Prob)
Test Image ( Test Image
0.2 Noise
( 0.3 Noise
Prob)
Prob)
Test Image
( 0.4 Noise
Prob)
AH 64
1.6954X10-2 1.6789X10-2 1.6034X10-2
1.5674X10-2
1.5045X10-2
C5
1.9653X10-2 1.8965X10-2 1.8463X10-2
1.8062X10-2
1.7453X10-2
B2
2.4239X10-2 2.2346X10-2 2.21567X10-2 2.1866X10-2
1.9889X10-2
CONCLUSION
• COMBINING MOMENTS FEATURES
EXTRACTION WITH BAYESIAN CLASSIFICATION
WHILE USING LEE FILTERS IN PREPROCESSING
• INCREASES THE CHANCES OF CORRECT
IDENTIFICATION AS COMPARED TO NON USE
OF THE FILTERS
• USE OF OTHER TYPES OF FILTERS THIS IS SEEN
BY THE INCREASE OF THE POSTERIOR
PROBABILITY VALUES.
References
• [1] Richard O. Duda,Peter E. Hart and David G.
Stork.Pattern Classification 2nd edition John Wiley
and Sons,US,2007
• [2] Rafael C. Gonzalez,Richard E. Woods and
Steven L. Eddins . Digital image processing using
matlab 2nd edition Pearson/Prentice
Hall,US,2004
• [3] William K. Pratt. Digital image processing
4th edition John Wiley,US,2007
• [4] Anil K. Jain. Fundamentals of Digital Image
Processing Prentice Hall,US,1989
References
• [5] Wei Cao, Shaoliang Meng, “Imaging systems
and
Techniques”,IEEE International
Workshop,
IST.2009.5071625,pp 164-167,
Shenzhen, 2009
• [6] Bouguila.N, Elguebaly.T , “A Bayesian
approach for texture images classification and
retrieval”,International Conference on
Multimedia Computing and Systems,