igarss1792_v2.ppt
TRANSCRIPT
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Keng-Hao Liu and Chein-I ChangKeng-Hao Liu and Chein-I Chang
Remote Sensing Signal and Image Processing Laboratory Remote Sensing Signal and Image Processing Laboratory (RSSIPL)(RSSIPL)
Department of Computer Science and Electrical Department of Computer Science and Electrical EngineeringEngineering
University of Maryland, Baltimore County (UMBC)University of Maryland, Baltimore County (UMBC)Baltimore, MD 21250Baltimore, MD 21250
Dynamic Band SelectionDynamic Band SelectionFor Hyperspectral ImageryFor Hyperspectral Imagery
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Motivation
Band Selection (BS) is one of commonly used Band Selection (BS) is one of commonly used approaches that take advantage of high inter-approaches that take advantage of high inter-band correlation to remove band redundancy in band correlation to remove band redundancy in order to achieve a wide range of applications. order to achieve a wide range of applications.
However, there are several crucial issues However, there are several crucial issues arising in implementation of BS. One of these arising in implementation of BS. One of these issues is how to estimate the number of bands, issues is how to estimate the number of bands, pp, required to be selected?, required to be selected?
How to find How to find pp??
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Outline
Dynamic Band Selection (DBS)Dynamic Band Selection (DBS) - Virtual Dimensionality (VD) - Band Dimensionality Allocation (BDA)
- Progressive Band Dimensionality Process (PBDP) - Criteria for Band Prioritization (BP) ExperimentsExperiments - HYDICE - AVIRIS (Purdue) Data ConclusionsConclusions
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Issues of Conventional BS
Require knowing the number of bands required for BS, p, a priori
The value of p is fixed at a constant and cannot be adaptive.
Need an exhaustive search required to find an optimal set of p bands among all possible combinations out of the total number of bands.
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Progressive Band Dimensionality Process
(PBDP) Using a criterion prioritizes all Using a criterion prioritizes all LL spectral bands and removes spectral bands and removes
highly correlated bands then selects bands progressively in a highly correlated bands then selects bands progressively in a forward or backward manner depending upon how to retain forward or backward manner depending upon how to retain band information in increasing or decreasing order.band information in increasing or decreasing order. Forward Progressive Band Dimensionality Process Forward Progressive Band Dimensionality Process
(FPBDP) (FPBDP) Backward Progressive Band Dimensionality Process Backward Progressive Band Dimensionality Process
(BPBDP) (BPBDP)
The PBDP process is continued on until it reaches a specific The PBDP process is continued on until it reaches a specific number of bands, number of bands, pp. So the . So the pp is considered as variable instead is considered as variable instead of fixed value.of fixed value.
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Band Prioritization (BP) Criteria for PBDP
Band Prioritization Criteria for PBDPBand Prioritization Criteria for PBDP
Second order statistic-based BP criteriaSecond order statistic-based BP criteria - Variance - Signal-to-Noise Ratio (SNR or MNF)
High order statistic-based BP criteriaHigh order statistic-based BP criteria - Skewness - Kurtosis
Infinite order Statistics BP criteriaInfinite order Statistics BP criteria - Entropy - Information Divergence (ID) - Neg-entropy (combination of 3rd and 4th order))
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Virtual Dimensionality (VD)
LL
LL
LL
LL
K of seigenvalue
R of seigenvalue
Matrix Covariance Sample K
Matrix nCorrelatoi Sample R
L21
L21
:
:ˆˆˆ
:
:
VD1,2,m )(ˆmm FPf
Use VD [Chang 2003] to determine the number of Use VD [Chang 2003] to determine the number of components required for Hyperspectral images.components required for Hyperspectral images.
We assume one spectrally distinct signature can be We assume one spectrally distinct signature can be accommodated by one band. So the number of bands accommodated by one band. So the number of bands required to be selected must be equal or greater than the required to be selected must be equal or greater than the VD.VD.
Band Dimensionality Allocation(BDA)
Concept is derived from information theory where a source Concept is derived from information theory where a source SS is is emitted by a set of source alphabets that are used to represent the emitted by a set of source alphabets that are used to represent the source with a given probability distribution where source with a given probability distribution where ppjj is the probability is the probability
of the occurrence of the source alphabet of the occurrence of the source alphabet aajj
Similarly, assumes Similarly, assumes mmjj is material substance signature to be analyzed, is material substance signature to be analyzed,
then the then the nnjj denotes the number of components (bands) required to denotes the number of components (bands) required to
represent represent mmjj. . In other word, In other word, nnjj is actually determined by how difficult is actually determined by how difficult
the the mmjj is discriminated in terms of spectral similarity. is discriminated in terms of spectral similarity.
In conventional BS, it assumes In conventional BS, it assumes nnjj=p =p for allfor all signatures. In this cases signatures. In this cases
all substance are assumed to have equal difficulty to be discriminated all substance are assumed to have equal difficulty to be discriminated by spectral similarity. Generally it is not true in hyperspectral data. by spectral similarity. Generally it is not true in hyperspectral data.
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Band Dimensionality Allocation (BDA) for signatures
• Select a spectral similarity measure and a reference signature s.
• Calculate spectral similarity values for each signature and normalize them to a probability vector.
• Find self-information.• Find the smallest integer qj larger than these self-
information. • Define dimensionality allocation
then assigned it to jth signature, mj. jj qnn VD
BDA Procedures:
Determines the number Determines the number of signatures to be used of signatures to be used
for data analysisfor data analysis
Additional number requiredAdditional number requiredfor mfor mj j to distinguish itself fromto distinguish itself from
other signatures.other signatures.
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Band Dimensionality Allocation (BDA) for signatures
Three techniques used to find BDAThree techniques used to find BDA Shannon coding Huffman coding Hamming coding
Candidates that can be used for spectral similarity Candidates that can be used for spectral similarity measure: measure: Spectral angle mapper (SAM) Spectral information divergence (SID)
Candidates that can be used as reference signature (s):Candidates that can be used as reference signature (s):• Data sample mean• Signature mean or any signature
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Dynamic Band Selection (DBS)
Custom design a criterion for Band Custom design a criterion for Band Prioritization (BP) Prioritization (BP)
Implement PBDP Implement PBDP Apply Band De-correlation (BD) Apply Band De-correlation (BD) Band Dimensionality Allocation (BDA)Band Dimensionality Allocation (BDA)
DBS steps:
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Hyperspectral Images Used for Experiments (1)
HYDICE Data: 64x64 169 bands hyperspectral image with spatial
resolution is 20m.
Ground truth(desired signatures)
Image scene
p11, p12, p13
p211, p22, p23 p221
p311, p312, p32, p33
p411, p412, p42, p43
p511, p52, p53
p521
interferer
grass
tree
road
0 20 40 60 80 100 120 140 160 180 0
1000
2000
3000
4000
5000
6000
7000
8000 p1 p2 p3 p4 p5
undesired signatures
Spectral of five panels
Classifier: FCLS
Band De-correlation (BD) is applied after BP
withσ= 0.1
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HYDICE Data Experiments
signature mj nVD πj qj nj (BDA)
Shannon coding
m1=p1
(panels in row1) 9SID 0.0172 15
SAM 0.0462 14
m2=p2
(panels in row2) 9SID 0.0295 15
SAM 0.0779 13
m3=p3
(panels in row3) 9SID 0.0358 14
SAM 0.0897 13
m4=p4
(panels in row4) 9SID 0.0695 13
SAM 0.1004 13
m5=p5
(panels in row5) 9SID 0.1070 13
SAM 0.1140 13
m6 (grass)9
SID 0.1007 13
SAM 0.1396 12
m7 (road)9
SID 0.0565 14
SAM 0.1035 13
m8 (tree)9
SID 0.2869 12
SAM 0.1479 12
m9 (interferer)9
SID 0.2969 11
SAM 0.1808 12
5.8591 6 4.4350 5
5.0832 6
3.6822 4
4.8055 5
3.4794 4
3.8466 4
3.3163 4
3.2246 4
3.1331 4
3.3114 4
2.8403 3
4.1463 5 3.2727 4
1.8014 2
2.7571 3 1.7518 2
2.4674 3
Shannon BDA results of HYDICE Data
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HYDICE Data ExperimentsUnmixed abundance fractions of 19 panel pixels by FCLS Unmixed abundance fractions of 19 panel pixels by FCLS
nVD Shannon coding Huffman coding Hamming coding 2nVD total Optimal
p = Number of selected bands 9 15 14 13 18 65 to 7065 to 70
p11 Variance 0.44 0.63 0.6 0.54 0.73 0.78(65) 0.78(32)
Skewness 0.27 0.84 0.84 0.82 0.85 0.81(70) 0.92(36)
Entropy 0.83 0.87 0.85 0.84 0.88 0.77(68) 1(24)
p12 Variance 0.66 0.46 0.48 0.51 0.43 0.56(65) 0.68(11)
Skewness 0.54 0.53 0.36 0.3 0.52 0.56(70) 0.68(38)
Entropy 0.93 0.9 0.86 0.86 0.72 0.53(68) 0.93(10)
p13 Variance 0 0 0 0 0 0(65) 0(10)
Skewness 0 0 0 0 0 0.05(70) 0.23(34)
Entropy 0.68 0.69 0.67 0.69 0.67 0.01(68) 0.83(12)
p = Number of selected bands 9 15 14 13 18
p211 Variance 0.85 0.87 0.87 0.87 0.87 0.89(65) 0.89(65)
Skewness 0.84 0.95 0.96 0.95 0.95 0.89(70) 0.99(36)
Entropy 1.2 0.88 0.87 0.87 0.88 0.92(68) 1.2(9)
p221 Variance 0.53 0.71 0.7 0.7 0.72 0.75(65) 0.75(65)
Skewness 0.72 0.95 0.96 0.96 0.96 0.77(70) 1(37)
Entropy 0 0.21 0.19 0.25 0.22 0.81(68) 1(38)
p22 Variance 0.75 0.86 0.86 0.85 0.81 0.78(65) 0.86(14)
Skewness 0.87 0.74 0.75 0.8 0.7 0.79(70) 0.87(9)
Entropy 0.64 0.6 0.62 0.61 0.6 0.77(68) 0.78(67)
p23 Variance 0.46 0.49 0.49 0.49 0.48 0.46(65) 0.49(14)
Skewness 0.38 0.24 0.24 0.24 0.22 0.45(70) 0.45(70)
Entropy 0 0.23 0.19 0.18 0.19 0.44(68) 0.44(68)
VD BDA
HYDICE Data Experiments
ROC performance of 5 row panels using FCLSROC performance of 5 row panels using FCLS
Panels in row 1 Panels in row 2 Panels in row 3
Panels in row 4 Panels in row 5
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
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Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
BDA
VD
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Y axis: Area under curve of ROC (PD versus PF )X axis: Number of selected bands, p
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HYDICE Data Experiments
Average ROC performance of 5 row panelsAverage ROC performance of 5 row panels
Average performance of 5 row panels
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Number of selected bands (p)
Are
a u
nd
er
curv
es
of R
OC
: (P D
,PF)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
BDA range
VD
2VD
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Some notes forHYDICE Data Experiments
Classifying subpixels panels requires more bands than pure pixels.
High order statistics BPC generally requires a smaller number of bands than 2nd order statistic BPC. The skewness seems to work the best for HYDICE data.
To unmix panels, p=nVD=9 seems to be insufficient. But they achieve considerable performance within p=2nVD=18. It implies that the BDA provides a better way to predict cut-off band than VD.
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Hyperspectral Images Used for Experiments (2)
3 3
2
5 10 12
15 16 12
15 11
14
10
2 3
4
12
3
5
11
11 11
11 10 2 2
5 7 1
2
2 6
6 6 6
5
8
14
14
13
3
10
9
17
17
17
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Class map
AVIRIS (Purdue) Data: 145x145 202 bands hyperspectral image.
Image scene
class1 class2 class3 class4 class5 class6 class7 class8 class9 class10
class11 class12 class13 class14 class15 class16
17 Classes maps
Data samples are heavily-mixed
Classifier: MLC
Band De-correlation (BD) is applied after BP
withσ= 0.1
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Purdue Data ExperimentsBDA results of Purdue Data
6.2933 7 4.5159 5
4.6748 5
6.1622 7 2.8986 3
4.9826 5
7.9007 8
6.5866 7
6.0226 7
4.2035 5
4.3798 5
4.5388 5
5.1716 6
2.1248 3 4.1082 5
2.2483 3 5.3868 6
signature mj nVD πj qj j nj (BDA)
Shannon coding
m1 (class 1) 29 SID 0.0128 36
m2 (class 2) 29 SID 0.0437 34
m3 (class 3) 29 SID 0.0392 34
m4 (class 4) 29 SID 0.0140 36
m5 (class 5) 29 SID 0.1341 32
m6 (class 6) 29 SID 0.0316 34
m7 (class 7) 29 SID 0.0042 37
m8 (class 8) 29 SID 0.0104 36
m9 (class 9) 29 SID 0.0154 36
m10 (class 10) 29 SID 0.0543 34
m11 (class 11) 29 SID 0.0480 34
m12 (class 12) 29 SID 0.0430 34
m13 (class 13) 29 SID 0.0277 35
m14 (class 14) 29 SID 0.2293 32
m15 (class 15) 29 SID 0.0580 34
m16 (class 16) 29 SID 0.2105 32
m17 (BKG) 29 SID 0.0239 35
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Purdue Data ExperimentMLC classification results of 16 classes
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
Variance
Skewness
Kurtosis
EntropyID
Negentropy
SNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
Variance
Skewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)C
lass
ifica
tion
ra
te (
%)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
Variance
Skewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
Negentropy
SNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
Negentropy
SNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
Negentropy
SNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
Variance
Skewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
Negentropy
SNR
class1 class2 class3 class4 class5
class6 class7 class8 class9 class10
BDA
VD
Y axis: MLC classification rate in percent%X axis: Number of selected bands, p
Classes 1 to 10
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Purdue Data Experiment
0 10 20 30 40 50 600
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
Average performance of 16 classes
MLC classification results
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
Variance
Skewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
Negentropy
SNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
0 10 20 30 40 50 60 70 800
10
20
30
40
50
60
70
80
90
100
Number of selected bands (p)
Cla
ssifi
catio
n r
ate
(%
)
VarianceSkewness
Kurtosis
Entropy
ID
NegentropySNR
class11 class12 class13 class14 class15
class16
VD
2VDBDA range
Classes 11 to 16
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Some Notes forPurdue Data Experiments
Second order statistic BPC generally perform better than High order statistic BPC due to
- the land covers of this particular scene are large - the data samples are heavily mixed because of low spatial resolution and their contributions to statistics are mainly 2nd order statistics
In most of classes using fewer dimensions for MLC can perform In most of classes using fewer dimensions for MLC can perform as well the using all bands. For instance, classes 7, 9, 13, and 16 as well the using all bands. For instance, classes 7, 9, 13, and 16 do not require more bands to produce the best results. do not require more bands to produce the best results.
Only 5 classes, 2, 3, 4, 8, and 15 which required almost full Only 5 classes, 2, 3, 4, 8, and 15 which required almost full dimensions to produce the best MLC results. dimensions to produce the best MLC results.
DBS provide some guidelines in selecting appropriate DBS provide some guidelines in selecting appropriate pp for for MLC to perform reasonably.MLC to perform reasonably.
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Summary of DBS
The DBS is achieved by implementing the PBDP The DBS is achieved by implementing the PBDP conjunction with BDA.conjunction with BDA.
DBS provides a guideline to decide how many bands is DBS provides a guideline to decide how many bands is needed for each different signature.needed for each different signature.
The selection of BP criteria has huge influence on the The selection of BP criteria has huge influence on the unmixing/classification results. Different applications unmixing/classification results. Different applications may requires different BP criteria to produce the best may requires different BP criteria to produce the best performance.performance.
VD is indeed a good estimate.VD is indeed a good estimate.
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Progressive Band Dimensionality Process (PBDP) Progressive Band Dimensionality Process (PBDP) provides a way to estimate provides a way to estimate pp adaptively by increasing adaptively by increasing bands in a forward manner and decreasing bands in a bands in a forward manner and decreasing bands in a backward manner.backward manner.
Since various material substance signatures require Since various material substance signatures require different values of the different values of the pp for data processing, the Band for data processing, the Band Dimensionality Allocation (BDA) is further developed Dimensionality Allocation (BDA) is further developed to determine different numbers of spectral bands to determine different numbers of spectral bands required by individual signatures.required by individual signatures.
Conclusions
