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Classification of species and age composition of forest stands from - - PowerPoint PPT Presentation
Classification of species and age composition of forest stands from - - PowerPoint PPT Presentation
International Conference ENVIROMIS-2014 Classification of species and age composition of forest stands from hyperspectral airborne remote sensing data Session 6. Observational and ICT infrastructure support of regional scale environmental
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Multispectral and hyperspectral images
Multispectral Hyperspectral
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Supervised classification
(problem statement)
( ) a x
- set of features
X
- set of class labels
Y
x X ∈
290 spectral bands
Spectrum-based classification
The classification algorithm is optimized on the learning set . If the optimization consists in estimating parameters .
1
{ ( ), ( )}
N N i
X x i y i
=
= ( ) a x ( ) ( , ) a x a x = Θ Θ
spectrum of the reflected radiation point in the feature space
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Statistical classification
The optimal algorithm corresponds to a minimum of the average risk function
( ) ( | )
ys y s y Y s Y
R a P P A y λ
∈ ∈
=∑∑ { | ( ) },
s
A x X a x s = ∈ =
ys
λ
- the loss function
( , ) ( ) ( | ) p x y P y p x y = ( , ) x y X Y ∈ ×
Maximum likelihood principle where If then is the total probability of error of the algorithm
0, , 1, ,
ys
s y s y λ = ⎧ = ⎨ ≠ ⎩ ( ) R a ( ) a x
Classifiers based on the Bayesian decision rule are useful as a benchmark to test other classifiers in the simulated data.
Bayesian classification algorithm
( ) argmax ( )
y y y Y
a x P p x
∈
=
( ) ( | )
y
p x p x y =
- probability density functions of each of classes y
Y ∈
y
P
- prior probabilities of the classes (are given or can be obtained from texture analysis)
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Training problems
- verfitting
curse of dimensionality
The classifier is too complex. The number of estimated parameters of the classifier is close to the number of training samples. The discriminant surface is very sensitive to small changes of the training set. As a result, the classifier works well for training samples and badly for independent samples. The classifier uses too much features. The dimension
- f the feature space used is close to the number of
training samples. The discriminant surface separates well the samples of the training set, however the independent samples are classified badly.
As a matter of fact these problems are equivalent.
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Stepwise forward selection algorithm
for finding the most informative features
The disadvantage of this method consists in the instability of the "optimal" subset of the selected features. As a rule, the sequence obtained is very sensitive to small changes of the training set.
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Increasing the stability of the feature selection
(main steps)
- 2. Selecting the leading feature
Finding the spectral channel providing an exact classification of as much well discriminated objects as possible (for instance, it can be typical water, soil and vegetation). The leading channel can be found using the direct search or using more weak condition, when the classification error is estimated from the series of launches of the hold-out cross validation.
- 3. Selecting the most informative features for different
(intersecting) subclasses
Reduction of the feature space with regards to particular classification problem, for instance, water and soil subclasses, vegetation species and age groups.
- 1. Removing channels with significant radiometric distortion
Tests based on the binary classification can help to reveal some fine radiometric artifacts.
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Increasing the stability of the feature selection
(step 3)
leading feature forward selection algorithm with employing 50% hold-out cross validation for the estimation of the classification error sequence of selected features series of launches ensemble of the sequences
- f selected features
the most probable sequence
- f selected features
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Finding the most probable sequence of selected features
5 11 16 18 6 30
- 28
6 19 1
- 20
3 14 26 15 9
- 5
25 3 14 4 29 28 20 11 14 10 21 4 2 20 3 18 19 21 15
- 20
13 14 7 1 30
- 3
26 5 4 9 22 7 20 3 14 26 15
- 3
14 13
- 20
3 14 16 11 2 30 20 3 14 24 9
- finding the most
frequent feature
- n the level 1
(in the case of a few equivalent the random choice is used)
selecting corresponded subset of sequences finding the most frequent feature
- n the level 2
(in the case of a few equivalent the random choice is used)
etc selecting corresponded subset of sequences
Example
most probable sequence random choice
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- kernel: continuous, limited in L2, even function, satisfying the condition
1 1
1 1 ˆ ( )
j j n m i h i j j j
x x p x K m h h
= =
⎛ ⎞ − = ⎜ ⎟ ⎜ ⎟ ⎝ ⎠
∑∏
( ) argmax ( )
y y y Y
a x P p x
∈
=
Parzen-Rosenblatt estimate
K
( ) 1
X
K z dz =
∫
Choice of the test classifier
- 1. Non-parametric approach
( )
y
p x
approximated with no any supposition of function class.
Disadvantage: the corresponded classifiers suffer very strongly from the curse dimensionality problem
- 2. Parametric approach
( )
y
p x
is chosen from the supposed parametric family of functions Normal Bayesian classifier
1
1 1 ( ) argmax ln( ( ~ )) ( ) ( ) ln(det( )) 2 2
T i i i i i i
a x P x D x m C x m C
−
⎛ ⎞ = − − − − ⎜ ⎟ ⎝ ⎠
Disadvantage: the normality of in-class distribution of features is supposed
The preliminary tests showed that the disadvantage of the Normal Bayesian classifier is not so important in the considered case. Thus we used it as a test classifier.
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Processing of compound classes
{ }
( )
1 1 1
( ) 1 1 | ( ), ( ), ( ) exp ( ( )) ( )( ( )) 2 det( ( )) (2 )
x
M M T i i i i i i i N i i
w y p x w y y y x y y x y y µ µ µ π
− =
⎡ ⎤ Σ = − − Σ − ⎢ ⎥ Σ ⎣ ⎦
∑
min
max( )
y
p P <
Gaussian mixture Unrecognized objects
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Flights over Savvatyevskoe forestry (Tver, Russia)
Airborne hyperspectral measurements
AN2 Before and during the flight
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Hyperspectrometer AV-VD
(NPO Lepton, Zelenograd, Moscow, Russia)
Basic technical parameters: 1) work spectral range – 401-1017 nm; 2) number of spectral bands – 287 (+3 dark); 3) spectral resolution – 0.36 - 14 nm; 4) pixel size – 0.55 m /1000 m; 5) field of view – 15.8°; 6) span (pixels) – 500; 7) solar angles – 30° - 90°; 8) power: – 7 W; 9) weight – 2 kg; 10) bit capacity of video signal – 12 bit.
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Comparison of Russian and foreign HSCs
Sensor name AisaEAGLET CASI1500 Sokol-GCP (Сокол-ГЦП) Reagent (Реагент) Fregat (Фрегат) AV-VD (АВ-ВД) Developer Spectral Imaging Ltd., Finland ITRES Research Ltd, Canada FNCP OAO Krasnogorsky plant S.A.Zverev ZAO Reagent, Moscow NIU ITMO, S.Peterburg NPO Lepton, Zelenograd, Moscow Spectral range, nm 400-1000 380-1050 530-1000 450-900 400-1000 400-1000 Number of channels 820 288 105 106-250 70 287 Spectral resolution, nm 3.3 2.4 4.6-7.1 1.6-16 7 0.5-15 Binning yes yes no no no no Calibration yes yes yes no yes Space resolution 0.33-0.4m/1km 0.4m/1km 0.75m/1km 1.4m/1km 1m/1km 0.56 m/1km Span (pixels) 1600 1500 ? 250 ? 500 Bit capacity 12 14 14 14 ? 12 Weight, kg 3.5 (10.5 all) 25 (43 all) (50 all) ? 8 2 Power, W 100 ? 250 7-12 10 7
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Data quality
Spa$al ¡and ¡spectral ¡resolu$on ¡ Distor$ons ¡ Frame ¡rate ¡and ¡data ¡output ¡
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Calibration
HSC ¡calibra+on ¡implies ¡the ¡following ¡informa+on ¡ Data Purpose Spectral calibration Central wavelength for each channel Radiometric calibration Matrix of coefficients for the transformation of the signal to the spectral radiance Geometric calibration (sensor model) Matrix of viewing angles for each pixel Pixel quality map Indexes characterizing defective, high noise and nonlinear pixels Dark signal matrix Signal at the closed shutter
It ¡is ¡necessary ¡to ¡perform ¡tests ¡of ¡the ¡calibra$on ¡for ¡the ¡tolerance ¡to ¡impacts, ¡vibra$ons ¡and ¡ temperature ¡changes. ¡Also ¡it ¡is ¡important ¡to ¡no$fy ¡how ¡o?en ¡ ¡recalibra$on ¡is ¡needed. ¡
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AV-VD HSC central wavelengths and spectral resolution
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Choice of the binning intervals
(reduction of the spectral resolution)
2 nm
Noise contribution Channel number
5 nm 30 nm
Noise contribution Channel number Noise contribution Channel number Noise contribution Channel number
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Stability of the recognition results
(processing of two different overlapping hyperspectral images, Zmeevo airport zone, Tver region)
Zmeevo1 : 2011-08-12 12-27-53 Zmeevo2 : 2011-08-12 12-35-44
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Classification of overlapping images
scene containing a variety of man-made objects (airport zone)
unrecognized verdure helipad sand grassland conifer forest deciduous forest asphalt 3 asphalt 2 asphalt 1 water
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Degrees of illumination of the forest canopy
We have taken into consideration three illumination gradations which can be named as fully illuminated, half shadowed and fully shadowed. The discriminability of these gradations depends on the age of trees, it has maximum value for mature forest stands and for the young coppice it is very small.
Wavelength, nm Wavelength, nm Spectral radiance, W/(sm2 ster mkm) Normalized spectral radiance, 1/sm2 Pine, 66 years Pine, 66 years Wavelength, nm Wavelength, nm Pine, 13 years Spectral radiance, W/(sm2 ster mkm) Normalized spectral radiance, 1/sm2 Pine, 13 years
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Sets of spectral channels selected
for different subclasses of objects
Waters
- Ch. number
64 42 10 31 51 6 7
- Cent. wav., nm
790.39 636.71 451.81 569.91 700.88 430.61 436.09 Soils
- Ch. number
64 4 53 34 8 23 9
- Cent. wav., nm
790.39 420.01 719.08 588.81 441.34 523.59 446.60 Asphalts
- Ch. number
64 79 3 or 4 52 75 20
- Cent. wav., nm
790.39 919.09 414.73 or 420.01 709.75 878.72 506.85 Grasses
- Ch. number
64 29 or 32 12 55
- Cent. wav., nm
790.39 558.61 or 575.93 462.36 736.58 Tree species (young forest: pine, birch, aspen; fully illuminated)
- Ch. number
64 25 46 18 43
- Cent. wav., nm
790.39 534.89 662.34 495.93 642.78 Tree species (young forest: pine, birch, aspen; fully shadowed)
- Ch. number
64 23 47 53 25 49 9
- Cent. wav., nm
790.39 523.59 669.38 719.08 534.89 684.40 446.60 Tree species (mature forest: pine, birch; fully illuminated)
- Ch. number
64 70 85 1
- Cent. wav., nm
790.39 834.91 990.02 404.21 Tree species (mature forest: pine, birch; fully shadowed)
- Ch. number
64 43 66 1
- Cent. wav., nm
790.39 642.78 804.37 404.21 Age composition of the pine forest, (fully illuminated)
- Ch. number
64 53 35 81 52 24 47
- Cent. wav., nm
790.39 719.08 595.69 941.27 709.75 529.10 669.38 Age composition of the birch forest, (fully illuminated)
- Ch. number
64 52 17 or 18 47 or 48 30 50
- Cent. wav., nm
790.39 709.75 495.93 or 490.36 676.72 or 669.38 564.14 692.44
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Confusion matrix for the age composition
pine, fully illuminated parts of crowns
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Confusion matrix for the age-classes
pine and birch, fully illuminated parts of crowns
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Test region
(Tver, Savvatyevskoe forestry)
N ¡quarter ¡ N ¡sector ¡ area ¡ yield ¡ ag.cl. ¡ age ¡ bon ¡ dens ¡ type ¡ D ¡ H ¡ species ¡ 58 ¡ 16 ¡ 17,00 ¡ 320 ¡ 6 ¡ 110 ¡ 3 ¡ 8 ¡ ДМ ¡ 24 ¡ 23 ¡ 10С ¡ 58 ¡ 19 ¡ 2,50 ¡ 230 ¡ 3 ¡ 57 ¡ 2 ¡ 9 ¡ БР ¡ 16 ¡ 17 ¡ 10С ¡ 58 ¡ 22 ¡ 1,90 ¡ 310 ¡ 7 ¡ 125 ¡ 2 ¡ 7 ¡ ЧЕР ¡ 32 ¡ 27 ¡ 6С4Е ¡ 58 ¡ 24 ¡ 0,80 ¡ 140 ¡ 5 ¡ 45 ¡ 2 ¡ 8 ¡ ЧЕР ¡ 16 ¡ 17 ¡ 7Б3С ¡ 59 ¡ 7 ¡ 1,00 ¡ 330 ¡ 4 ¡ 70 ¡ 1 ¡ 8 ¡ ЧЕР ¡ 24 ¡ 24 ¡ 4С4Е2Б ¡ 59 ¡ 20 ¡ 4,00 ¡ 260 ¡ 4 ¡ 70 ¡ 2 ¡ 8 ¡ БР ¡ 20 ¡ 20 ¡ 10С ¡ 59 ¡ 23 ¡ 1,40 ¡ 330 ¡ 5 ¡ 90 ¡ 2 ¡ 8 ¡ ЧЕР ¡ 24 ¡ 24 ¡ 10С ¡ 59 ¡ 24 ¡ 1,60 ¡ 280 ¡ 4 ¡ 70 ¡ 2 ¡ 8 ¡ БР ¡ 24 ¡ 21 ¡ 10С ¡ 72 ¡ 1 ¡ 2,50 ¡ 330 ¡ 5 ¡ 100 ¡ 2 ¡ 8 ¡ ДМ ¡ 26 ¡ 24 ¡ 10С ¡ 72 ¡ 2 ¡ 3,50 ¡ 50 ¡ 3 ¡ 25 ¡ 4 ¡ 7 ¡ ДМ ¡ 6 ¡ 8 ¡ 8Б2С ¡ 72 ¡ 3 ¡ 0,70 ¡ 260 ¡ 8 ¡ 80 ¡ 2 ¡ 9 ¡ ЧЕР ¡ 26 ¡ 24 ¡ 8Б2С ¡ 72 ¡ 4 ¡ 0,40 ¡ 330 ¡ 5 ¡ 90 ¡ 2 ¡ 8 ¡ ДМ ¡ 24 ¡ 24 ¡ 8С2Б ¡ 72 ¡ 5 ¡ 2,50 ¡ 320 ¡ 4 ¡ 70 ¡ 1 ¡ 8 ¡ ЧЕР ¡ 24 ¡ 23 ¡ 10С ¡ 72 ¡ 6 ¡ 1,20 ¡ 300 ¡ 4 ¡ 80 ¡ 2 ¡ 8 ¡ ЧЕР ¡ 20 ¡ 22 ¡ 9С1Б ¡ 72 ¡ 7 ¡ 6,00 ¡ 110 ¡ 5 ¡ 90 ¡ 4 ¡ 5 ¡ СФ ¡ 18 ¡ 15 ¡ 10С ¡ 73 ¡ 1 ¡ 2,50 ¡ 360 ¡ 4 ¡ 80 ¡ 2 ¡ 9 ¡ ЧЕР ¡ 24 ¡ 23 ¡ 7С3Б ¡ 73 ¡ 2 ¡ 0,40 ¡ 110 ¡ 5 ¡ 45 ¡ 3 ¡ 8 ¡ ДМ ¡ 14 ¡ 15 ¡ 7Б3С ¡ 73 ¡ 3 ¡ 1,00 ¡ 320 ¡ 5 ¡ 90 ¡ 2 ¡ 8 ¡ ДМ ¡ 24 ¡ 23 ¡ 9С1Б ¡ 73 ¡ 4 ¡ 2,00 ¡ 360 ¡ 4 ¡ 80 ¡ 2 ¡ 9 ¡ ЧЕР ¡ 24 ¡ 23 ¡ 10С ¡ 73 ¡ 7 ¡ 1,90 ¡ 300 ¡ 5 ¡ 90 ¡ 3 ¡ 9 ¡ ДМ ¡ 22 ¡ 20 ¡ 10С ¡
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2 2
ˆ ˆ ( ( ) ( ) ) ( ( ) ( ) ) ( ) 2
pine pine birch birch
p i p i p i p i i ε − + − =
Validation (1)
20 1
( ) ( )
total i
i W i ε ε
=
= ∑
Area of region ( ) Total area of regions W i =
The total weighted error amounts to 12.2%, for shadowed pixels it is 13.4%, for partly illuminated – 11.1% and for completely illuminated – 12.3%.
tree species
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Номер региона Квартал Выдел площ. возр бонит тип D H состав 1 64 2 1,70 75 2 БР 22 21 10С 2 64 4 2,90 70 2 БР 22 21 10С 3 64 5 3,60 80 2 БР 24 23 10С 4 64 6 4,00 57 2 БР 16 16 10С 5 64 7 0,70 65 2 БР 18 18 8С2Б 6 64 8 8,40 65 2 ЧЕР 20 19 8С2Б 7 64 9 0,60 50 2 ЧЕР 14 18 8Б2С 8 64 10 3,00 75 2 БР 24 20 10С 9 64 11 5,60 60 2 ЧЕР 18 21 7Б3С 10 64 12 1,80 51 2 БР 16 16 10С 11 64 13 2,80 60 2 ЧЕР 20 23 7Б3С 12 64 15 4,00 65 2 ЧЕР 20 19 7С3Б
Validation (2)
tree species
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Validation
middle-aged birch mature birch middle-aged pine mature pine shaded
age classes
unrecognized
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Conclusions
- 1. The method of the selection of most informative spectral bands for the
thematic processing of hyperspectral images is proposed. It can be used for regularization of classification problem by optimal reduction of the feature space. The selection results are stable in comparison with the standard stepwise forward selection method.
- 2. Sequences of spectral bands optimized to different classification
problems are obtained with employing airborne hyperspectral data collected in summer 2011 for Tver forestry. The variety of the sequences underlines the importance of the use of hyperspectral measurements for remote sensing problems.
- 3. The problem of the recognition of forest ages is considered. The