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 studies. Organizers Vladimir Krutikov and Michael Kabanov Dmitriev E.V. (INM RAS), Kozoderov V.V. (MSU), Sokolov A.A. (ULCO)
Forest inventory maps and data
Multispectral and hyperspectral images Multispectral Hyperspectral
Supervised classification (problem statement) a x ( ) X - set of features Y - set of class labels x X ∈ N N a x ( ) X { ( ), ( )} x i y i = The classification algorithm is optimized on the learning set . i 1 = a x ( ) a x ( , ) = Θ Θ If the optimization consists in estimating parameters . Spectrum-based classification spectrum of the reflected radiation point in the feature space 290 spectral bands
Statistical classification Maximum likelihood principle p x y ( , ) P y p x y ( ) ( | ) ( , ) x y X Y = ∈ × The optimal algorithm corresponds to a minimum of the average risk function R a ( ) P P A ( | ) y = ∑∑ λ ys y s y Y s Y ∈ ∈ A { x X a x | ( ) s }, where - the loss function = ∈ = λ ys s 0, s y , = ⎧ a x ( ) R a ( ) If then is the total probability of error of the algorithm λ = ⎨ ys 1, s y , ≠ ⎩ Bayesian classification algorithm a x ( ) argmax P p ( ) x = y y y 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) y Classifiers based on the Bayesian decision rule are useful as a benchmark to test other classifiers in the simulated data.
Training problems curse of dimensionality overfitting The classifier is too complex. The number of estimated The classifier uses too much features. The dimension parameters of the classifier is close to the number of of the feature space used is close to the number of training samples. The discriminant surface is very training samples. The discriminant surface separates sensitive to small changes of the training set. As a well the samples of the training set, however the result, the classifier works well for training samples and independent samples are classified badly. badly for independent samples. As a matter of fact these problems are equivalent.
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.
Increasing the stability of the feature selection (main steps) 1. Removing channels with significant radiometric distortion Tests based on the binary classification can help to reveal some fine radiometric artifacts. 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.
Increasing the stability of the feature selection (step 3) series of launches forward selection algorithm with leading employing 50% hold-out cross sequence of selected feature validation for the estimation of features the classification error ensemble of the sequences of selected features the most probable sequence of selected features
Finding the most probable sequence of selected features finding the most finding the most selecting selecting frequent feature frequent feature corresponded corresponded on the level 1 on the level 2 etc subset of subset of (in the case of a few (in the case of a few sequences sequences equivalent the random equivalent the random choice is used) choice is used) Example 5 11 16 18 6 30 - 28 6 19 1 - - - most probable 20 3 14 26 15 9 - sequence 5 25 3 14 4 29 28 20 11 14 10 21 4 2 20 3 18 19 21 15 - random choice 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 - -
Choice of the test classifier a x ( ) argmax P p ( ) x = y y y Y ∈ 1. Non-parametric approach p ( ) x approximated with no any supposition of function class. y Parzen-Rosenblatt estimate j j 1 m n 1 ⎛ x x ⎞ − ˆ ( ) p x K i ∑∏ = ⎜ ⎟ h ⎜ ⎟ m h h i 1 j 1 ⎝ ⎠ = j j = K K z dz = ( ) 1 - kernel: continuous, limited in L 2, even function, satisfying the condition ∫ X Disadvantage: the corresponded classifiers suffer very strongly from the curse dimensionality problem 2. Parametric approach p ( ) x is chosen from the supposed parametric family of functions y Normal Bayesian classifier 1 1 ⎛ ⎞ T 1 a x ( ) argmax ln( ( ~ P x D )) ( x m ) C ( x m ) ln(det( C )) − = − − − − ⎜ ⎟ i i i i i 2 2 ⎝ ⎠ i 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.
Processing of compound classes Gaussian mixture 1 M w y ( ) 1 ⎡ ⎤ ( M ) T 1 p x | w y ( ), ( ), y ( ) y i exp ( x ( )) y ( )( y x ( )) y { } ∑ − µ Σ = − − µ Σ − µ ⎢ ⎥ i i i i i i 1 2 N det( ( )) y (2 ) Σ ⎣ ⎦ π x i 1 = i Unrecognized objects max( p ) P < y min
Airborne hyperspectral measurements Flights over Savvatyevskoe forestry (Tver, Russia) Before and during the flight AN2
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.
Comparison of Russian and foreign HSCs Sensor name AisaEAGLET CASI1500 Sokol-GCP Reagent Fregat AV-VD ( Сокол - ГЦП ) ( Реагент ) ( Фрегат ) ( АВ - ВД ) Developer Spectral ITRES FNCP OAO ZAO Reagent, NIU ITMO, NPO Lepton, Imaging Ltd., Research Ltd, Krasnogorsky Moscow S.Peterburg Zelenograd, Finland Canada plant Moscow S.A.Zverev Spectral range, 400-1000 380-1050 530-1000 450-900 400-1000 400-1000 nm Number of 820 288 105 106-250 70 287 channels Spectral 3.3 2.4 4.6-7.1 1.6-16 7 0.5-15 resolution, nm Binning yes yes no no no no Calibration yes yes yes no yes Space 0.33-0.4m/1km 0.4m/1km 0.75m/1km 1.4m/1km 1m/1km 0.56 m/1km resolution 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
Data quality Distor$ons ¡ Spa$al ¡and ¡spectral ¡resolu$on ¡ Frame ¡rate ¡and ¡data ¡output ¡
Calibration HSC ¡calibra+on ¡implies ¡the ¡following ¡informa+on ¡ Data Purpose Spectral calibration Central wavelength for each channel Radiometric Matrix of coefficients for the calibration transformation of the signal to the spectral radiance Geometric calibration Matrix of viewing angles for each (sensor model) pixel Pixel quality map Indexes characterizing defective, high noise and nonlinear pixels Dark signal matrix Signal at the closed shutter It ¡is ¡necessary ¡to ¡perform ¡tests ¡of ¡the ¡calibra$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. ¡
AV-VD HSC central wavelengths and spectral resolution
Choice of the binning intervals (reduction of the spectral resolution) 2 nm Noise contribution Noise contribution Channel number Channel number 5 nm 30 nm Noise contribution Noise contribution Channel number Channel number
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
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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