Multiple Endmember Spectral Mixture Analysis (MESMA) for Dryland Applications

Transcription

1 Multiple Endmember Spectral Mixture Analysis (MESMA) for Dryland Applications M. Bachmann Hyper-I-Net 1st School on Hyperspectral Imaging October 29-31, 2007 Cáceres, Spain

2 Tutorial Structure Recapitulation: Basics of Spectral Unmixing (see talk by José Bioucas) MESMA Basic principle Different approaches Specific parameters Application Example Mapping Ground Cover Fractions in Drylands Methodological approach Results Conclusions Recommended Reading Folie 2

3 Spectral Unmixing Basics Linear Spectral Unmixing Subpixel classifier / subpixel detection i.e., objects smaller than one pixel can be detected Fuzzy classifier i.e., one pixel can belong to multiple classes Quantitative classifier i.e., results are area coverage of materials. Unit: % of pixel area [m 2 ] Physically based model - no statistical approach! i.e., (approx.) linear relationship between reflectance value of a pixel and the area of materials within this pixel Folie 3

4 Spectral Unmixing Basics Causes of spectral mixtures: Object borders Discrete objects Intimate material mixture Shading Adjacency effects PSF effects Multiple scattering not all can be addressed by linear spectral unmixing! Folie 4

5 Spectral Unmixing Basics ρ = ρ * ρ + ρ measured material_ 1 f material_1+ material_2* fmaterial_2+... material_ n* f material_ n Where a mn : reflectance of EM n in band m b m : measured reflectance in band m x m : abundance for EM n Where A: m*n EM-matrix x: abundance vector for n EM b: measured spectrum in m bands if A quadratic (i.e., m=n): Using hyperspectral data: normally overdetermined (m >> n), thus solving by least-squares approximation, e.g. Pseudo-Inverse (Moore-Penrose-inversion) where Folie 5

6 Spectral Unmixing Basics Since not all parameters are known exactly and can be included: introducing error term e: and minimizing error function F in least-squares sense: The RMS error of the mixing model is: i.e., the difference between measured signal (b) and modelled signal (b*) over all bands. Residual spectrum: bandwise difference r i = b i - b i * Folie 6

7 Spectral Unmixing Basics Matrix inversion may result in numerical problems! Linear dependencies between spectrally similar classes Higher number of EM higher probability of linear dependencies Result: ill-conditioned problem Thus check: Condition number of EM matrix A: where denotes euklidian L2-norn Κ >> 1: ill-conditioned problem Eigenvalues 0 of EM correlation matrix DET(A T A) 0 Folie 7

8 MESMA Introduction Multiple Endmember Spectral Mixture Analysis Linear spectral unmixing approach where particular EMs used to model a pixel number of EMs to be used vary on a per-pixel basis Folie 8

9 MESMA Introduction Change in lithology & soil types RMS, Fixed EM RMS, MESMA Folie 9

10 MESMA Basic Principle Linear spectral mixture model: ρ = ρ * f + ρ * f ρ measured material_ 1 material_1 material_2 material_2 material_ n* f material_ n Unmixing: solve overdetermined linear equation system for using constrained least-squares approaches (non-negative, sum-to-one) f material_1... n If we don t know which materials are in the pixel, why not include all EM spectra in one model? Linear dependencies between EM spectra (ill-conditioned EM-matrix) (Intrinsic) data dimensionality restricts number of EMs Folie 10

11 MESMA Basic Principle Example using 3 EM-Classes: - PV: photosynthetic active vegetation - NPV: non-photosynthetic active veg. - Soil: soils & rocks Thus using MESMA: only a small number of EMs are used at the same time, but EM can vary. 2 approaches: Unmix using all combinations of 2,3 n EMs & select best-fitting model or: Group EM into (thematic) classes and vary EM within these classes Folie 11

12 MESMA Basic Principle PV: photosynthetic active vegetation NPV: non-photosynthetic active veg. Soil: soils & rocks MESMA assuming 3 classes PV, NPV & Soil per pixel with l, m, and n EM 1st model: EM_PV-1, EM_NPV-1, EM_Soil-1 2nd model: EM_PV-1, EM_NPV-1, EM_Soil-2 nth model: EM_PV-1, EM_NPV-1, EM_Soil-n n+1 th model: EM_PV-1, EM_NPV-2, EM_Soil-1 2*n th model: EM_PV-1, EM_NPV-2, EM_Soil-n 2n+1 th model: EM_PV-1, EM_NPV-3, EM_Soil-1 m*n th model: EM_PV-1, EM_NPV-m, EM_Soil-n m*n+1 th model: EM_PV-2, EM_NPV-m, EM_Soil-n l*m*n th model: EM_PV-l, EM_NPV-m, EM_Soil-n Folie 12

13 MESMA Parameters How many EM models i.e., how many EM classes? and how many EM per class? Large numer of EM: more materials & spectral variability considered. But: calculation time increases Large numer of EM classes: more parts of image can be modeled / higher thematical content But: more problems with linear dependencies between EM Unmixing with large number of EM classes will (almost always) have smaller RMSE But: reasonable or only mathematical optimization? Test: if plenty of pixels have small EM-fractions (<10% abundance) => likely to be only mathematical optimization Folie 13

14 MESMA Parameters Thus: use as few EM classes as possible Calculate with n and n+1 EM-classes, analyze RMSE & then select model per pixel Or: fixed nummer of EM-classes & use algorithm like BVLS which can exclude EM classes Depending on application / study area typically EM classes for urban applications: Pervious Impervious ( Shade), PV NPV Roofs Other for dryland applications: Green Veg Dry Veg Soils ( Shade) Thematically reasonable number of classes In total about EM models with 3-15 EM per class Folie 14

15 MESMA Parameters Model Selection Criteria: EM model with minimum RMSE same with 0.95 f same with no residual deviation in the same direction in more than n successive bands (n ~ 7) Automated residual analysis Check residual spectra for diagnostic absorption features Identify & parameterize these features Take advantage of spectroscopic data! Folie 15

16 Selecting EM for MESMA Derivation of Image EM: As for all unmixing approaches (see papers by PLAZA et al.) First step: selection of spectrally extreme pixels using AMEE, SMACC, 2nd step: identification of these EM spectra Selection of EM for MESMA: 3rd step: selection of a suitable EM subset: Datatests like Class / EM Average RMSE (CAR, EAR) (DENNISON & ROBERTS) EM which model most (subset) pixels Manual interpretation & selection of EM candidates, field knowledge Recently no optimal automated & data-driven solution exists 4th step depending on MESMA approach: grouping of suitable EM into EM classes Folie 16

17 MESMA Published Approaches I MESMA Approaches for EM model selection Brute Force (i.e., calculation of all EM combinations) Pro: best EM model guaranteed Con: time consuming Monte Carlo approach (ASNER et al., randomly selecting EM from bundles of similar spectra) Pro: fast Con: monte carlo approach possible selection of unsuitable EM model Iterative EM selection based on residual analysis (BACHMANN et al.) Pro: fast (7x), adjusted to improved model selection criteria Con: decreased accuracy (by 2-7% abundance absolute) Folie 17

18 MESMA Published Approaches II MESMA Approaches for EM model selection Cont Neighborhood to crisp classes (SEGL et al.) Pro: fast, good probability for best EM model Con: existence of pure pixels, depending on crisp pre-classification Colinearity factor (GARCIA-HARO et al., pre-selection of promising EM models) Pro: fast Con: - Note: final EM selection is done brute force Segment-based EM model selection as a modification of these approaches Folie 18

19 Application Example Ground Cover Fractions Folie 19

20 Application Example Ground Cover Fractions Geographical Background Main study area: National Parc Cabo de Gata, Province Almeria, SE Spain Small-scaled mosaic of vegetation patches (tussock and annual grasses, palms & small bushes) and bare soil / rubble areas. Various vegetation conditions (green dry dead plants & plant parts) Type, degree and distribution of ground cover define degradation potential, and indicate disturbance & dangers. Thus, cover-percentage is a frequent parameter in land degradation models. Folie 20

21 Main Testsite: ational Parc Cabo de Gata, Province Almeria, SE Spain Folie 21

22 Application Example Ground Cover Fractions Database: HyMap-Datasets System corrected to at-sensor radiance Geocoded using ORTHO Atmospheric correction, terrain correction & empirical BRDFcorrection using ATCOR Field Spectra Field measurements of ground cover Folie 22

23 Spectral Variability in Dryland Vegetation Folie 23

24 EM Derivation & Selection Hyperspectral Data (atm., terrain & BRDF corrected) Image EM derived by two-stage approach SMACC (Sequential max. angle convex cone) on masked image Masking (classes, bad pixels) Optional: Additional generalized EM SMACC EM-Measures: EAR, myear, CAR, SID Collinearity & Condition of EMs Spectral Identification Scene- Specific EM Manual Check Prozess Additional EM after 1st unmixing iteration (like IEA) EM Selection Subprocess Optional (Manual) Subprocess... In simulations: ~70% of all EM could be automatically retrieved But: what are EM in reality? Spectral Identification Manual Check Additional EM Candidates 1. EM-Set Parametrization of EMs 1st Unmixing Iteration EM-Measures: EAR, myear, CAR, SID Hyperspectral Data (atm., terrain & BRDF corrected) Collinearity & Condition of EMs EM Selection Final EM-Set Hyperspectral Data 2nd & 3rd Unmixing (atm., terrain & BRDF Folie 24 Institut für Methodik Iteration corrected) der Fernerkundung bzw. Deutsches Fernerkundungsdatenzentrum

25 Iterative MESMA Parameterization of all EM spectra (diagnostic absorption bands related to bio-/geophysical properties, e.g., 2.2µm) Select new PV-EM, NPV-EM, Soil-EM Unmixing using current EM-Model Calculate model RMSE and abundances Check for physically unrealistic abundances Suggest potentially better PV-EM, NPV-EM, Soil-EM Residual analysis: identification & parameterization of absorption features (e.g., over- / under-determination of clay) Next iteration: select EM with desired properties (e.g., more / less clay) Yes Use current abundances as preliminary model Identify spectral features in residuum Calculate combined error score (based on weighted RMSE, residual features, unrealistic abundances) Test, if current error score is lower than preliminary error score Test, if a potentially better EM- Set exists (based on residual analysis) No Keep preliminary model Yes No Use preliminary result as final Folie 25 result. Continue with next pixel

26 Inclusion of Spatial Neighborhood Information 3 MESMA Iterations Unconstrained Unmixing & Residual Analysis Pixel properly modeled? No Current EM-Set Classify spectrum & check, if new EM EM Determination Iteration Constrained Unmixing & Residual Analysis Improved EM-Set Main Iteration Without / With eighborhood Iteration Modal Soil-EM selected in neighborhood? No Constrained Unmixing & Residual Analysis Neighborhood Iteration Check, if model only slightly detoriated Folie 26

27 Influence of View Angle Effects Local Incidence Angle Transition to Rough Terrain Maximum Underestimation of Soil [%] Influence of Local Incidence Angle Soil Abundances Local Incidence Angle [ ] without correction Folie 27 with empirical correction

28 Reliability Measure Linear Spectral Unmixing already offers measure for goodness of fit, i.e. the model RMSE Improved detection of pixels which are likely error-prone based on: Residual analysis & model RMSE Empirical regression model between cover and band indices Local incidence angle L2 data quality flags (from pre-processing) Folie 28

29 Results I HyMap (true colour) Soil EM (areas with soil abundance <30% masked out)) Soil EM spectra Soil abundance [%] NPV abundance [%] Folie 29

30 Results II Unmixing Abundance Sim. Model Nr. Reference Abundance Abundance error - PV Abundance error - NPV Abundance error per single simulation model Abundance error - Soil Histogram abundance error NPV Folie 30

31 Results III Simulations: Mean error: 5% - 10% abundance absolute (depending on scenario), R 2 between 0.65 and 0.85 (significance p < ) 50% of simulated models with error <3% abundance absolute, single errors up to 60% abundance absolute Contribution of errors caused by EMs: 60% - 80% Real-world data: Mean error: 9.6% abundance absolute, R 2 between 0.76 and 0.86 (significance p < 0.005), single errors up to 20% abundance absolute Literature values for MESMA: Mean errors: 5 15% abundance absolute, depending on applications & methods Folie 31

32 Results IV Factors influencing the unmixing accuracy: MESMA (~4% abundance absolute, 30% - 50% relative) EM selection (~4% abundance absolute, 20-40%% relative, might significantly increase if wrong EM) Model selection criterion (~3% abundance absolute, 20-25% relative, important when not all EM were found) Solving algorithm / constraints (up to 20%) Empirical correction of local view angle effects (~2% abundance absolute, 20% relative) Shading (<2% abundance absolute, <10% relative) but these numbers are case-specific! Folie 32

33 MESMA Summary When to use MESMA? Heterogeneous scenes Large number of materials to be mapped High spectral variability within material classes No fast / real-time processing is required Why use MESMA? Increased unmixing accuracy High number of EM possible Spectral variability explicitly modeled Appropriate EM for each pixel are automatically selected Reduced problems with EM collinearity thus (often) stable mixing model Folie 33

34 Selected References on MESMA: ROBERTS, D.A. ; GARDNER, M. ; CHURCH, R. ; USTIN, S. ; SCHEER, G. ; GREEN, R.O.: Mapping Chaparral in the Santa Monica Mountains Using Multiple Endmember Spectral Mixture Models. In: Remote Sensing of Environment 65 (1998), S DENNISON, P.E. ; HALLIGAN, K.Q. ; ROBERTS, D.A.: A Comparison of Error Metrics and Constraints for Multiple Endmember Spectral Mixture Analysis and Spectral Angle Mapper. In: Remote Sensing of Environment 93 (2004), S BALLANTINE, J.-A. ; OKIN, G.S. ; PRENTISS, D.E. ; ROBERTS, D.A.: Mapping North African Landforms Using Continental Scale Unmixing of MODIS Imagery. In: Remote Sensing of Environment 97 (2005), S ASNER, G.P. ; LOBELL, D.B.: A Biogeophysical Approach for Automated SWIR Unmixing of Soils and Vegetation. In: Remote Sensing of Environment 74 (2000), S ASNER, G.P. ; ELMOR, A.J. ; HUGES, R.F. ; WARNER, A.S. ; VITOUSEK, P.M.: Ecosystem Structure along Bioclimatic Gradients in Hawaii from Imaging Spectroscopy. In: Remote Sensing of Environment 96 (2005), S SEGL, K. ; ROESSNER, S. ; HEIDEN, U. ; KAUFMANN, H.: Fusion of Spectral and Shape Features for Identification of Urban Surface Cover Types Using Reflective and Thermal Hyperspectral Data. In: ISPRS Journal of Photogrammetry & Remote Sensing 58 (2003), S GARCIA-HARO, F. ; SOMMER, S. ; KEMPER, T.: A New Tool for Variable Multiple Endmember Spectral Mixture Analysis (VMESMA). In: International Journal of Remote Sensing 26 (2005), Nr. 10, S BACHMANN, M.; MÜLLER, A.; HABERMEYER, M.; SCHMIDT, M.; DECH, S.: Iterative MESMA Unmixing for Fractional Cover Estimates - Evaluating the Portability. In: Proceedings of the 4th EARSeL Workshop on Imaging Spectroscopy. Warsaw, 2005 Folie 34

35 Vacant Hyper-I-Net Position: ESR2 - Improved hyperspectral sensor design Topic: Design & implementation of a modular sensor simulation tool. Incl. spectral, radiometric, and geometric instrument characterization. Background: Degree in Physics, Meteorology or Engineering Sciences Institutions: German Aerospace Center (DLR), Oberpfaffenhofen, Germany Kayser-Threde GmbH (KT), Munich, Germany. Contact: Andreas Müller Stefan Hofer Rudolf.Richter@dlr.de Folie 35

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37 MESMA Parameters Red line: reference soil spectrum Green line: same soil with clay absorption (abs. depth 4% reflectance absolute) Black line: reduced overall albedo by 1% absolute Differences Red-Green: 0.3% of overall albedo Difference Red-Black: 2.9% of overall albedo Folie 37

38 MESMA Approaches Overview Folie 38

39 Shade Component Shade component Not necessary in MESMA since EM with different overall brightness can be used Flat shade spectrum is oversimplified! Ratio direct / diffuse irradiation and/or leaf transmission spectra are required (=> blue XXX) Or: radiative transfer model in order to calculate shaded surfaces incl. multiple scattering effects Inclusion of a flat shade component may result in an ill-conditioned mixing model When using shade component: Better: Check that spatial distribution of shade-em (mostly) corresponds to terrain patterns! Terrain correction to remove topograhic illumination effects Image EM implicitly include canopy shade & multple scattering effects Simulation of (partially) shaded soil-ems (ADLER-GOLDEN for SAM) Then unmixing without shade Or: normalization of image & EM Folie 39