• Spatial Resolution: 17m • Band number: 18
• • • • • • • •
Target Name: Beijing Image Date: 2005-09-17 LL:039.97, 0116.37 Solar Zenith Angle: 039 Solar Azimuth Angle: -14.367 Observation Zenith Angle: 52.59 Observation Azimuth Angle: 359.41 CHRIS Mode: 3 (LAND CHANNELS)
3) INVERSION
• Least square
ˆ min r XF
2
ˆ U (XT X)1 XT S F • Unconstrained solution • Sum-to-one constrained solution
U ˆF F ˆ U ( XT X) 1 ZT Z( XT X) 1 ZT 1 (Zα ˆ F b)
• In interactive endmember determination, image endmember selection is achieved through an educated trial-and-error approach. An analyst has some knowledge of the field site or data set, and a set of objectives for conducting the analysis.
• QuickBird
• Endmember Selection
• Refer to QB image
0.3
Reflectance
0.1
Reflectance
Vegetation
Soil
Impervious
(a)
0.2
Vegetation
0.3
(b)
0.2
Soil
• Number of endmembers
• Should be smaller than band number • Fewer endmembers is preferred if most variance has been explained
• Spectra of endmembers
• Reference endmember • Image endmember
其中: Z 1,...,1 , b 1
T
• Non-negativity constraint • Full Constrained Least Square (FCLS)
• Heinz, 2001
RESIDUAL ERROR VS. RETRIEVAL ERROR
• Residual error
(Keshava & Mustard, IEEE Signal Processing Magazine, 2002,)
• Graphical illustration of linear mixture models
(Keshava & Mustard, IEEE Signal Processing Magazine, 2002,)
One Peak
Scatter Plot of CHRIS (17m)
WHY WE NEED IT?
• Mixed pixels commonly exist for two reasons
• Spatial resolution of a sensor is low enough that disparate materials can jointly occupy a single pixel • Mixed pixels can result when distinct materials are combined into a homogeneous mixture
混合像元分解
陈学泓
RELATIVE TERMS
• Spectral Unmixing • Spectral Mixture Analysis (SMA) • Sub-Pixel Analysis • Soft Classification
Special issue in IEEE TGRS
1. INTRODUCTION
• Basis of Linear Model
• The reflecting surface is portrayed as a checkerboard mixture, and any given package of incident radiation only interacts with one component (i.e., no multiple scattering between components).
2) ENDMEMBER DETERMINATION
• Reference endmember: in situ measurement
• Calibration is required
• Image endmember: convenient
2) ENDMEMBER DETERMINATION
2. LIL MIXTURE MODEL
• Linear Model
S fi xi w XF w
i 1 m
subject to: fi 1, fi 0, i 1,..., n
i 1
m
其中 S: 表示混合像元反射光谱, S ( s1 , s2 ,..., sL )T , L表示光谱波段数 X : L m矩阵, 表示端元反射光谱,X (x1 , x 2 ,...x m ), xi 表示第i个端元的光谱 F : 表示端元的丰度, F ( f1 ,f 2 , ..., f m )T ,m为端元的数目 w : 误差
WHY WE NEED IT?
• Hard classification: Continuous spectra information are transformed into distinct labels.
Two Peaks
Hard classification is not enough
Scatter Plot of QuickBird
1) DIMENSION REDUCTION
• Maximum Noise Fraction (MNF)
噪声白化
• 与PCA相比，MNF引入噪声的波段相关模型
2) ENDMEMBER DETERMINATION
• Estimate the set of distinct spectra (endmembers) that constitute the mixed pixels in the scene.
ˆ e r XF
• Retrieval error
ˆ F F F true
• They are not equivalent, residual error sometime indicates a lower error than it should be.
EXAMPLES
• Data: CHRIS/PROB
• ii: then the volume of the simplex is
• iii: a trial volume is calculated for every pixel in each endmember position by replacing that endmember and recalculating the volume • iv: repeat until the volume does not inrease
• Automated algorithms may employ statistics to capture variability, but their analytical determination may result in endmember estimates that satisfy some optimality criterion, but are physically unrealistic.
GENERAL UNMIXING PROCEDURE
• Dimension reduction • Endmember determination • Inversion
1) DIMENSION REDUCTION
• Dimension Reduction
• Reduce the dimension of the data in the scene. This step is optional and is only invoked by some algorithms to simplify the operations of subsequent steps. • Principle Component Analysis (PCA) • Maximum Noise Fraction (MNF) • Singular Value Decomposition (SVD)
• Automated method
2) ENDMEMBER DETERMINATION
• Pure Pixel Index (PPI): indicates the purity of each index
• Randomly generating L lines in the N-D space (PCA/MNF space) • Ones falling at the extremes of each line are counted.
WHAT IS SPECTRAL UNMIXING?