1. Image Pre-Processing Continuation… Spectral Enhancement Image Pre-Processing Continuation… Spectral Enhancement

2. Image Pre-Processing Radiometric Enhancement:Radiometric Enhancement: Image RestorationImage Restoration Atmospheric CorrectionAtmospheric Correction Contrast EnhancementContrast Enhancement Solar Angle AdjustmentSolar Angle Adjustment Conv. to Exo-Atmos. ReflectanceConv. to Exo-Atmos. Reflectance Spectral Enhancement:Spectral Enhancement: Spectral IndicesSpectral Indices PCA, IHS, Color TransformsPCA, IHS, Color Transforms T-Cap, BGWT-Cap, BGW Radiometric Enhancement:Radiometric Enhancement: Image RestorationImage Restoration Atmospheric CorrectionAtmospheric Correction Contrast EnhancementContrast Enhancement Solar Angle AdjustmentSolar Angle Adjustment Conv. to Exo-Atmos. ReflectanceConv. to Exo-Atmos. Reflectance Spectral Enhancement:Spectral Enhancement: Spectral IndicesSpectral Indices PCA, IHS, Color TransformsPCA, IHS, Color Transforms T-Cap, BGWT-Cap, BGW Consists of processes aimed at the geometric and radiometric correction, enhancement or standardization of imagery to improve our ability to interpret qualitatively and quantitatively image components. ImagePre-Processing Spatial Enhancement:Spatial Enhancement: Focal AnalysisFocal Analysis Edge-DetectionEdge-Detection High/Low Pass FiltersHigh/Low Pass Filters Resolution MergesResolution Merges Statistical FilteringStatistical Filtering Adaptive FilteringAdaptive Filtering Texture FiltersTexture Filters Geometric CorrectionGeometric Correction Polynomial TransformationPolynomial Transformation Ground Control PointsGround Control Points ReprojectionsReprojections Spatial Enhancement:Spatial Enhancement: Focal AnalysisFocal Analysis Edge-DetectionEdge-Detection High/Low Pass FiltersHigh/Low Pass Filters Resolution MergesResolution Merges Statistical FilteringStatistical Filtering Adaptive FilteringAdaptive Filtering Texture FiltersTexture Filters Geometric CorrectionGeometric Correction Polynomial TransformationPolynomial Transformation Ground Control PointsGround Control Points ReprojectionsReprojections

3. Principal Component Analysis PCA PCA Principal Components Analysis is a procedure for transforming a set of correlated variables into a new set of uncorrelated variables. This transformation is a rotation of the original axes to new orientations that are orthogonal to each other with little or no correlation between variables Where digital image processing is concerned, this procedure is predominantly exploratory in nature and is used to help in the extraction of features and to reduce dimensionality of data

4. Source: http://umbc7.umbc.edu/~tbenja1/exer1.html After Lillesand and Keifer, 1994 This scatterplot between two spectral bands implies a strong correlation. One band can be used to predict (to a certain level) the response of the other. Principal Component Analysis PCA Reduces these data into two orthogonal components. The first (CI) contains the common information between bands 1 and 2. The second (CII) contains residual, or independent, information. Depending on the amount of covariance between bands 1 and 2, the second component may not contain a significant amount of information and can be eliminated. This scatterplot between two spectral bands implies a strong correlation. One band can be used to predict (to a certain level) the response of the other. Principal Component Analysis PCA Reduces these data into two orthogonal components. The first (CI) contains the common information between bands 1 and 2. The second (CII) contains residual, or independent, information. Depending on the amount of covariance between bands 1 and 2, the second component may not contain a significant amount of information and can be eliminated.

5. Landsat Thematic Mapper image of Curlew Valley taken on July 4 th, 1999 with a 4,3,2 (RGB) band combination.

6. Eigenmatrix Eigenvalues The Eigenvalues show the amount of information contained within each component. The Eigenmatrix contains the coefficients used to calculate each component for the input image. This matrix is a direct result of the covariance between each band.

7. Factor loadings = what type of component (i.e. visible, infrared) is it? R kp : Factor loading a kp :Eigenvector for band k and component p λ p : Eigenvalue for the pth component S k : Standard deviation for band k

9. Landsat Thematic Mapper image of Curlew Valley taken on July 4 th, 1999 converted to a principal component image with a 1,2,3 (RGB) PCA channel combination.

10. PCA1 = (TM-B1)0.194 + (TM-B2)0.0413 + (TM-B3) ‑ 0.332 + (TM-B4)0.196 + (TM-B5) ‑ 0.078 + (TM-B6)0.640 + (TM-B7) ‑ 0.628 PCA2 = (TM-B1)0.222 + (TM-B2)0.102 + (TM-B3) ‑ 0.406 + (TM-B4)0.220 + (TM-B5) ‑ 0.142 + (TM-B6)0.370 + (TM-B7)0.754 PCA3 = (TM-B1)0.348 + (TM-B2)0.092 + (TM-B3) ‑ 0.495 + (TM-B4)0.312 + (TM-B5) ‑ 0.209 + (TM-B6)-0.670 + (TM-B7)-0.184 Accounts for - 72.28% of variation Accounts for – 22.07% of variation Accounts for – 2.62% of variation

11. PCA4 = (TM-B1)-0.232 + (TM-B2)0.962 + (TM-B3)0.045 + (TM-B4)0.071 + (TM-B5)0.105 + (TM-B6)-0.011 + (TM-B7)-0.034 PCA5 = (TM-B1)0.556 + (TM-B2)0.202 + (TM-B3)0.439 + (TM-B4)-0.289 + (TM-B5)-0.608 + (TM-B6)0.050 + (TM-B7)-0.009 PCA5 = (TM-B1)0.201 + (TM-B2)-0.053 + (TM-B3)0.533 + (TM-B4)0.801 + (TM-B5)0.170 + (TM-B6)0.017 + (TM-B7)0.023 Accounts for – 1.84% of variation Accounts for – 0.90% of variation Accounts for – 0.22% of variation

12. PCA5 = (TM-B1)0.622 + (TM-B2)-0.094 + (TM-B3)-0.022 + (TM-B4)-0.289 + (TM-B5)0.720 + (TM-B6)-0.011 + (TM-B7)0.018 Accounts for – 0.07% of variation Components 1 – 3 account for 96.97% of the total variation While the remaining components only account for a combined 3.03% of the total variation, there may be spatial information available.