1. Lecture 12: Image Processing Friday 11 February 2011 Last lecture: Earth-orbiting satellites Reading Ch 7.1 - 7.6

2. Image Processing Because of the way most remote-sensing texts are organized, what strikes most students is the vast array of algorithms with odd names and obscure functions What is elusive is the underlying simplicity. Many algorithms are substantially the same – they have similar purposes and similar results

3. Image Processing There are basically five families of algorithms that do things to images: 1)Radiometric algorithms change the DNs Calibration Contrast enhancement 2) Geometric algorithms change the spatial arrangement of pixels or adjust DN’s based on their neighbors’ values Registration “Visualization” Spatial-spectral transformation Spatial filtering

4. Enhancement: Imagine a DN histogram centered at 75 DN and running from 50 to 100. In lab, you would move sliders to 50 and 100 DN to display it well. Mathematically, you are saying that (100-50)=50 DN’s are going to be packed into 256 gray levels, DN’. Furthermore, the center of the distribution will be 128 DN’. DN’=gain *DN+offset So the amplification factor or gain will be 256/(100-50)=5.12: DN’=5.12*DN+offset Now if we take 75 DN, the central value that we want to be 128, and multiply it by 5.12, we get 384 DN’, so we need to subtract 256 to get the right answer: DN’=5.12*DN-256. Check: DN’=5.12*50-256 = 0; DN’=5.12*75-256=128; DN’=5.12*100-256=156 Calibration: We measure radiance in DNs, but we want to know reflectance. So we can take a known target (say, black and white cardboard with reflectances measured in the lab of 5 and 25%) and image them to find out what radiance DN’s they give (say, 13 and 47, respectively). Then we can do a controlled contrast stretch to give the image in reflectance units: Now, the gain will be  DN /  refl = (25-5)/(47-13)=0.59 (That is, refl=0.59*DN+offs, and we find offset by Knowing 0.59*13=5, or offset = 5-0.59*13=5-7.67=-2.67, so refl=0.59*DN-2.67. Check: 25=0.59*47-2.67=25.06 (roundoff) Calibration is just a special kind of contrast stretch Contrast stretching & calibration

5. Geometric registration Acquired image, distorted Map with locations of control points Pixel locations in original and corrected images DN values in corrected image are found by interpolation from the nearest neighbors in the acquired image

6. Image Processing 3) Spectral analysis algorithms are based on the relationship of DNs within a given pixel Color enhancement Spectral transformations (e.g., PCA) Spectral Mixture Analysis 4) Statistical algorithms characterize or compare groups of radiance data Estimate geophysical parameters Spectral similarity (classification, spectral matching) Input to GIS

7. Image Processing 5) Modeling calculate non-radiance parameters from the radiance and other data Estimate geophysical parameters Make thematic maps Input to GIS

8. Image Processing There is a dazzling array of things for the future professional to become familiar with I’m trying to over-simplify it to begin with Most algorithms are handled pretty well in most remote-sensing texts. Spectral Mixture Analysis is an exception, so… - we’ll look at Spectral Mixture Analysis next lecture

9. Raw image data Instrument calibration Image rectification, cartographic projection, registration, geocoding Atmospheric compensation Pixel illumination-viewing geometry (topographic compensation) Image display/inspection 1. 2. 3. 4. 5. Pre-processing Image Processing Sequence (single image) Working image data

10. Image Processing Sequence (single image) Working image data Product Further image processing Selection of training data/endmembers Initial classification or other type of analysis Interpretation/verification or further analysis 6. 7. 8. 9. Processing Spectral analysis 10.

11. Ratios in 2-space TM4 TM3 Ratio – 11 TM4TM3 Ratio – 1.5 Ratio - 1.1 sunlit shadowed shadow

12. The Vegetation Index (VI) = DN 4 /DN 3 is a ratio. Ratios suppress topographic shading because the cos(i) term appears in both numerator and denominator. Ratios

13. NDVI Normalized Difference Vegetation Index DN 4 -DN 3 is a measure of how much chlorophyll absorption is present, but it is sensitive to cos(i) unless the difference is divided by the sum DN 4 +DN 3.

14. Dimension rotation x y x’ y’ 0.7x,0.7y -0.7x, 0.7y 0.5x,0.87y y y x x x’ y’ -087x,0.5y 0x,1y -1x,0y + + +

15. Principal Component Analysis (PCA) Designed to reduce redundancy in multispectral bands Topography - shading Spectral correlation from band to band Either enhancement prior to visual interpretation or pre-processing for classification or other analysis Compress all info originally in many bands into fewer bands http://en.wikipedia.org/wiki/Principal_component_analysis

16. Principal Component Analysis (PCA) - The math behind the button In the simple case of 45º axis rotation, Finding  http://en.wikipedia.org/wiki/Principal_component_analysis DN 1 ’ DN 2 ’ [] = [] cos  sin  -sin  cos  [] DN 1 DN 2 cov  []        = 45º PC 1 PC 2 ’ [ ] = http://www.cs.otago.ac.nz/cosc453/student_tutorials/principal_components.pdf Cov’=R T covR; cov’ is the matrix having eigenvalues as diagonal elements and R T is the transpose of R. Eigenvalues can be found by diagonalizing cov. R has eigenvectors as column vectors

17. Principal Component Analysis In the simple case of 45º axis rotation, PC 1 PC 2 The rotation in PCA depends on the data. In the top case, all the image data have similar DN 2 /DN 1 ratios but different intensities, and PC 1 passes through the elongated cluster. In the bottom example, vegetation causes there to be 2 mixing lines (different DN 4 /DN 3 ratios (and the “tasseled cap” distribution such that PC 1 still passes through the centroid of the data, but is a different rotation that in the top case.

18. Tasseled Cap Transformation Transforms (rotates) the data so that the majority of the information is contained in 3 bands that are directly related to physical scene characteristics Brightness (weighted sum of all bands – principal variation in soil reflectance) Greenness (contrast between NIR and VIS bands Wetness (canopy and soil moisture)

19. Green Soil TCT is a fixed rotation that is designed so that the mixing line connecting shadow and sunlit green vegetation parallels one axis and shadow-soil another. It is similar to the PCT. Tasseled Cap Transformation (TCT)

20. Next lecture – Spectral Mixture Analysis