1. Multi-image manipulation
Lecture 5
prepared by R. Lathrop 10/99
Updated 8/03
Readings:
ERDAS Field Guide 6th Ed. Ch 5:

2. Feature Space Image
Visualization of 2 bands of image data simultaneously through a 2 band scatterplot - the graph of the data file values of one band of data against the values of another band
Feature space - abstract space that is defined by spectral units

3. Each dot represents a pixel; the warmer the colors, the higher the frequency of pixels in that portion of the feature space

4. Spectral ratioing
Enhancements resulting from the division of BV values in one spectral band by the corresponding values in another band
BVi,j,r = BVi,j,k/BVi,j,l
Useful for discriminating subtle spectral variations that are masked by the brightness variations in images
Useful for eliminating brightness variations due to topographic slope effects

5. Terrain Shadowing Sunlight Shadow
Land cover Band A BandB Ratio A/B Sunlit Shadow
Sunlit Shadow
Deciduous
Conifer
Adapted from Lillesand & Kiefer, 3rd ed

6. Spectral ratioing
Ratioing compensates for multiplicative rather than additive illumination effects
2 * BVi,j,k = BVi,j,k * BVi,j,l BVi,j,l
2 + BVi,j,k NEQ BVi,j,k BVi,j,l BVi,j,l

7. Spectral Ratioing: for Enhancement
Objective: enhance particular absorption features of materials of interest vs. background reflectance
Numerator is a baseline of background absorption
Denominator is an absorption peak for the material of interest (based on absorption spectra)
As material concentration increases, denominator decreases, index increases

8. Spectral Ratioing: Geological Indices
TM5/TM7 to enhance clay minerals
TM5: 1.55->1.75um provides background reflectance
TM7: 2080->2350um: specific absorption peak for clay minerals
To more effectively discriminate between the various types of clay minerals can use hyperspectral ratios kaolinite: /2190nm montmorillonite 2220/2250nm illite /2488nm
From ERDAS Field Guide 4th ed.

9. Normalized Difference Ratioing
Objective: contrast bands where there is high absorption (low reflectance) vs. low absorption (high reflectance)
Numerator is the difference between two bands where B1 has high reflectance and B2 has lo reflectance for the feature of interest
Denominator is the sum B1 + B2
Normalizes the difference with the overall scene brightness
B1 – B2 / B1 + B2

10. Normalized Difference Snow Index (NDSI)
Snow reflectance high in the visible ( um) and low in the short-wave infrared (1-4um)
MODIS B4 (0.555um) visible
B6 (1.640 um) short-wave infrared
NDSI = B4 – B6 / B4 + B6
TM R-G-B
Fore more info: Salomonson et al, RSE 89:

11. Vegetation Indices
Linear combination of image bands used to extract information about vegetation: biomass, leaf area, productivity
Most vegetation indices (VI’s) based on the differential reflectances of healthy green vegetation, dead/senescent vegetation and soil in visible vs. near IR wavelengths

12. Reflectance from green plant leaves
Chlorophyll absorbs large % of red and blue for photosynthesis- and strongly reflects in green (.55um)
Peak reflectance in leaves in near infrared (.7-1.2um) up to 60% of infrared energy per leaf is scattered up or down due to cell wall size, shape, leaf condition (age, stress, disease), etc.
Reflectance in Mid IR (2-4um) influenced by water content-water absorbs IR energy, so live leaves reduce mid IR return

13. Vegetation indices Simple ratio: nir/red
Normalized Difference VI (NDVI): nir - red nir + red NDVI ranges from -1 to + 1
Transformed VI to eliminate negative values: TVI : /NDVI + 0.5

14. Vegetation indices
Perpendicular VI determines a pixel’s orthogonal distance from the soil line in image feature space (X axis: red; Y axis: NIR)
The objective is to remove the effect of soil brightness and isolate reflectance changes due to vegetation only

15. Sub-pixel Estimation Spectral Feature Space N I R Re f l e c tance
Sand/Concrete
Increasing Vegetation
Example
Pixel X proportions:
IS: 50%
Grass: 30%
Trees: 20%
Soil Line
Dark Soil/Asphalt
Red Reflectance
Water

16. Vegetation indices
Numerous studies have explored the relationship between remotely sensed vegetation indices and field measured estimates of vegetation amount: above-ground biomass, leaf area
Goal is to be able to estimate and map these key variables of ecosystem state
Best relationships obtained in closed canopy crops. Woody material complicates but does not invalidate the relationship

17. Global Biosphere Vegetation Monitoring
NOAA AVHRR used to create global “greenness” maps based on NDVI. Composited over biweekly to monthly intervals.

18. Global NDVI summed over an entire year

19. Principal Components Analysis (PCA)
Multispectral image data may have extensive inter-band correlation - i.e. two bands may be similar and convey essentially the same information
PCA used to reduce the dimensionality of a data set - i.e. compress the information contained in an original n-channel data set into fewer than n “new” channels or components

20. Principal Components Analysis (PCA)
N-dimensional ellipsoid in image feature space
Goal of PCA is to translate the original axes to a new set of axes, with each axis orthogonal to the others
1st axis or PC is associated with the maximum amount of variance (the ellipsoid’s major axis)
2nd axis (orthogonal to the 1st) contains the next highest amount of variation and so on …

21. Principal Components Analysis (PCA)
Matrix algebra used in PCA, computed from the covariance matrix
Eigenvector provides the direction of the new axes; column of numbers with one coefficient for each of the original input bands
Eigenvalue (l) provides the length of the new axes; one value for each PC

22. Principal Components Analysis (PCA)
The magnitude of the eigenvalue provides an index of the information content explained by that PC
Sum of Variances = total information content = S eigenvalue lp
To calculate proportion of the total information content explained by each PC
%lp = eigenvalue lp x 100
S eigenvalue lp

23. PCA: Example Eigenvector Matrix for PNR_110494.img
PC1 PC2 PC3 PC4 PC5 PC6 PC7
‑ ‑ ‑
‑ ‑0.8714
‑ ‑
‑ ‑
‑ ‑ ‑0.0830 ‑
‑ ‑ ‑ ‑

24. PCA: Example S Variance = 303.32 Covariance matrix for PNR_110494.img
S Variance =

25. PCA: Example The Eigenvalues for PNR_110494.img PC1 256.55 PC2 23.69PC PC PC PC PC PC PC
  S eigenvalue lp =

26. Principal Components Analysis (PCA)
Factor loading: the correlation of each original band with each PC, used to interpret the physical meaning of the PC axes
PCA is heavily data dependent, unique for each image data set – not fixed like Tasseled Cap
Corr (PC1,B1) = (e11 * /l1 ) / /s11
e11 = eigenvector for row (band) 1, col (PC) 1
l1 = eigenvalue for PC 1
s11 = variance for band 1

27. PCA: Example Corr (PC1,B1) = (e11 * / l1 ) / /s11
e11 = eigenvector for row (band) 1, col (PC) 1
l1 = eigenvalue for PC 1
s11 = variance for band 1
Corr (PC1,B1) = ( * /256.55) / /20.29
= ( * ) / 4.50
= 0.813

28. Tasseled Cap Transform
Fixed feature space transformation designed specifically for agricultural monitoring, stable from scene to scene
Red-NIR feature space shows a triangular distribution described as a “tasseled cap”. Over the growing season, crop pixels moved from the base “plane of soils” up the tasseled crop and then back down
Linear transformation of original image data to new axes: brightness, greenness, wetness

29. Sub-pixel Estimation Spectral Feature Space N I R Re f l e c tance
Sand/Concrete
Increasing Vegetation
Example
Pixel X proportions:
IS: 50%
Grass: 30%
Trees: 20%
Soil Line
Dark Soil/Asphalt
Red Reflectance
Water

30. Tasseled Cap Transform
Landsat Thematic Mapper 4 coefficients
Brightness = .3037(TM1) (TM2) (TM3) (TM4) (TM5) (TM7)
Greenness = (TM1) (TM2) (TM3) (TM4) (TM5) (TM7)
Wetness = .1509(TM1) (TM2) (TM3) (TM4) (TM5) (TM7)
Haze = .8832(TM1) (TM2) (TM3) (TM4) (TM5) (TM7)
From ERDAS Field Guide 4th Ed.

31. Multisensor fusion
Various techniques have been developed to merge low spatial resolution (but high spectral resolution) with high spatial resolution (but low spectral resolution, e.g., panchromatic) imagery example: TM and ETM+ PAN
Multisensor fusion will become more common as the new high spatial resolution PAN imagery becomes more widely available

32. One meter Pan-sharpened Multispectral IKONOS imagery (simulated)
Tennis courts in Washington Park, Denver, CO

33. Example: IHS Color-space transform
RGB to IHS: transform fro Red-Green-Blue color space to Intensity-Hue-Saturation
Low and high resolution images are co-registered and resampled to same GRC
3 bands of the multispectral image converted to IHS space then PAN band substituted for the Intensity component, then back-transformed into RGB color space
A disadvantage is that only 3 bands may be transformed simultaneously

34. Intensity, Hue & Saturation color coordinate system
255
Intensity
blue
Saturation
255
255,0
green
red
Hue

35. Example: PCA Spectral domain fusion
Low and high resolution images are co-registered and resampled to same GRC
PCA of multispectral image
Substitution of PAN image for 1st PC, often the “brightness component”, then backtransform to image space
This technique can be used for any number of bands
Generally a good compromise between limited spectral distortion and visually attractiveness

36. Example: High Pass Filter (HPF) method
Capture high frequency information from the high spatial resolution panchromatic image using some form of high pass filter
This high frequency information then added into the low spatial resolution multi-spectral imagery
Often produces less distortion to the original spectral characteristics of the imagery but also less visually attractive

37. Example: Brovey Transform fusion
For each spectral band i
[DNBi / (DNB1 + DNB2 + DNB3)] x (DN high res. Image)
Brovey transform was developed to increase contrast in the low and high tails of the image histogram for visual interpretation- doesn’t preserve the original scene radiometry.
Other methods: Multiplicative
Spherical Coordinates
Wavelets