Multi-image manipulationLecture 5

prepared by R. Lathrop 10/99

Updated 8/03

Readings:

ERDAS Field Guide 6th Ed. Ch 5:149-164

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

Red Reflectance

NIRReflectance

Spectral Feature Space

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

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

Sunlight Terrain Shadowing

Shadow

Land cover Band A BandB Ratio A/B Sunlit 140 150 0.93 Shadow 56 61 0.92

Sunlit 102 145 0.70 Shadow 41 58 0.71

Deciduous

Conifer

Adapted from Lillesand & Kiefer, 3rd ed

Spectral ratioing

• Ratioing compensates for multiplicative rather than additive illumination effects

• 2 * BVi,j,k = BVi,j,k 2 * BVi,j,l BVi,j,l

• 2 + BVi,j,k NEQ BVi,j,k 2 + BVi,j,l BVi,j,l

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

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

From ERDAS Field Guide 4th ed.

To more effectively discriminate between the various types of clay minerals can use hyperspectral ratios kaolinite: 2160/2190nm montmorillonite 2220/2250nm illite 2350/2488nm

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

Normalized Difference Snow Index (NDSI)

• Snow reflectance high in the visible (0.5-0.7um) 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

Fore more info: Salomonson et al, 2004. RSE 89:351-360.

TM 4-5-2 R-G-B

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

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

Vegetation indices

• Simple ratio: nir/red

• Normalized Difference VI (NDVI):nir - rednir + red

NDVI ranges from -1 to + 1

• Transformed VI to eliminate negative values:

TVI : /NDVI + 0.5

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

Red Reflectance

N I R Re f l e c tance

Spectral Feature Space

Example

Pixel X proportions:

IS: 50%

Grass: 30%

Trees: 20%

Sub-pixel Estimation

Soil Line

Increasing Vegetation

Water

Sand/Concrete

Dark Soil/Asphalt

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

Global Biosphere Vegetation Monitoring

NOAA AVHRR used to create global “greenness” maps based on NDVI. Composited over biweekly to monthly intervals.

Global NDVI summed over an entire year

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

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 …

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 () provides the length of the new axes; one value for each PC

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 = eigenvalue p

• To calculate proportion of the total information content explained by each PC

%p = eigenvalue p x 100

--------------------------

eigenvalue p

 

PCA: ExampleEigenvector Matrix for PNR_110494.img

 

PC1 PC2 PC3 PC4 PC5 PC6 PC7

0.2285 0.1188 ‑0.5739 0.3363 ‑0.5816 ‑0.3576 0.1576

0.1687 0.1584 ‑0.3570 0.0624 0.1299 0.1967 ‑0.8714

0.3008 0.0935 ‑0.4488 ‑0.0253 0.2900 0.6445 0.4461

0.2294 0.9171 0.2814 ‑0.0990 0.0275 ‑0.1079 0.0685

0.7790 ‑0.2903 0.4305 0.0155 ‑0.2958 0.1695 ‑0.0830

0.0365 0.0081 0.1955 0.9000 0.3827 ‑0.0462 0.0394

0.4097 ‑0.1625 ‑0.1970 ‑0.2492 0.5708 ‑0.6126 0.0594

PCA: ExampleCovariance matrix for PNR_110494.img

1 2 3 4 5 6 7

20.29 13.51 21.60 13.28 40.93 0.78 25.00

13.51 10.54 16.07 11.62 30.09 0.64 18.17

21.60 16.07 27.64 17.56 56.24 1.46 32.46

13.28 11.62 17.56 34.81 41.53 3.03 19.85

40.93 30.09 56.24 41.53 161.0 8.49 81.15

0.78 0.64 1.46 3.03 8.49 3.44 2.95

25.00 18.17 32.46 19.85 81.15 2.95 45.60

Variance = 303.32

PCA: ExampleThe Eigenvalues for PNR_110494.img

 

PC1 256.55

PC2 23.69

PC3 16.70

PC4 2.73

PC5 1.64

PC6 1.46

PC7 0.55

  eigenvalue p = 303.32

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 * 1 ) / 11

 

e11 = eigenvector for row (band) 1, col (PC) 1

1 = eigenvalue for PC 1

11 = variance for band 1

PCA: ExampleCorr (PC1,B1) = (e11 * 1 ) / 11

 

e11 = eigenvector for row (band) 1, col (PC) 1

1 = eigenvalue for PC 1

11 = variance for band 1

Corr (PC1,B1) = (0.2285 * 256.55) / 20.29

= (0.2285 * 16.017) / 4.50

= 0.813

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

Red Reflectance

N I R Re f l e c tance

Spectral Feature Space

Example

Pixel X proportions:

IS: 50%

Grass: 30%

Trees: 20%

Sub-pixel Estimation

Soil Line

Increasing Vegetation

Water

Sand/Concrete

Dark Soil/Asphalt

Tasseled Cap Transform• Landsat Thematic Mapper 4 coefficients• Brightness = .3037(TM1) + .2793(TM2) + .4743(TM3)

+ .5585(TM4) + .5082(TM5) + .1863(TM7)• Greenness = -.2848(TM1) - .2435(TM2) - .5436(TM3)

+ .7243(TM4) + .0840(TM5) - .1800(TM7)• Wetness = .1509(TM1) +.1973(TM2) + .3279(TM3)

+ .3406(TM4) - .7112(TM5) - .4572(TM7)• Haze = .8832(TM1) - .0819(TM2) - .4580(TM3)

- .0032(TM4) - .0563(TM5) + .0130(TM7)

From ERDAS Field Guide 4th Ed.

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

One meter Pan-sharpened Multispectral IKONOS imagery (simulated)

Tennis courts in Washington Park, Denver, CO

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

Intensity, Hue & Saturation color coordinate system

Saturation

Hue

Intensity

0

255

0255

redgreen

blue

255,0

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

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

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