Image transformations Digital Numbers may be composed of three elements: Atmospheric interference (e.g. haze) ATCOR Illumination (angle of reflection) - transforms Albedo (surface cover) Image transformations Ratios enhance albedo contrasts by reducing inter-band similarities (topography) and enlarging spectral differences e.g. Near-IR / Red to identify vegetation Higher values (IR/red) = more vegetation (biomass) 1
Ratio (A/B) created in Raster Calculator or Image Arithmetic (ARI) or Ratio (RTR) Resulting DNs are saved in 16-bit layer or using a scalar multiplier 2
Normalised Difference Vegetation Index NDVI Division compensates for differential lighting It gives a close estimate of biomass This yields values between -1 and 1, a 32 bit channel.. or an 8 bit channel by scaling (+1 and *255) Negative values of NDVI (values approaching -1) correspond to water. Values close to zero (-0.1 to 0.1) = barren areas of rock, sand, or snow. low, positive values represent shrub and grassland (approximately 0.2 to 0.4), high values indicate temperate and tropical rainforests (values approaching 1) Special sensors for NDVI SPOT 5 has extra bands / wide sensor in visible/nir with 1 km resolution to capture a repeat 2400 km swath for global coverage MODIS and NOAA-AVHRR have red /near-ir bands for NDVI NDVI is used measure vegetation amount or biomass, in regional and global estimates. "NDVI is directly related to the photosynthetic capacity and hence energy absorption of plant canopies" 3
Tasseled Cap Transformation Three new channels are created by applying coefficients to the input bands: So each pixel is assigned a new DN in 3 new created channels. TC1,2,3 (Landsat MSS) = a * MSS1 + b* MSS2 + c * MSS3 + d * MSS4 TC1,2,3 (Landsat TM) = e *TM1 + f*tm2 + g*tm3 + h*tm4 + j*tm5 + k*tm7 MSS data, the 4-band dataset created channels: Brightness, Greenness and Yellowness TM data, the 6-band (no thermal) creates: Brightness, Greenness and Wetness The technique was named after the pattern of spectral change of agricultural crops during senescence, plotting brightness against greenness. The sequence is: 1. Bare fields / newly planted crops - high brightness, low greenness (spring) 2. Plant Growth - (slight?) <-<- brightness (early summer) 3. Maturity: -> -> greenness (late summer) 4. Senescence (harvest) - bare field/stubble: <-<-greenness, ->-> brightness (Fall) Tasseled Cap reduces an overlapping multispectral dataset by linear transformation into a lower number of channels (3) which respond to particular scene characteristics. 4
Tasseled Cap Transformation Landsat 5 TM coefficients for the Tasseled Cap Band Brightness Greenness Wetness 1.3037 -.2848.1509 2.2793 -.2435.1973 3.4743 -.5436.3279 4.5585.7243.3406 5.5082.0840 -.7112 7.1863 -.1800 -.4572 Kauth, R. J. and Thomas, G. S., 1976, The tasseled cap --a graphic description of the spectral-temporal development of agricultural crops as seen in Landsat, in Proceedings on the U.S. Department of the Interior 9 U.S. Geological Survey Symposium on Machine Processing of Remotely Sensed Data, West Lafayette, Indiana, June 29 -- July 1, 1976, 41-51. Brightness, greenness, wetness tasseled cap channels see Thayer Watkins website 5
NDVI v Tasseled Cap greenness TCA Greenness is similar to NDVI, with subtle differences and is used in habitat studies. http://www.geospatialworld.net/paper/application/articleview.aspx?aid=460 Principal Components Analysis (PCA) (Like TC) PCA is a mathematical transformation that converts original data into new data channels that are uncorrelated and minimise data redundancy. Differences with TCA : 1. PCA transformation is scene specific - TCA coefficients are 'global 2. TCA creates three new transformed channels, PCA generates as many as there are input channels e.g. for Landsat TM, there could be 6-7 new component channels There is a high correlation between all greenness channels: NDVI, 4/3 ratio, TCA greenness, PCA component 2 (usually) 6
http://geology.wlu.edu/harbor/geol260/lecture_notes/notes_rs_pc.html The bands can be reduced to their respective 'components', by an 'axial rotation' Helpful teapot analogy video: http://www.youtube.com/watch?v=bftmmodfxye The bands can be reduced to their respective 'components', by an 'axial rotation' The main axis through the points is a 'component'; if all points were on it, correlation=1, the first component (PC1) would 'explain' all the variation. The 2nd component (PC2) is normal to PC1, uncorrelated and hence two bands are converted to two components, but most variation is explained by the first (the 2nd is always smaller) PC1= what is explained in both bands (images) PC2= what is different between them (similar to a band ratio) PCA consists of : eigenvectors: the loadings for each band to create new components eigenvalues: how much variance is explained by each component 7
PCA channels (PG scene) Eigenvectors of covariance matrix (arranged by rows): TM1 2 3 4 5 6 7 PC1 0.22 0.15 0.29 0.16 0.75 0.33 0.40. loading for each band PC2-0.28-0.14-0.29 0.82 0.23-0.25-0.16 PC3 0.51 0.31 0.43 0.49-0.46-0.05-0.00 PC4-0.09-0.09-0.19 0.19-0.23 0.91-0.18 PC5 0.31 0.13 0.05-0.12 0.35-0.00-0.86 PC6 0.69-0.16-0.68-0.01 0.01-0.04 0.19 PC7-0.19 0.90-0.39-0.04 0.00 0.00 0.06. Loadings getting smaller PC1: Brightness, PC2: Greenness, PC3: Swirness / Wetness PCA channels (PG scene) Eigenvectors of covariance matrix (arranged by rows): TM1 2 3 4 5 6 7 PC1 0.22 0.15 0.29 0.16 0.75 0.33 0.40 PC2-0.28-0.14-0.29 0.82 0.23-0.25-0.16 PC3 0.51 0.31 0.43 0.49-0.46-0.05-0.00 PC4-0.09-0.09-0.19 0.19-0.23 0.91-0.18 PC5 0.31 0.13 0.05-0.12 0.35-0.00-0.86 PC6 0.69-0.16-0.68-0.01 0.01-0.04 0.19 PC7-0.19 0.90-0.39-0.04 0.00 0.00 0.06 Component Brightness Greenness Swirness / Wetness Impact of TM6 Band 5 v 7 (MIR) Band 1 v 3 (B v R) Band 2 v 3 (Yellowness) PC1: Brightness, PC2: Greenness, PC3: Swirness / Wetness 8
PC components (for PG scene) PC4: TM6, PC5: 5/7, PC6: 1/3, PC7: 2/3 Principal Components Analysis ( Hotelling ) Can also load bands (channels) from multiple dates Why Use PCA? (reduces multiband dataset).. but are they useful? PC1 = what is common between images (no change) PC2 = what is different between most different sets PC3... = what is another difference and so on Analogy e.g. group faces 9
PCA Time series analysis Eastman and Fulk, 1993, "Long sequence time series evaluation using standardized principal components" Photogrammetric Engineering and Remote Sensing, 59, 8, (August) 1307-1312. 36 monthly AVHRR NDVI images for 3 years PC1: average NDVI PC2: = seasonal change PC3: May versus Nov PC4: Oct /April v Feb/Aug Loadings (eigenvectors) (= correlation with original images) PC1 and PC2 Overall brightness / summer-winter difference PC3 and PC4 May/November ; Oct /April v Feb/Aug 10
Sensor changes due to orbit time drift later time of day PC5 Apparent increase in NDVI from sensor drift (Red affected more than NIR) PC6 decreasing amplitude of NDVI effect in forests El Nino effects PC7 PC8 There could be up to 36 components: the rest will show local differences or noise 11