Hyperspectral Analysis Techniques Identifying Spectral Endmembers Identifying Target Materials Mapping Materials

Almost every pixel is a "mixed pixel" at some scale Mixed pixels contain areas with different spectral reflectance Can be different materials or different light environments (e.g., shadow) Total reflectance from a mixed pixel is a mixture of the reflectance of individual components Common with moderate resolution data in arid and semi-arid environments (like Wyoming) Can be viewed as a challenge or an opportunity

How do spectral signatures mix? Two possibilities: Linear (proportional) mixing Non-linear mixing Typically assume the former but in reality are often dealing with the latter!

Linear mixture schematic No internal reflectance…independent light paths

Non-linear mixing schematic Internal/multiple interacting reflectance paths

Spectral endmembers Spectral endmembers are the spectrally “pure” components of a pixel. Should include all major pixel components in mixture analysis To unmix pixels, you need pure spectra of endmembers Typically collected in the field (or lab) with a spectrometer Can be extracted from the imagery if you can find pixels with each of the pure components and no spectral contaminants Remember that if endmember spectra are measured on ground the aerial imagery MUST be corrected/calibrated for analysis!

How will pixels 1, 2, and 3 be interpreted spectrally? Mixed “pixels” How will pixels 1, 2, and 3 be interpreted spectrally? From U. of Conn. website

Pure sand, pure salt, 50/50 mix spectral signatures. Linear?

Same as previous with linear mixture prediction (in red)

But…most analyses assume linear mixing Point is that one should be aware that nonlinear mixing might be a possibility In case of preceding graphs, the grain sizes of the salt and sand are similar and there is lots of internal reflection. But…most analyses assume linear mixing If salt and sand were arranged in a checkerboard pattern (rather than homogenously mixed) the linear model would work Linear mixing often works as a reasonable approximation of pixel components but can be erroneous Non-linear unmixing models are more complex but can be developed

Hyperspectral data provide ability to solve for many endmembers Multiple endmembers require multiple linear equations to solve Can write one equation for each band Hyperspectral = many bands = many equations = many endmembers

Proportion of each constituent in pixel (These are the variables that we must solve for)

Example: 3 endmembers x = fraction of pixel occupied by Endmember A y = fraction of pixel occupied by Endmember B z = fraction of pixel occupied by Endmember C You want to find (solve for) x, y and z So for one band (b1) you can write an equation: Total Pixel Reflectance in b1 = x*Apure + y*Bpure + z*Cpure where Apure, Bpure, and Cpure are reflectances of pure A, B, and C.

Solving for 3 unknowns requires 3 equations which means you need 2 bands (and the sum of the fractions) Rb1 = xApure1 + yBpure1 + zCpure1 Rb2 = xApure2 + yBpure2 + Cpure2 Also know that: x + y + z = 1.0 Solve system of equations to find proportions x, y, z

Solving systems of equations For a few endmembers (a few equations) you can use algebra to solve simultaneous equations For many endmembers (many equations) it is more efficient to use linear (matrix) algebra Some software can do this for you. A good exercise is to do this yourself for a small number of endmembers (2 or 3)

Using feature space to identify endmembers From the Map and Image Processing System (MIPS) User Guide

Procedure for finding endmembers Compute Minimum Noise Fraction (MNF) components Necessary because you want to work with a feature space defined by a small number of information rich (low noise) components Original bands highly correlated and potentially noisy. Use MNF feature space and look for “extreme pixels” around the margins. Various techniques available for doing this – Pixel Purity Index (PPI) is commonly used.

Pixel Purity Index (PPI) Generate a series of random vectors from origin of feature space through data cloud Project all of the data cloud pixels onto each vector Record low and high extreme pixels and tally how many times a particular pixel is “extreme” Pick extreme pixels and visualize them (computer visualization) in an n-dimensional space Choose pixels that correspond to “protuberances” on the cloud Map the pixels back onto original image and generate spectra

N-dimensional visualizer in ENVI Can choose bands (on right highlighted white) and rotate data cloud in resulting feature space.

Maps of 3 endmembers in the Big Horn Basin (from an ENVI tutorial) After unmixing, you can create images showing fractions of each endmember. Maps of 3 endmembers in the Big Horn Basin (from an ENVI tutorial)

Identifying target materials One goal in hyperspectral analysis is to identify materials in an image For example, an economically valuable mineral or particular plant species. Requires a spectral matching algorithm that compares pixel spectra to the target spectrum Spectral Angle Mapping (SAM) Spectral Correlation Mapper Constrained Energy Minimization May benefit from “continuum removal”

Continuum removal Specific spectral features (e.g., absorption dips) are often diagnostic – we don’t care about the rest of the spectral curve. Continuum removal highlights spectral features. Calculated by dividing the reflectance (A) by the continuum value (B) for each band. Figure from online MIPS manual

Spectral Angle Mapper (SAM) Feature space spectral mapping tool Each spectrum can be represented by a vector in an n- dimensional feature space with tail at origin. Length of vector can vary with overall brightness, illumination, etc. Angle of vector determined by spectral characteristics Compare angle between unknown pixel spectrum and known target spectrum. Pixels with small angle more likely to be target material. “Quick and dirty.” Works well but there are better methods. Often used, however, because easy to calculate.

Target spectrum Pixel spectrum Spectral Angle

Spectral Correlation Mapper (SCM) Similar to SAM, but vectors are normalized to the mean of the two vectors. Similar to Pearson’s Correlation Coefficient in statistics – can better estimate if the two vectors are truly similar Deals better with differences in illumination than SAM. Considered an improvement over SAM (but more computationally intensive)

Constrained Energy Minimization (CEM) Works well for situations where the target occurs in mixed pixels (e.g., sparse vegetation or mixed mineral signatures) Tries to maximize target spectral features and suppress background spectral features. Requires some knowledge of the common background materials – doesn’t work as well when there are unknown or unexpected background materials. Somewhat influenced by differences in illumination.

Mapping Materials Making maps of the distribution of a material is also a spectral matching procedure that results in a map of all occurrences of a target material. Can also map multiple materials using multiple library spectra Uses same algorithms as for material identification SAM, SCM, CEM, etc.

Another hyperspectral application: Leaf nutrient analysis Leaf nutrient content affects the spectral response of leaves and can be assessed with high spectral resolution data Nitrogen, for example, is an important leaf nutrient that is related to forage value and important for ecosystem biogeochemical cycling

Plant chemometrics Hyperspectral data can be used to estimate chemical constituents of plants (and water content) Chlorophyll concentrations Other plant pigments (e.g., xanthophylls) Plant nutrient content (e.g., nitrogen) Similar in theory to other types of hyperspectral analysis: the magnitude of some spectral response must be related to the chemical of interest.

Leaf N From online pdf by Gregory Asner (Stanford University) URL: http://cao.stanford.edu/publications/asner_hyperspectral_chapter121806.pdf

From Gregory Asner (web pdf)

Amount of leaf nitrogen predicted by spectral analysis of hyperspectral data vs. measured amount –good agreement. (from Smith et al. IEEE submission)

Summary Hyperspectral data are powerful but require expertise to interpret Spectral unmixing may be a key to picking apart image components where mixed pixels are prevalent (like Wyoming) but difficult to apply over large areas Spectral matching allows identification and mapping of specific materials (e.g., minerals, plant species) Detailed spectral analysis can be used to map things like leaf nutrient content (just one example) which is important for understanding the spatial nature of ecosystem function