Radiometric Correction

Lecture 4

February 11, 2005

Procedures of image processing

Preprocessing Radiometric correction is concerned with improving the accuracy of surface spectral

reflectance, emittance, or back-scattered measurements obtained using a remote sensing system. Detector error correction, Atmospheric and topographic corrections

Geometric correction is concerned with placing the above measurements or derivativeproducts in their proper locations.

Information enhancement Point operations change the value of each individual pixel independent of all other

pixels Local operations change the value of individual pixels in the context of the values of

neighboring pixels. Information enhancement includes image reduction, image magnification, transect

extraction, contrast adjustments (linear and non-linear), band ratioing, spatial filtering, fourier transformations, principle components analysis, and texture transformations

Information extraction Post-classification Information output

Image or enhanced image itself, thematic map, vector map, spatail database, summary statistics and graphs

Why corrections

The perfect remote sensing system has yet to be developed. The Earth’s atmosphere, land, and water are amazingly complex

and do not lend themselves well to being recorded by remote sensing devices.

Error sources: Internal errors are introduced by the remote sensing system. They are

generally systematic (predictable) and may be identified and then corrected based on prelaunch or in-flight calibration measurements. For example, n-line striping in the imagery may be caused by a single detector that has become uncalibrated. In many instances, radiometric correction can adjust for detector miscalibration.

External errors are introduced by phenomena that vary in nature through space and time. External variables that can cause remote sensor data to exhibit radiometric and geometric error include the atmosphere, terrain elevation, slope, and aspect. Some external errors may be corrected by relating empirical ground observations (i.e., radiometric and geometric ground control points) to sensor measurements.

Types of radiometric correction

Detector error or sensor error (internal error) Atmospheric error (external error) Topographic error (external error)

1. Correcting detector or sensor error

Ideally, the radiance recorded by a remote sensing system in various bands is an accurate representation of the radiance actually leaving the feature of interest (e.g., soil, vegetation, atmosphere, water, or urban land cover) on the Earth’s surface or atmosphere. Unfortunately, noise (error) can enter the data-collection system at several points. For example, radiometric error in remotely sensed data may be introduced by the sensor system itself when the individual detectors do not function properly or are improperly calibrated. Several of the more common remote sensing system–induced radiometric errors are:

random bad pixels (shot noise),

line-start/stop problems,

line or column drop-outs,

partial line or column drop-outs, and

line or column striping.

1.1 Random bad pixels (shot noise)Sometimes an individual detector does not record spectral data for an individual pixel. When this occurs randomly, it is called a bad pixel. When there are numerous random bad pixels found within the scene, it is called shot noise because it appears that the image was shot by a shotgun. Normally these bad pixels contain values of 0 or 255 (in 8-bit data) in one or more of the bands. Shot noise is identified and repaired using the following methodology. It is first necessary to locate each bad pixel in the band k dataset. A simple thresholding algorithm makes a pass through the dataset and flags any pixel (BVi,j,k) having a brightness value of zero (assuming values of 0 represent shot noise and not a real land cover such as water). Once identified, it is then possible to evaluate the eight pixels surrounding the flagged pixel, as shown below:

Sometimes an individual detector does not record spectral data for an individual pixel. When this occurs randomly, it is called a bad pixel. When there are numerous random bad pixels found within the scene, it is called shot noise because it appears that the image was shot by a shotgun. Normally these bad pixels contain values of 0 or 255 (in 8-bit data) in one or more of the bands. Shot noise is identified and repaired using the following methodology. It is first necessary to locate each bad pixel in the band k dataset. A simple thresholding algorithm makes a pass through the dataset and flags any pixel (BVi,j,k) having a brightness value of zero (assuming values of 0 represent shot noise and not a real land cover such as water). Once identified, it is then possible to evaluate the eight pixels surrounding the flagged pixel, as shown below:

a) Landsat Thematic Mapper band 7 (2.08 – 2.35 m) image of the Santee Delta in South Carolina. One of the 16 detectors exhibits serious striping and the absence of brightness values at pixel locations along a scan line. b) An enlarged view of the bad pixels with the brightness values of the eight surrounding pixels annotated. c) The brightness values of the bad pixels after shot noise removal. This image was not destriped.

a) Landsat Thematic Mapper band 7 (2.08 – 2.35 m) image of the Santee Delta in South Carolina. One of the 16 detectors exhibits serious striping and the absence of brightness values at pixel locations along a scan line. b) An enlarged view of the bad pixels with the brightness values of the eight surrounding pixels annotated. c) The brightness values of the bad pixels after shot noise removal. This image was not destriped.

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1.2 line-start/stop problems

Occasionally, scanning systems fail to collect data at the beginning or end of a scan line, or they place the pixel data at inappropriate locations along the scan line. For example, all of the pixels in a scan line might be systematically shifted just one pixel to the right. This is called a line-start problem. Also, a detector may abruptly stop collecting data somewhere along a scan and produce results similar to the line or column drop-out previously discussed. Ideally, when data are not collected, the sensor system would be programmed to remember what was not collected and place any good data in their proper geometric locations along the scan. Unfortunately, this is not always the case. For example, the first pixel (column 1) in band k on line i (i.e., BV1,i,k) might be improperly located at column 50 (i.e., BV50,i,k). If the line-start problem is always associated with a horizontal bias of 50 columns, it can be corrected using a simple horizontal adjustment. However, if the amount of the line-start displacement is random, it is difficult to restore the data without extensive human interaction on a line-by-line basis. A considerable amount of MSS data collected by Landsats 2 and 3 exhibit line-start problems.

Infrared imagery of the Four Mile Creek thermal effluent plume entering the Savannah River

1.3 line or column drop-outs

An entire line containing no spectral information may be produced if an individual detector in a scanning system (e.g., Landsat MSS or Landsat 7 ETM+) fails to function properly. If a detector in a linear array (e.g., SPOT XS, IRS-1C, QuickBird) fails to function, this can result in an entire column of data with no spectral information. The bad line or column is commonly called a line or column drop-out and contains brightness values equal to zero. For example, if one of the 16 detectors in the Landsat Thematic Mapper sensor system fails to function during scanning, this can result in a brightness value of zero for every pixel, j, in a particular line, i. This line drop-out would appear as a completely black line in the band, k, of imagery. This is a serious condition because there is no way to restore data that were never acquired. However, it is possible to improve the visual interpretability of the data by introducing estimated brightness values for each bad scan line.

It is first necessary to locate each bad line in the dataset. A simple thresholding algorithm makes a pass through the dataset and flags any scan line having a mean brightness value at or near zero. Once identified, it is then possible to evaluate the output for a pixel in the preceding line (BVi – 1, j, k) and succeeding line (BV i + 1, j, k) and assign the output pixel (BV i, j, k) in the drop-out line the average of these two brightness values

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1.4 partial line or column drop-outs

Only portion of a line or column drop-outs

1.5 line or column striping Sometimes a detector does not fail completely, but simply goes out of radiometric

adjustment. For example, a detector might record spectral measurements over a dark, deep body of water that are almost uniformly 20 brightness values greater than the other detectors for the same band. The result would be an image with systematic, noticeable lines that are brighter than adjacent lines. This is referred to as n-line striping. The maladjusted line contains valuable information, but should be corrected to have approximately the same radiometric scale as the data collected by the properly calibrated detectors associated with the same band.

To repair systematic n-line striping, it is first necessary to identify the miscalibrated scan lines in the scene. This is usually accomplished by computing a histogram of the values for each of the n detectors that collected data over the entire scene (ideally, this would take place over a homogeneous area, such as a body of water). If one detector’s mean or median is significantly different from the others, it is probable that this detector is out of adjustment. Consequently, every line and pixel in the scene recorded by the maladjusted detector may require a bias (additive or subtractive) correction or a more severe gain (multiplicative) correction. This type of n-line striping correction a) adjusts all the bad scan lines so that they have approximately the same radiometric scale as the correctly collected data and b) improves the visual interpretability of the data. It looks better.

To repair non-systematic striping, there is no easy way.

Systematic stripping

Non-systematic Striping

CPCACPCA

Combined Principle Combined Principle Component AnalysisComponent Analysis

Xie et al. 2004

2. Atmospheric correction

There are several ways to atmospherically correct remotely sensed data. Some are relatively straightforward while others are complex, being founded on physical principles and requiring a significant amount of information to function properly. This discussion will focus on two major types of atmospheric correction:

Absolute atmospheric correction, and

Relative atmospheric correction.

Solar irradiance

Reflectance from study area,

Various Paths of Satellite Received Radiance

Diffuse sky irradiance

Total radiance at the sensor

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Reflectance from study area,

Various Paths of Satellite Received Radiance

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Scattering, AbsorptionRefraction, Reflection

Path 1 contains spectral solar irradiance ( ) that was attenuated very little before illuminating the terrain within the IFOV. Notice in this case that we are interested in the solar irradiance from a specific solar zenith angle ( ) and that the amount of irradiance reaching the terrain is a function of the atmospheric transmittance at this angle ( ). If all of the irradiance makes it to the ground, then the atmospheric transmittance ( ) equals one. If none of the irradiance makes it to the ground, then the atmospheric transmittance is zero

Path 1 contains spectral solar irradiance ( ) that was attenuated very little before illuminating the terrain within the IFOV. Notice in this case that we are interested in the solar irradiance from a specific solar zenith angle ( ) and that the amount of irradiance reaching the terrain is a function of the atmospheric transmittance at this angle ( ). If all of the irradiance makes it to the ground, then the atmospheric transmittance ( ) equals one. If none of the irradiance makes it to the ground, then the atmospheric transmittance is zero

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Path 2 contains spectral diffuse sky irradiance ( ) that never even reaches the Earth’s surface (the target study area) because of scattering in the atmosphere. Unfortunately, such energy is often scattered directly into the IFOV of the sensor system. As previously discussed, Rayleigh scattering of blue light contributes much to this diffuse sky irradiance. That is why the blue band image produced by a remote sensor system is often much brighter than any of the other bands. It contains much unwanted diffuse sky irradiance that was inadvertently scattered into the IFOV of the sensor system. Therefore, if possible, we want to minimize its effects. Green (2003) refers to the quantity as the upward reflectance of the atmosphere ( ).

Path 2 contains spectral diffuse sky irradiance ( ) that never even reaches the Earth’s surface (the target study area) because of scattering in the atmosphere. Unfortunately, such energy is often scattered directly into the IFOV of the sensor system. As previously discussed, Rayleigh scattering of blue light contributes much to this diffuse sky irradiance. That is why the blue band image produced by a remote sensor system is often much brighter than any of the other bands. It contains much unwanted diffuse sky irradiance that was inadvertently scattered into the IFOV of the sensor system. Therefore, if possible, we want to minimize its effects. Green (2003) refers to the quantity as the upward reflectance of the atmosphere ( ).

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Path 3 contains energy from the Sun that has undergone some Rayleigh, Mie, and/or nonselective scattering and perhaps some absorption and reemission before illuminating the study area. Thus, its spectral composition and polarization may be somewhat different from the energy that reaches the ground from path 1. Green (2003) refers to this quantity as the downward reflectance of the atmosphere ( ).

Path 3 contains energy from the Sun that has undergone some Rayleigh, Mie, and/or nonselective scattering and perhaps some absorption and reemission before illuminating the study area. Thus, its spectral composition and polarization may be somewhat different from the energy that reaches the ground from path 1. Green (2003) refers to this quantity as the downward reflectance of the atmosphere ( ).

ddE ddE

Path 4 contains radiation that was reflected or scattered by nearby terrain ( ) covered by snow, concrete, soil, water, and/or vegetation into the IFOV of the sensor system. The energy does not actually illuminate the study area of interest. Therefore, if possible, we would like to minimize its effects.

Path 2 and Path 4 combine to produce what is commonly referred to as Path Radiance, Lp.

Path 4 contains radiation that was reflected or scattered by nearby terrain ( ) covered by snow, concrete, soil, water, and/or vegetation into the IFOV of the sensor system. The energy does not actually illuminate the study area of interest. Therefore, if possible, we would like to minimize its effects.

Path 2 and Path 4 combine to produce what is commonly referred to as Path Radiance, Lp.

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Path 5 is energy that was also reflected from nearby terrain into the atmosphere, but then scattered or reflected onto the study area.

Path 5 is energy that was also reflected from nearby terrain into the atmosphere, but then scattered or reflected onto the study area.

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The total radiance reaching the sensor is:

The total radiance reaching the sensor is:

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This may be summarized as:

This may be summarized as:

2.1 Absolute atmospheric correction

Solar radiation is largely unaffected as it travels through the vacuum of space. When it interacts with the Earth’s atmosphere, however, it is selectively scattered and absorbed. The sum of these two forms of energy loss is called atmospheric attenuation. Atmospheric attenuation may 1) make it difficult to relate hand-held in situ spectroradiometer measurements with remote measurements, 2) make it difficult to extend spectral signatures through space and time, and (3) have an impact on classification accuracy within a scene if atmospheric attenuation varies significantly throughout the image.

The general goal of absolute radiometric correction is to turn the digital brightness values (or DN) recorded by a remote sensing system into scaled surface reflectance values. These values can then be compared or used in conjunction with scaled surface reflectance values obtained anywhere else on the planet.

2.1.1 Radiative transfer-based atmospheric correction algorithms

Much research has been carried out to address the problem of correcting images for atmospheric effects. These efforts have resulted in a number of atmospheric radiative transfer codes (models) that can provide realistic estimates of the effects of atmospheric scattering and absorption on satellite imagery. Once these effects have been identified for a specific date of imagery, each band and/or pixel in the scene can be adjusted to remove the effects of scattering and/or absorption. The image is then considered to be atmospherically corrected.

Unfortunately, the application of these codes to a specific scene and date also requires knowledge of both the sensor spectral profile and the atmospheric properties at the same time. Atmospheric properties are difficult to acquire even when planned. For most historic satellite data, they are not available. Even today, accurate scaled surface reflectance retrieval is not operational for the majority of satellite image sources used for land-cover change detection. An exception is NASA's Moderate Resolution Imaging Spectroradiometer (MODIS), for which surface reflectance products are available.

Cont’ Most current radiative transfer-based atmospheric correction algorithms can

compute much of the required information if a) the user provides fundamental atmospheric characteristic information to the program or b) certain atmospheric absorption bands are present in the remote sensing dataset. For example, most radiative transfer-based atmospheric correction algorithms require that the user provide:

latitude and longitude of the remotely sensed image scene, date and exact time of remote sensing data collection, image acquisition altitude (e.g., 20 km AGL) mean elevation of the scene (e.g., 200 m ASL), an atmospheric model (e.g., mid-latitude summer, mid-latitude winter, tropical), radiometrically calibrated image radiance data (i.e., data must be in the form W

m2 mm-1 sr-1), data about each specific band (i.e., its mean and full-width at half-maximum

(FWHM), and local atmospheric visibility at the time of remote sensing data collection (e.g., 10

km, obtained from a nearby airport if possible).

Cont’

These parameters are then input to the atmospheric model selected (e.g., mid-latitude summer) and used to compute the absorption and scattering characteristics of the atmosphere at the instance of remote sensing data collection. These atmospheric characteristics are then used to invert the remote sensing radiance to scaled surface reflectance. Many of these atmospheric correction programs derive the scattering and absorption information they require from robust atmosphere radiative transfer code such as MODTRAN 4+ or Second Simulation of the Satellite Signal in the Solar Spectrum (6S).

Examples include: ACORN ATCOR ATREM FLAASH (we have)

a) Image containing substantial haze prior to atmospheric correction. b) Image after atmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the German Aerospace Centre).

a) Image containing substantial haze prior to atmospheric correction. b) Image after atmospheric correction using ATCOR (Courtesy Leica Geosystems and DLR, the German Aerospace Centre).

2.1.2 Empirical Line Calibration

Absolute atmospheric correction may also be performed using empirical line calibration (ELC), which forces the remote sensing image data to match in situ spectral reflectance measurements, hopefully obtained at approximately the same time and on the same date as the remote sensing overflight. Empirical line calibration is based on the equation:

Absolute atmospheric correction may also be performed using empirical line calibration (ELC), which forces the remote sensing image data to match in situ spectral reflectance measurements, hopefully obtained at approximately the same time and on the same date as the remote sensing overflight. Empirical line calibration is based on the equation:

Reflectance (field spectrum) = gain x radiance (image) + offset

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a) Field crew taking a spectroradiometer measurement (total incoming radiance) from a calibrated white board on the tripod.

b) 8 8 m black and white calibration targets at the Savannah River Site to be measured as reflected or outgoing radiance

a) Field crew taking a spectroradiometer measurement (total incoming radiance) from a calibrated white board on the tripod.

b) 8 8 m black and white calibration targets at the Savannah River Site to be measured as reflected or outgoing radiance

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A instrument and data acquirementdemo by Blake Weissling

• If the in situ was not possible, you can use the Spectral library or measurements after.

•The point is to find several homogeneous targets (white and black)

•The example here only used one pixel of water and one pixel of beach

•Result indicates correct chlorophyll absorption in the blue (band 1) and red (band 3) portions of the spectrum and the increase in near-infrared reflectance

2.2 relative radiometric correction

When required data is not available for absolute radiometric correction, we can do relative radiometric correction

Relative radiometric correction may be used to Single-image normalization using histogram

adjustment Multiple-data image normalization using

regression

2.2.1 Single-image normalization using histogram adjustment

The method is based on the fact that infrared data (>0.7 m) is free of atmospheric scattering effects, whereas the visible region (0.4-0.7 m) is strongly influenced by them.

Use Dark Subtract to apply atmospheric scattering corrections to the image data. The digital number to subtract from each band can be either the band minimum, an average based upon a user defined region of interest, or a specific value

Dark Subtract using band minimum

2.2.2 Multiple-data image normalization using regression

Selecting a base image and then transforming the spectral characteristics of all other images obtained on different dates to have approximately the same radiometric scale as the based image.

Selecting a pseudo-invariant features (PIFs) or region (points) of interest is important: Spectral characteristic of PIFs change very little through time, (deep

water body, bare soil, rooftop) PIFs should be in the same elevation as others No or rare vegetation, The PIF must be relatively flat

Then PIFs will be used to normalize the multiple-date imagery

Example

SPOT image of 8/10/1991 is selected as the base image PIFs (wet and dry) were selected for generating the relationship between the base image and

others The resulted regression equation will be used to normalize the entire image of 4/4/87 to

8/10/91 for change detection. The additive component corrects the path radiance among dates, and multiplicative term

correct the detector calibration, sun angle, earth-sun distance, atmospheric attenuation, and phase angle between dates.

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Regression equations for all images, all based on the SPOT image of 8/10/91

2.2.3 other relative radiometric correction methods (ENVI)

Use Flat Field calibration to normalize images to an area of known "flat" reflectance. This is particularly effective for reducing hyperspectral data to relative reflectance. The method requires that you select a Region Of Interest (ROI) prior to execution. The average spectrum from the ROI is used as the reference spectrum, which is then divided into the spectrum at each pixel of the image

Use IAR Reflectance calibration (Internal Average Relative Reflectance) to normalize images to a scene average spectrum. This is particularly effective for reducing hyperspectral data to relative reflectance in an area where no ground measurements exist and little is known about the scene. It works best for arid areas with no vegetation. An average spectrum is calculated from the entire scene and is used as the reference spectrum, which is then divided into the spectrum at each pixel of the image

3. Topographic correction

Topographic slope and aspect also introduce radiometric distortion (for example, areas in shadow)

The goal of a slope-aspect correction is to remove topographically induced illumination variation so that two objects having the same reflectance properties show the same brightness value (or DN) in the image despite their different orientation to the Sun’s position

Based on DEM, sun-

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3. statistical-empirical correction

4. C correction

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2. Minnaert correction

Image acquisition geometry

Sun zenith angle is the angle of Sun away from verticalSun elevation angle is the angle of Sun away from horizontalSensor elevation angle is the angle away from horizontalSensor azimuth angle and Sun azimuth are clockwise from the north

Source: IKONOS geometry at http://www.utsa.edu/LRSG/Teaching/ES6973/geometry.pdf

computing the cosine of the solar incidence angle

where, δ declination of the earth (positive in summer in northern hemisphere) φ latitude of the pixel (positive for northern hemisphere) s slope in radians, where s=0 is horizontal and s=π/2 is vertical downward (s is

always positive and represents a downward slope in any direction) γ surface azimuth angle. γ is the deviation of the normal to the surface from the local

meridian, where γ = 0 for aspect that is due south, γ = - for east and γ = + for western aspect. γ = -π/2 represents an east-facing slope and γ = +π/2 represents an west-facing slope. γ = -π or γ = π represents a north-facing slope.

ω hour angle. ω = 0 at solar noon, ω is negative in morning and ω is positive in afternoon

cos(i)

Source: Duffie,J.A. and W.A.Beckman, 1991. Solar engineering of thermal processes. John Wiley and Sons, NY.

If you are interested in, please read this source paper from: Law and Nichol