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:
a) Landsat Thematic Mapper band
7 (2.08 – 2.35 mm) 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.
BVi , j ,k
 8

  BVi 

 int  i 1
 8 


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
BVi , j ,k
 BVi 1, j ,k  BVi 1, j ,k 
 int 

2


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
CPCA
Combined Principle
Component Analysis
Xie et al. 2004
2. Atmospheric correction
Various Paths of
Satellite Received Radiance

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.
Total radiance
LS
at the sensor
Solar
irradiance
E
0
Lp
90Þ
T
T
Ed
1
1,3,5
4
v
0
3
LI
5
Scattering, Absorption
Refraction, Reflection
LT
0
2
Diffus e s ky
irradiance
Remote
sens or
detector
Reflectance from
neigh boring area,
Reflectance from
study area,
r n
r
v
60 miles
or
100km
Atmos phere
Path 1 contains spectral solar
irradiance ( Eo ) 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 ( o ) and
that the amount of irradiance
reaching the terrain is a
function of the atmospheric
transmittance at this angle ( T
). If all of the irradiance
makes it to the ground, then
the atmospheric
transmittance ( T ) equals
one. If none of the irradiance
makes it to the ground, then
the atmospheric
transmittance is zero

o
o
Path 2 contains spectral diffuse sky
irradiance ( E d ) 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 ( Edu
).


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
( Edd ).

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.
n
Path 2 and Path 4 combine to
produce what is commonly
referred to as Path Radiance,
Lp .
Path 5 is energy that was also
reflected from nearby terrain
into the atmosphere, but then
scattered or reflected onto the
study area.
The total radiance reaching the sensor
is:
1
LS   T v EoT o cos  o   Ed   L p

This may be summarized
as:
LS  LT  L p
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:

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
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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).
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:
Reflectance (field spectrum) = gain x radiance (image) + offset
outgoing _ radiance
 
total _ inco min g _ radiance
A instrument and data acquirement
demo by Blake Weissling
reflectivity from in situ
measurements
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
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
y = 7.1264x - 0.1736
R2 = 0.9401
0
0.05
0.1
radiance from image
0.15
0.2
• 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 mm) is free of atmospheric
scattering effects, whereas the visible region
(0.4-0.7 mm) 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
SPOT Band 1, 8/10/91
SPOT Band 3, 8/10/91
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.

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-
1. Cosine correction
cos  0
LH  LT
cos i
2. Minnaert correction
cos  0 k
LH  LT (
)
cos i
3. statistical-empirical correction
LH  LT  m cos i  b  LT
4. C correction
cos  0  c
LH  LT
cos i  c
Image acquisition geometry
Sun zenith angle is the angle of Sun away from vertical
Sun elevation angle is the angle of Sun away from horizontal
Sensor elevation angle is the angle away from horizontal
Sensor 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
cos(i)
cos   sin(  ) sin(  ) cos( s )  sin(  ) cos( ) sin( s ) cos( )
 cos( ) cos( ) cos( s ) cos( )
 cos( ) sin(  ) sin( s ) cos( ) cos( )
 cos( ) sin(  ) sin( s ) sin(  )

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
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