preprocessingdial/ece531/correction...preprocessing •required for certain sensor characteristics...
TRANSCRIPT
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ECE/OPTI 531 – Image Processing Lab for Remote Sensing Fall 2005
Correction and CalibrationCorrection and Calibration
Reading: Chapter 7, 8.1–8.3Reading: Chapter 7, 8.1–8.3
Fall 2005Correction and Calibration 2
Preprocessing
• Required for certain sensor characteristics andsystematic defects
• Includes:– noise reduction– radiometric calibration– distortion correction
• Usually performed by the data provider, asrequested by the user (see Data Systems)
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Fall 2005Correction and Calibration 3
Correction and Calibration
• Noise Reduction• Radiometric Calibration• Distortion Correction
Fall 2005Correction and Calibration 4
Noise Reduction
• Requires knowledge of noise characteristics• Since noise is usually random and unpredictable,
we have to estimate its characteristics fromnoisy images
• Global Noise– Random DN variation at every pixel– LPFs will reduce this noise, but also smooth image– Edge-preserving smoothing algorithms attempt to
reduce noise and preserve signal
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Fall 2005Correction and Calibration 5
• Average moving window pixels that are within athreshold difference from the DN of the centerpixel,
c
c
edge feature
5 x 5 window:
row m, column n
row m, column n+1
c
c
crow m, column n+2
line feature
only the green
pixels are
averaged for
the output
pixel c
sigma filter near edges and lines
Sigma Filter
Fall 2005Correction and Calibration 6
Nagao-Matsuyama Filter
• Calculate the variance of 9 subwindows within a5×5 moving window
• Output pixel is the mean of the subwindow withthe lowest variance
c
c c c c
c c cc
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Fall 2005Correction and Calibration 7
Example: SAR Noise Reduction
original 5 x 5 LPF 5 x 5 sigma (k=2) Nagao-Matsuyama
Fall 2005Correction and Calibration 8
Noise Reduction (cont.)
• Local Noise– Individual bad pixels or lines– Often DN = 0 (“pepper”), 255 (“salt”) or 0 and 255
(“salt and pepper”)– Median filter reduces local noise because it is
insensitive to outliers (Chapter 6)• For bad lines, set filter window vertical
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Fall 2005Correction and Calibration 9
Example: Bad-line Removal
single noisy partial scanline(Landsat MSS)
after 3 x 1 median filter
horizontal image details also removed
Fall 2005Correction and Calibration 10
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1.05
0 0.02 0.04 0.06 0.08 0.1 0.12
CD
F
!
0.5%1%2%
squared-difference image !ij between each pixel
and its immediate neighbor in the preceding line
CDF of left image
Selective Median Filter
• Detection by spatial correlation– Use global spatial correlation statistics to limit median
filter
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Fall 2005Correction and Calibration 11
Selective Median Filter (cont.)
horizontal image details
preserved98% threshold mask
for median filterafter 3 x 1 selective
median filter
Fall 2005Correction and Calibration 12
PCT Component Filter• Detection by spectral correlation
– Use PCT to isolate spectrally-uncorrelated noise intohigher order PCs
– Remove noise and do inverse PCTTM2 TM3 TM4
PC1 PC2 PC3
noise from TM3
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Fall 2005Correction and Calibration 13
Periodic (Coherent) Noise
• Repetitive pattern, either consistent throughoutthe image (global) or variable (local)
• Destriping– Striping is caused by unequal detector gains and
offsets in whiskbroom and pushbroom scanners– Destripe before geometric processing– Global, linear detector matching
• Adjust pixel DNs from each detector i to yield the samemean and standard deviation over the whole image
– Nonlinear detector matching• Adjust each detector to yield the same histogram over the
whole image (CDF reference stretch)
Fall 2005Correction and Calibration 14
Periodic Noise (cont.)
• Spatial filteringapproaches– Detector striping causes
characteristic “spikes”in the Fourier transformof the image
– For line striping, thespike is vertical alongthe v-axis of the Fourierspectrum
– A “notch” amplitudefilter (removes selectedfrequency components)can reduce stripingwithout degradingimage
FT
FT -1
designfilter
phasespectrum
amplitudespectrum
noisy
cleanedimage
image
data flow for amplitude Fourier filtering
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Fall 2005Correction and Calibration 15
Destriping Examples
original spectrumnoisy image
striping notch-filter
striping and within-line-filter
removed noise
removed noise
Fall 2005Correction and Calibration 16
Automatic Destriping• “Automatic” periodic noise
filter design– Attempt to avoid manual
noise identification inspectrum
– Requires two thresholds
1. Apply “soft” (Gaussian) high-pass filter to noisyimage to remove image components
2. Threshold HPF-filtered spectrum to isolate noisefrequency components
3. Convert thresholded spectrum to 0 (noise) and 1 (non-noise) to create noise amplitude notch filter
4. Apply filter to noisy image
Automatic Periodic Noise Filter
HPF spectrum noise filter
cleaned image removed noise
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Fall 2005Correction and Calibration 17
1 row x 101 column LPF
33 row x 1 column HPF
1 row x 31 column LPF
*
*
*
!
noisyimage
cleanedimage
Debanding
• Use combination of LPFs and HPFs (Crippen,1989)
Fall 2005Correction and Calibration 18
Example: TM Debanding
original
water-masked
101 column LP 33 row HP
31 column LP water-masked
filtered
water-masked
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Fall 2005Correction and Calibration 19
Correction and Calibration
• Noise Reduction• Radiometric Calibration• Distortion Correction
Fall 2005Correction and Calibration 20
Radiometric Calibration• Many remote sensing
applications requirecalibrated data– comparison of
geophysical variablesover time
– comparison ofgeophysical variablesderived from differentsensors
– generation ofgeophysical variablesfor input to climatemodels
• Extent of calibrationdepends on the desiredgeophysical parameterand available resourcesfor calibration
at-sensor radiance
surface reflectance
DN
sensorcalibration
• cal_gain and cal_offset coefficients
atmosphericcorrection
• image measurements
• ground measurements
• atmospheric models
solar and
correction
• solar exo-atmospheric
surface radiance
topographic
• DEM
spectral irradiance
• solar path atmospheric transmittance
• view path atmospheric transmittance
• down-scattered radiance
• view path atmospheric radiance
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Fall 2005Correction and Calibration 21
Sensor Calibration
• Calibrate sensor gain and offset in each band(and possibly for each detector) to get at-sensorradiance
• Use pre-launch or post-launch measured gainsand offsets
pre-flight TM calibration coefficients
Fall 2005Correction and Calibration 22
Atmospheric Correction
• Estimate atmospheric path radiance and view-path transmittance to obtain at-surfaceradiance (sometimes called surface-leavingradiance)
– Solve for at-surface radiance
– In terms of calibrated at-sensor satellite data
At-sensor:
Earth-surface:
Earth-surface:
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Fall 2005Correction and Calibration 23
In-Scene Methods
• Path radiance can be estimated with the DarkObject Subtraction (DOS) technique– In-scene method assumes dark objects have zero
reflectance, and any measured radiance is attributed toatmospheric path radiance only
– Subject to error if object has even very low reflectance– View-path atmospheric transmittance is not corrected
by DOS
1. Identify “dark object” in the scene2. Estimate lowest DN of object,3. Assume4. DN values (calibrated to at-sensor radiance) within
the dark object assumed to be due only to atmosphericpath radiance
5. Subtract from all pixels in band b
Dark-Object Subtraction
Fall 2005Correction and Calibration 24
Atmospheric Modeling
• DOS can be improved by incorporatingatmospheric models– Reduces sensitivity to dark object characteristics– For example, coarse atmospheric characterization
(Chavez, 1989)
– Can also fit DN0b with λ-K function to determine K, anduse fitted model instead of DN0b
• View-path atmospheric transmittance can beestimated using atmospheric models, such asMODTRAN
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Fall 2005Correction and Calibration 25
Atmospheric Modeling (cont.)
• Atmospheric modeling requires knowledge ofmany parameters– Imaging geometry– Atmospheric profile and aerosol model
0
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1
0.4 0.8 1.2 1.6 2 2.4
view path, nadirview path, view angle = 40 degrees
tran
smit
tance
wavelength (µm)
Fall 2005Correction and Calibration 26
Solar Geometry and Topography
• Further calibration to reflectance requires 3more parameters
– solar path atmospheric transmittance (from model ormeasurements)
– exo-atmospheric solar spectral irradiance (known)– incident angle (from DEM)
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Fall 2005Correction and Calibration 27
Example: MSI Calibration
• Partial calibration with correction for sensorgains and offsets and DOS
band1
2
3
DN at-sensor radiance scene radiance
(blue)
(green)
(red)
note the
strong
correction for
Rayleigh
scattering
Fall 2005Correction and Calibration 28
Example: Partial Calibration
band
1
2
3
DN at-sensor radiance scene radiance
4
5
7
(blue)
(green)
(red)
(NIR)
(SWIR)
(SWIR)
Rayleigh
scattering
correction
low solar
irradiance
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Fall 2005Correction and Calibration 29
Hyperspectral Normalization
• Calibration of hyperspectral imagery isparticularly important because:– High sensitivity to narrow atmospheric absorption
features or the edges of broader spectral features– Spectral band shift in operating sensor– Need for precise absorption band-depth measurements– Computational issues
• A number of “normalization” techniques thatuse scene models have been developed topartially calibrate hyperspectral data
Fall 2005Correction and Calibration 30
Normalization (cont.)
effectiveness of various normalization techniques for calibration
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Fall 2005Correction and Calibration 31
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alunite (IARR)
alunite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
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1
1.1
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1.4
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buddingtonite (IARR)buddingtonite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
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1
1.1
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1.3
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kaolinite (IARR)
kaolinite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
0
50
100
150
200
250
2000 2050 2100 2150 2200 2250 2300 2350 2400
alunite (radiance)
buddingtonite (radiance)
kaolinite (radiance)
at-
sen
sor
rad
ian
ce (
W-m
-2-s
r-1- µ
m-
1)
wavelength (nm)
mineral
discrimination
confused by solar
background and
topographic
shading
Example: HSI Normalization
• Radiance normalized by flatfield and IARR techniques
AVIRIS at-sensor radiance
Fall 2005Correction and Calibration 32
Example (cont.)
• Radiance normalized by flat fielding, comparedto reflectance data
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Alunite GDS84
alunite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
0
0.2
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0.8
1
2000 2050 2100 2150 2200 2250 2300 2350 2400
Buddingtonite GDS85
buddingtonite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
0
0.1
0.2
0.3
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Kaolinite CM9
kaolinite (flat field)
rela
tiv
e r
efl
ecta
nce
wavelength (nm)
similarity implies
we can use
reflectance library
data for image
class identification
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Fall 2005Correction and Calibration 33
Example (cont.)
• Radiance normalized by continuum removal
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alunite (radiance)
alunite continuum
alunite/continuum
at-
sen
sor
rad
ian
ce (
W-m
-2-s
r-1-µ
m-1)
rela
tive v
alu
e
wavelength (nm)
60
80
100
120
140
160
180
200
0
0.2
0.4
0.6
0.8
1
2000 2050 2100 2150 2200 2250 2300 2350 2400
buddingtonite (radiance)
buddingtonite continuum
buddingtonite/continuum
at-
sen
sor
rad
ian
ce (
W-m
-2-s
r-1-µ
m-1)
rela
tive v
alu
e
wavelength (nm)
50
100
150
200
250
0
0.2
0.4
0.6
0.8
1
2000 2050 2100 2150 2200 2250 2300 2350 2400
kaolinite (radiance)
kaolinite continuum
kaolinite/continuum
at-
sen
sor
rad
ian
ce (
W-m
-2-s
r-1-µ
m-1)
rela
tive v
alu
e
wavelength (nm)
removes solar
background
Fall 2005Correction and Calibration 34
Correction and Calibration
• Noise Reduction• Radiometric Calibration• Distortion Correction
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Fall 2005Correction and Calibration 35
Distortion Correction
• Applications– correct system distortions– register multiple images– register image to map
• Three components to warping process– selection of suitable mathematical distortion model(s)– coordinate transformation– resampling (interpolation)
1. Create an empty output image (which is in thereference coordinate system)
2. Step through the integer reference coordinates, one ata time, and calculate the coordinates in the distortedimage (x,y) by Eq. 7-27
3. Estimate the pixel value to insert in the output imageat (xref,yref) from the original image at (x,y)(resampling)
Distortion Correction Implementation
Fall 2005Correction and Calibration 36
Definitions
• Registration: The alignment of one image toanother image of the same area.
• Rectification: The alignment of an image to amap so that the image is planimetric, just likethe map. Also known as georeferencing.
• Geocoding: A special case of rectification thatincludes scaling to a uniform, standard pixel GSI.
• Orthorectification: Correction of the image,pixel-by-pixel, for topographic distortion.
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Fall 2005Correction and Calibration 37
Example: TM Rectification
Original (Tucson, AZ)
Rectified
fill
Speedway
Speedway
Fall 2005Correction and Calibration 38
Coordinate Transformation
• Coordinates are mapped from the referenceframe to the distorted image frame
– “Backwards” mapping (xref,yref) —> (x,y) avoids “holes”or overlaying of multiple pixels in the processed image
reference frame image frame
column
row
column
row
(x,y)
(xref,yref)
20
Fall 2005Correction and Calibration 39
Polynomial Distortion Model
• Generic model useful for registration,rectification and geocoding
• Known as a “rubber sheet stretch”• Relates distorted coordinate system (x,y) to the
reference coordinate system (xref,yref)
• For example, a quadratic polynomial is writtenas:
Fall 2005Correction and Calibration 40
Distortion Types
• The coefficients in thepolynomial can beassociated withparticular types ofdistortion
original shift scale in x
sheary-dependent
scale in xquadratic scale in x
rotation quadratic
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Fall 2005Correction and Calibration 41
Affine Transformation
• A linear polynomial (number of terms K = 3)– Special case that can include:
• shift• scale• shear• rotation
– In vector-matrix notation
Fall 2005Correction and Calibration 42
Piecewise Polynomial Distortion
• For severely-distortedimages that can’t bemodeled with a single,global polynomial ofreasonable order
Example airborne scanner image
affinecorrection
quadraticcorrection
a
b
c
d
A
B
C
D
a
b
c
d
A
B
C
D
piecewise quadrilateral warping
piecewise triangle warping
reference frame distorted frame
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Fall 2005Correction and Calibration 43
Application to Wide FOV Sensors
• Comparison of actual distortion to globalpolynomial model– accurate for small FOV sensors such as Landsat, but not
for large FOV scanners such as AVHRR
0.995
1
1.005
1.01
-0.002
-0.001
0
0.001
-6 -4 -2 0 2 4 6
true distortionquadratic fit
% error
scal
e re
lati
ve
to n
adir
% erro
r
scale angle (degrees)
0.5
1
1.5
2
2.5
3
3.5
4
-20
-15
-10
-5
0
5
10
15
-60 -40 -20 0 20 40 60
true distortionquadratic fit
% error
scal
e re
lati
ve
to n
adir
% erro
r
scan angle (degrees)
± 5° FOV ± 50° FOV
Fall 2005Correction and Calibration 44
Ground Control Points (GCPs)
• Use to control the polynomial, i.e. to determineits coefficients– Characteristics:
• high contrast in all images of interest• small feature size• unchanging over time• all are at the same elevation (unless topographic relief is
being specifically addressed)– Often located by visual examination, but can be
automated to varying degree, depending on theproblem
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Fall 2005Correction and Calibration 45
Automatic GCP Location
• Use image “chips”– Small segments that contain one easily identified and
well-located GCP• Normalized cross-correlation between template
chip T (reference) and search area S in image tobe registered
– normalization adjusts for changes in mean DN withinarea
Fall 2005Correction and Calibration 46
Area Correlation
i,j = 0,0 i,j = 0,1
distorted imagereference image
+
+
+
+
+
+
T1
T2
T3
S1
S2
S3
target area T
search area S
two relative shift positions
Chip layout over full scene
Cross-correlation of one areasearch chip
search chip
target chip
target chip
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Fall 2005Correction and Calibration 47
Finding Polynomial Coefficients
• Set up system of simultaneous equations usingGCPs and solve for polynomial coefficients
• Example with quadratic polynomial (number ofterms K = 6)– Given M pairs of GCPs– For each GCP pair, m, create two equations
– Then, for all M GCP pairs, in vector-matrix notation
Fall 2005Correction and Calibration 48
Solving for Coefficients
• So, for each set of GCP x- and y-coordinate pairs,we can write a linear system– Determined case (M = K, just enough GCPs) solution:
• Exact solution which passes through GCPs, i.e. they aremapped exactly
– Overdetermined case (M > K, more than enough GCPs):
• is called the pseudoinverse of W• solution results in least-squares minimum error at GCPs:
M = K: solution:
M ≥ K: solution:
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Fall 2005Correction and Calibration 49
Example: 1-D Curve Fitting
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30
40
50
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80
90
0 10 20 30 40 50 60 70 80
y = 13.228 + 0.82085x R= 0.93425
y
x
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50
60
70
80
90
0 10 20 30 40 50 60 70 80
y
x
Y = M0 + M1*x + ... M8*x8 + M9*x
9
24.141M0
0.011693M1
0.0095018M2
0.95128R
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30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80
y
x
Y = M0 + M1*x + ... M8*x8 + M9*x
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-24.455M0
5.6886M1
-0.14393M2
0.0011585M3
0.98745R
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30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80
y
x
Y = M0 + M1*x + ... M8*x8 + M9*x
9
31.173M0
-2.5272M1
0.21642M2
-0.0049359M3
3.4942e-05M4
0.99999R
20
30
40
50
60
70
80
90
0 10 20 30 40 50 60 70 80y
x
Y = M0 + M1*x + ... M8*x8 + M9*x
9
33.718M0
-3.0378M1
0.2515M2
-0.0059674M3
4.8406e-05M4
-6.4246e-08M5
1R
linear second order
third order fourth order fifth order
Fall 2005Correction and Calibration 50
Example: Registration
• Register aerial phototo map in an urbanarea
• Locate 6 GCPs in each(black crosses)
• Locate 4 Ground Points(GPs) in each (redcircles)– not used for control,
only for testing
GCP1
GCP5
GCP6
GCP2
GCP1
GCP2
GCP3 GCP4
GCP5
GCP6
GCP3 GCP4
aerialphoto (x,y)
mapreference(xref,yref)
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Fall 2005Correction and Calibration 51
GCP Error
0
1
2
3
4
5
3 4 5 6
GCPs
GPs
RM
S d
evia
tio
n (
pix
els)
number of terms
Mapping of GCPs
Error at GCPs and Ground Points (GPs) as function of polynomial order
Fall 2005Correction and Calibration 52
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5 -1 -0.5 0 0.5 1 1.5
dev
iati
on i
n y
(pix
els)
deviation in x (pixels)
-1.5
-1
-0.5
0
0.5
1
1.5
-1.5 -1 -0.5 0 0.5 1 1.5
dev
iati
on i
n y
(pix
els)
deviation in x (pixels)
original six GCPs five GCPs, with outlier deleted
GCP Refinement
• Analyze GCP error and remove outliers
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Fall 2005Correction and Calibration 53
Final Registration Result
Fall 2005Correction and Calibration 54
Resampling
• The (x,y) coordinates calculated byare generally between the integer pixelcoordinates of the array
• Therefore, must estimate (interpolate orresample) a new pixel at the (x,y) location
reference frame image frame
column
row
column
row
DN(xref,yref)
DNr(x,y)
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Fall 2005Correction and Calibration 55
Resampling (cont.)
• Pixels are resampled using aweighted-average of theneighboring pixels
• Common weighting functions:– nearest-neighbor: fast, but
discontinuous
– bilinear: slower, but continuous
-0.2
0
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1.2
-3 -2 -1 0 1 2 3
n-nlinear
val
ue
! (pixels)
A
!x 1 - !x
!y
1 - !yDNr(x,y)
B
C D
E
F
INT(x,y)
• Implement 2-D bilinearresampling as two successive1-D resamplings– resample E between A and B– resample F between C and D– resample DN(x,y) between E
and F
resampling distances
Fall 2005Correction and Calibration 56
Resampling (cont).– bicubic: slowest, but results in sharpest image
• piecewise polynomial; special case of Parametric CubicConvolution (PCC)
where Δ is the distance from (x,y) to the grid points in 1-D• “standard” bicubic is α = -1; superior bicubic is α = -0.5• High-boost filter characteristics; amount of boost depends on
amplitude of side-lobe, which is proportional to α
-0.4
-0.2
0
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0.6
0.8
1
1.2
-4 -3 -2 -1 0 1 2 3 4
val
ue
! (pixels)
PCC, " = -1PCC, " = -0.5sinc
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Fall 2005Correction and Calibration 57
PCC Resampling
• PCC resampling procedure– resample along each row, A-D, E-H, I-L, M-P
etc.– resample along new column Q-T
!x 1 - !x
!y
1 - !yDNr(x,y)
R
S
Q
T
A C DB D
E GF H
I KJ L
M ON P
Fall 2005Correction and Calibration 58
Example: Magnification (“Zoom”)
nearest-neighbor bilinear
1×
2×
3×
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Fall 2005Correction and Calibration 59
Example: Rectification
nearest-neighbor bilinear
PCC (α = -0.5) PCC (α = -1.0)
Fall 2005Correction and Calibration 60
Interpolation Quality
nearest-neighbor
bilinear
resampled image surface plots (4x zoom)
parametric cubic convolution(α = -0.5)
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Fall 2005Correction and Calibration 61
Resampling Differences
• Difference images between different resampling functions
– polynomial distortion model affects global geometric accuracy– resampling function affects local radiometric accuracy
nearest-neighbor – bilinear bilinear – PCC