Preprocessingdial/ece531/Correction...Preprocessing •Required for certain sensor characteristics...

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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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Correction and Calibration

• Noise Reduction• Radiometric Calibration• Distortion Correction


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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• 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


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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Example: SAR Noise Reduction

original 5 x 5 LPF 5 x 5 sigma (k=2) Nagao-Matsuyama


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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Example: Bad-line Removal

single noisy partial scanline(Landsat MSS)

after 3 x 1 median filter

horizontal image details also removed


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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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Selective Median Filter (cont.)

horizontal image details

preserved98% threshold mask

for median filterafter 3 x 1 selective

median filter


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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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)


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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Destriping Examples

original spectrumnoisy image

striping notch-filter

striping and within-line-filter

removed noise

removed noise


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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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)


Example: TM Debanding

original

water-masked

101 column LP 33 row HP

31 column LP water-masked

filtered

water-masked

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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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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


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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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


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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Atmospheric Modeling (cont.)

• Atmospheric modeling requires knowledge ofmany parameters– Imaging geometry– Atmospheric profile and aerosol model

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view path, nadirview path, view angle = 40 degrees

tran

smit

tance

wavelength (µm)


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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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


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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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


Normalization (cont.)

effectiveness of various normalization techniques for calibration

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alunite (IARR)

alunite (flat field)

rela

tiv

e r

efl

ecta

nce

wavelength (nm)

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buddingtonite (IARR)buddingtonite (flat field)

rela

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efl

ecta

nce

wavelength (nm)

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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


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)

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Buddingtonite GDS85

buddingtonite (flat field)

rela

tiv

e r

efl

ecta

nce

wavelength (nm)

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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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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)

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200

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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)

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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




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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


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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Example: TM Rectification

Original (Tucson, AZ)

Rectified

fill

Speedway

Speedway


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)

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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:


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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Affine Transformation

• A linear polynomial (number of terms K = 3)– Special case that can include:

• shift• scale• shear• rotation

– In vector-matrix notation


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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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)

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true distortionquadratic fit

% error

scal

e re

lati

ve

to n

adir

% erro

r

scan angle (degrees)

± 5° FOV ± 50° FOV


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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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


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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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


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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Example: 1-D Curve Fitting

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y = 13.228 + 0.82085x R= 0.93425

y

x

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y

x

Y = M0 + M1*x + ... M8*x8 + M9*x

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24.141M0

0.011693M1

0.0095018M2

0.95128R

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60

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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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y

x

Y = M0 + M1*x + ... M8*x8 + M9*x

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31.173M0

-2.5272M1

0.21642M2

-0.0049359M3

3.4942e-05M4

0.99999R

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60

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90

0 10 20 30 40 50 60 70 80y

x

Y = M0 + M1*x + ... M8*x8 + M9*x

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33.718M0

-3.0378M1

0.2515M2

-0.0059674M3

4.8406e-05M4

-6.4246e-08M5

1R

linear second order

third order fourth order fifth order


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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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


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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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Final Registration Result


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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Resampling (cont.)

• Pixels are resampled using aweighted-average of theneighboring pixels

• Common weighting functions:– nearest-neighbor: fast, but

discontinuous

– bilinear: slower, but continuous

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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


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

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val

ue

! (pixels)

PCC, " = -1PCC, " = -0.5sinc

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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


Example: Magnification (“Zoom”)

nearest-neighbor bilinear

1×

2×

3×

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Example: Rectification

nearest-neighbor bilinear

PCC (α = -0.5) PCC (α = -1.0)


Interpolation Quality

nearest-neighbor

bilinear

resampled image surface plots (4x zoom)

parametric cubic convolution(α = -0.5)

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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

Preprocessingdial/ece531/Correction...Preprocessing •Required for certain sensor characteristics...

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Transcript of Preprocessingdial/ece531/Correction...Preprocessing •Required for certain sensor characteristics...