In-Flight Characterization of Image Spatial Quality using

Point Spread Functions

D. Helder, T. Choi, M. Rangaswamy

Image Processing Laboratory

Electrical Engineering Department

South Dakota State University

December 3, 2003

Outline Introduction

Lab-based methods In-flight measurements

Target Types and Deployment Edge, pulse and point targets

Processing Techniques Non-parametric and parametric methods

High Spatial Resolution Sensor Examples Edge and point method examples with Quickbird Pulse method examples with IKONOS

Conclusions

AcknowledgementThe authors gratefully acknowledge the support of the JACIE team at Stennis

Space Center.

Introduction

Resolving spatial objects is perhaps the most important objective of an imaging sensor.

One of the most difficult things to define is an imaging system’s ability to resolve spatial objects or its ‘spatial resolution.’

This paper will focus on using the Point Spread Function (PSF) as an acceptable metric for spatial quality.

Laboratory MethodsA sinusoidal input by Coltman (1954).Tzannes (1995) used a sharp edge with a small

angle to obtain a finely sampled ESF.A ball, wire, edge, and bar/space patterns were

used as stimuli for a linear x-ray detector Kaftandjian (1996).

Many other targets/approaches exist…

In-flight MeasurementsLandsat 4 Thematic Mapper (TM) using San

Mateo Bridge in San Francisco Bay (Schowengerdt, 1985).

Bridge width less than TM resolution (30 meters)

Figure 1. TM image of San Mateo Bridge Dec. 31, 1982.

In-flight MeasurementsTM PSF using a 2-D array of black squares on a

white sand surface (Rauchmiller, 1988).16 square targets were shifted ¼-pixel throughout

sub-pixel locations within a 30-meter ground sample distance (GSD).

(b) Band 3 Landsat 5 TM image on Jan 31,

1986.

(a) Superimposed over example TM pixel grid

Figure 2. 2-D array of black squares

In-flight MeasurementsMTF measurement for ETM+ by Storey (2001) using Lake

Pontchartrain Causeway.Spatial degradation over time was observed in the

panchromatic band by comparing between on-orbit estimated parameters.

Figure 3. Lake Pontchartrain Causeway, Landsat 7, April 26, 2000.

Target Types & DeploymentGeneral Attributes

For LSI systems—any target should work!Orientation—critical for oversamplingWell controlled/maintained/characterized—

homogeneity and contrast, size, SNRTime invariance—for measurement of

system degradation1-D or 2-D target?

Three target types have been found useful for high resolution sensors: edge, pulse, point

Figure 4. Quickbird panchromatic band image of Brookings, SD target site on August 25, 2002.

Mirror Point Sources

Stennis tarps—edge target

SDSU tarps—pulse target

Edge Targets Reflectance: exercise the dynamic range

of the sensorRelationship to surrounding area

Size: 7-10 IFOV’s beyond the edgeMake it long enough!

Uniformity Characterize it regularly ‘Natural’ and ‘man-made’ targets Optimal for smaller GSI’s (< 3 meters)

Figure 5. Edge target

Edge Target AttributesFlat spectral response as

shown in Figure 6.Orientation—critical for

edge reconstruction

Figure 6. Spectral response of Stennis tarps

Figure 7. Orientation for edge reconstruction

Pulse TargetAnother 1-D targetMore difficult to deploy:

2 straight edges3 uniform regions

More difficult to obtain PSFOptimal for 2-10m GSIOther properties similar to

edges

Figure 8. Pulse target

Pulse Target AttributesSpatial pulse = Fourier domain sinc( f ) Fourier transform of the pulse should avoid zero-

crossing points on significant frequencies.3 GSI is optimal to obtain a strong signal and maintain

ample distance from placing a zero-crossing at the Nyquist frequency as shown in Figure 9.

Figure 9. Nyquist frequency position on the input sinc function vs. tarp width

dsat

SunSatellite

C

f=R

/2

v

R

Figure 10. Convex mirror

geometry

Point TargetsArray of convex mirrors

or stars, asphalt in the desert, or…?20 is a good number…

Proper focal length to exercise sensor over its dynamic range.

Proper relationship to backgroundIs it really a point source?

Uniformity of mirrors and background

Convex mirror surface

Mirror Point Sources as viewed by Quickbird

Larry is outstanding in his field… of mirrors

Other attributes of point sources:Easy deploymentEasy maintenanceVery uniform backgrounds possible!

Point SourcesPhasing of convex mirror array

Figure 11. Physical layout of mirror array

Figure 12. Distribution of mirror samples in one Ground Sample Interval (GSI)

mD

y

x

o 20.7;7

2.10

25.1tantan 1

Processing Techniques

Non-parametric ApproachAssumes no underlying

modelMust estimate entire functionMore sensitive to noiseWhen no information is

available of the PSF.Will estimate ‘any’ PSF May be used for a first

approximation

Parametric ApproachAssumes underlying model

is knownOnly need to estimate a

‘few’ parametersLess sensitive to noiseWill only estimate 1 PSFGenerally preferred

approach

Figure 13. SNR definition for edge, pulse,

and point targets

Processing TechniquesSignal-to-Noise Ratio (SNR) definitionSimulations suggest SNR > 50 for acceptable results

Non-parametric Step 1: Sub-pixel edge detection and alignmentA model-based method is used to detect sub-pixel edge locationsThe Fermi function was chosen to fit transition region of ESF Sub-pixel edge locations were calculated on each line by finding

parameter ‘b’Since the edge is straight, a least-square line delineates final edge location in each row of pixels

d

cbx

axf

1

)(exp

)(

Figure 14. Parametric edge detection

Figure 15. mSG filtering

Non-parametric Step 2: Smoothing and interpolationNecessary for differentiation for Fourier transformationmodified Savitzky-Golay (mSG) filtering

mSG filter is applicable to randomly spaced inputBest fitting 2nd order polynomial calculated in 1-pixel window Output in center of window determined by polynomial value at that location Window is shifted at a sub-pixel scale, which determines output resolutionMinimal impact on PSF estimate

Non-parametric Step 3: Obtain PSF/MTFFor an edge target:

LSF is simple differentiation of the edge spread function (ESF) which is average profile.

Additional 4th order S-Golay filtering is applied to reduce the noise caused by differentiation.

MTF is calculated from normalized Fourier transformation of LSF.

For a pulse target:Since the pulse response function is obtained after

interpolation, the LSF cannot be found directly ( a deconvolution problem).

Instead the function may be transformed via Fast Fourier Transform and divided by the input sinc function to obtain the MTF after proper normalization.

.)1()()( nESFnESFnFSL

Parametric Approach (Point source Gaussian example) Step 1: Determine peak location of each point source to sub-pixel

accuracy. Step 2: Align each point source data set to a common reference

point. Step 3: Estimate PSF from over-sampled 2-D data set. Step 4: MTF is obtained by applying Fourier transform to the

normalized PSF.

Aligned PSF Modeled PSF MTFPSFImpulse

2D Model Fitting

Fourier Transform

Alignment

Figure 16. Point Technique using Parametric 2D Gaussian model approach

Peak position Estimation of Point source

Mirror image Raw data

2-D Gaussian model

Figure 17. Peak position estimation

X

Y=0

Y

X=0

PSF Estimation by 2D Gaussian model

Aligned point source data 2-D Gaussian model

1-D slice in X direction 1-D slice in Y direction

Figure 18. PSF estimation using 2-D

Gaussian model

High Spatial Resolution Sensor Examples

• Site Layout

Figure 18. Brookings, SD, site layout, 2002.

Edge Method Procedure

Figure 19. Panchromatic band analysis of Stennis tarp on July 20, 2002 from Quickbird satellite.

Edge Method ResultsQuickbird sensor, panchromatic bandThe FWHM values varied from 1.43 to 1.57

pixels MTF at Nyquist ranged from 0.13 to 0.18

Figure 20. LSF & MTF over plots of Stennis tarp target

Pulse Method Procedure

Figure 21. IKONOS blue band tarp target on June 27, 2002

Pulse Method Results IKONOS sensor, Blue band

Figure 22. Over plots of IKONOS blue band tarp targets with cubic interpolation and MTFC

Date 6/27/02 7/3/02 7/22/02

FWHM 2.9149 2.9689 2.8336

MTF 0.4722 0.4511 0.3347

SNR 55.7 102.0 82.1

351 359 365 366 352 354 438 927 450 356 339 521 1787 539 347 337 384 456 383 351 342 336 323 349 344

(a) Mirror image-4 (b) Pixel values

(c) Raw data (d) 2-D Gaussian model

Point source targets using Quickbird panchromatic data

305 296 255 294 324 312 371 781 674 290 317 410 1315 972 211 306 325 385 358 304 303 310 315 310 296

(a) Mirror image-7 (b) Pixel values

(c) Raw data (d) 2D Gaussian model

Peak estimation of September 7, 2002 Mirror 7 data

(a) Aligned mirror data (b) 2-D PSF

Least Square Error Gaussian Surface for aligned mirror data of August 25, 2002, Quickbird images

(a) Aligned mirror data (b) 2-D PSF

Least Square Error Gaussian Surface for aligned mirror data of September 7, 2002, Quickbird images.

(a) Sliced PSF plots in cross-track (b) Sliced PSF plots in along-track

 

Mirror data Full-Width at Half-Maximum Measurement[FWHM]

Overpass Date Cross-track[Pixel]

Along-track[Pixel]

August 25, 2002 1.427 1.428

September 07, 2002 1.396 1.398

Relative Error (%) 2.17 2.10

Comparison of Aug 25 and Sept 7 , 2002 PSF plots

(a) MTF plots in cross-track (b) MTF plots in along-track

Mirror data Modulation Transfer Function values @ Nyquist

Days / Direction Cross-track 

Along-track 

August 25, 2002 0.163 0.162

September 07, 2002 0.190 0.189

Relative Error (%) 16.60 16.70

Comparison of Aug 25 and Sept 7 , 2002 MTF plots

Conclusions In-flight estimation of PSF and MTF is possible with suitably

designed targets that are well adapted for the type of sensor under evaluation.

Edge targets are Easy to maintain, Intuitive, Optimal for many situations.

Pulse targets are Useful for larger GSI, More difficult to deploy/maintain, MTF estimates more difficult due to zero-crossings.

Point sources are Capable of 2-D PSF estimates, Show significant promise for sensors in the sub-meter to several meter

GSI range.

Conclusions (con’t.)

Processing methods are critical to obtaining good PSF estimates.

Non-parametric methods are Most advantageous when little is known about the imaging

system, Better able to track PSF extrema, More difficult to implement, More susceptible to noise.

Parametric methods are Superior when system model is known, Easier to implement, Less noise sensitive, Only work for one PSF function.

Many other targets types and processing methods are possible…