InFlight Characterization of Image Spatial Quality using Point Spread Functions

1
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

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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
• Acknowledgement
• The authors gratefully acknowledge the support of
  the JACIE team at Stennis Space Center.

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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 systems 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.

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• Laboratory Methods
• A 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

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• In-flight Measurements
• Landsat 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.
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• In-flight Measurements
• TM 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
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• In-flight Measurements
• MTF 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.
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Target Types Deployment

• General Attributes
• For LSI systemsany target should work!
• Orientationcritical for oversampling
• Well controlled/maintained/characterizedhomogenei
  ty and contrast, size, SNR
• Time invariancefor measurement of system
  degradation
• 1-D or 2-D target?

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

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SDSU tarpspulse target
Mirror Point Sources
Stennis tarpsedge target
Figure 4. Quickbird panchromatic band image of
Brookings, SD target site on August 25, 2002.
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• Edge Targets
• Reflectance exercise the dynamic range of the
  sensor
• Relationship to surrounding area
• Size 7-10 IFOVs beyond the edge
• Make it long enough!
• Uniformity
• Characterize it regularly
• Natural and man-made targets
• Optimal for smaller GSIs (lt 3 meters)

Figure 5. Edge target
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• Edge Target Attributes
• Flat spectral response as shown in Figure 6.
• Orientationcritical for edge reconstruction

Figure 7. Orientation for edge reconstruction
Figure 6. Spectral response of Stennis tarps
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• Pulse Target
• Another 1-D target
• More difficult to deploy
• 2 straight edges
• 3 uniform regions
• More difficult to obtain PSF
• Optimal for 2-10m GSI
• Other properties similar to edges

Figure 8. Pulse target
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• Pulse Target Attributes
• Spatial 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
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• Point Targets
• Array 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 background
• Is it really a point source?
• Uniformity of mirrors and background

Convex mirror surface
Figure 10. Convex mirror geometry
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Mirror Point Sources as viewed by Quickbird
Larry is outstanding in his field of mirrors
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• Other attributes of point sources
• Easy deployment
• Easy maintenance
• Very uniform backgrounds possible!

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• Point Sources
• Phasing of convex mirror array

Figure 12. Distribution of mirror samples in one
Ground Sample Interval (GSI)
Figure 11. Physical layout of mirror array
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Processing Techniques

• Parametric Approach
• Assumes underlying model is known
• Only need to estimate a few parameters
• Less sensitive to noise
• Will only estimate 1 PSF
• Generally preferred approach

• Non-parametric Approach
• Assumes no underlying model
• Must estimate entire function
• More sensitive to noise
• When no information is available of the PSF.
• Will estimate any PSF
• May be used for a first approximation

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• Processing Techniques
• Signal-to-Noise Ratio (SNR) definition
• Simulations suggest SNR gt 50 for acceptable
  results

Figure 13. SNR definition for edge, pulse, and
point targets
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• Non-parametric Step 1 Sub-pixel edge detection
  and alignment
• A model-based method is used to detect sub-pixel
  edge locations
• The 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

Figure 14. Parametric edge detection
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• Non-parametric Step 2 Smoothing and
  interpolation
• Necessary for differentiation for Fourier
  transformation
• modified Savitzky-Golay (mSG) filtering
• mSG filter is applicable to randomly spaced input
• Best 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 resolution
• Minimal impact on PSF estimate

Figure 15. mSG filtering
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• Non-parametric Step 3 Obtain PSF/MTF
• For 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.

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• 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.

Figure 16. Point Technique using Parametric 2D
Gaussian model approach
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Peak position Estimation of Point source
Mirror image
Raw data
Figure 17. Peak position estimation
2-D Gaussian model
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PSF Estimation by 2D Gaussian model
Aligned point source data
2-D Gaussian model
Figure 18. PSF estimation using 2-D Gaussian model
1-D slice in Y direction
1-D slice in X direction
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High Spatial Resolution Sensor Examples

• Site Layout

Figure 18. Brookings, SD, site layout, 2002.
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• Edge Method Procedure

Figure 19. Panchromatic band analysis of Stennis
tarp on July 20, 2002 from Quickbird satellite.
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• Edge Method Results
• Quickbird sensor, panchromatic band
• The 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
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• Pulse Method Procedure

Figure 21. IKONOS blue band tarp target on June
27, 2002
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• Pulse Method Results
• IKONOS sensor, Blue band

Figure 22. Over plots of IKONOS blue band tarp
targets with cubic interpolation and MTFC
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Point source targets using Quickbird panchromatic
data
(a) Mirror image-4
(b) Pixel values
(c) Raw data
(d) 2-D Gaussian model
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Peak estimation of September 7, 2002 Mirror 7 data
(a) Mirror image-7
(b) Pixel values
(c) Raw data
(d) 2D Gaussian model
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Least Square Error Gaussian Surface for aligned
mirror data of August 25, 2002, Quickbird images
(a) Aligned mirror data
(b) 2-D PSF
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Least Square Error Gaussian Surface for aligned
mirror data of September 7, 2002, Quickbird
images.
(a) Aligned mirror data
(b) 2-D PSF
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Comparison of Aug 25 and Sept 7 , 2002 PSF plots
 
(a) Sliced PSF plots in cross-track
(b) Sliced PSF plots in along-track
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Comparison of Aug 25 and Sept 7 , 2002 MTF plots
(a) MTF plots in cross-track
(b) MTF plots in along-track
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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.

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Conclusions (cont.)

• 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