In-Flight Characterization of the Spatial Quality using Point Spread

In-Flight Characterization of Image Spatial Quality using Point Spread Functions,D. Helder, T. Choi, M. RangaswamyImage Processing LaboratoryElectrical Engineering DepartmentSouth Dakota State UniversityDecember 3, 2003,Outline,IntroductionLab-based methodsIn-flight measurementsTarget Types and DeploymentEdge, pulse and point targetsProcessing TechniquesNon-parametric and parametric methodsHigh Spatial Resolution Sensor ExamplesEdge and point method examples with QuickbirdPulse method examples with IKONOS ConclusionsAcknowledgementThe 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 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.,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 -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 & Deployment,General AttributesFor LSI systemsany target should work!Orientationcritical for oversamplingWell controlled/maintained/characterizedhomogeneity and contrast, size, SNRTime invariancefor 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 tarpsedge target,SDSU tarpspulse target,Edge TargetsReflectance: exercise the dynamic range of the sensorRelationship to surrounding areaSize: 7-10 IFOVs beyond the edgeMake it long enough!UniformityCharacterize it regularlyNatural and man-made targetsOptimal for smaller GSIs ( 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 bSince the edge is straight, a least-square line delineates final edge location in each row of pixels,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.,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,Peak position Estimation of Point source,Mirror image,Raw data,2-D Gaussian model,Figure 17. Peak position estimation,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 ResultsIKONOS sensor, Blue band,Figure 22. Over plots of IKONOS blue band tarp targets with cubic interpolation and MTFC,(a) Mirror image-4 (b) Pixel values,(c) Raw data (d) 2-D Gaussian model,Point source targets using Quickbird panchromatic data,(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,Comparison of Aug 25 and Sept 7 , 2002 PSF plots,(a) MTF plots in cross-track (b) MTF plots in along-track,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 areEasy to maintain, Intuitive,