The Importance of Spatial Quality

1. The Importance of Spatial Quality Mary Pagnutti Robert E. Ryan Kara Holekamp Innovative Imaging and Research Building 1103 Suite 140 C Stennis Space Center, MS 39529 • 18th William T. Pecora Memorial Remote Sensing Symposium • Herndon, Virginia • November 16, 2011

2. What is Spatial Resolution? • Spatial Resolution is the minimum distance between two adjacent features or the minimum size of a feature, that can be detected by a remote sensing system. (www.geocomm.com) • Spatial Resolution is not simply ground sample distance • Also depends on how well a system is focused • Point Spread Function (PSF)

3. Point Spread Function-PSF • PSF describes the response that an electro-optical system has to a point source • The sharper the function, the sharper the object will appear in the system output image • In practice, directly estimating PSF can be challenging due to sampling and SNR issues FWHM

4. Image Formation Example I GSD 1 m Sampling Blurred Image 20 m x 20 m Target Input Image 20 m x 20 m Target GSD 2 m + PSF 4 m FWHM GSD 4 m

5. Image Formation Example II GSD 1 m Sampling Input Image 20 m x 20 m Target Blurred Image 20 m x 20 m Target GSD 2 m GSD 2 m + GSD 4 m PSF 1 m FWHM GSD 4 m

6. Quantifying Spatial Resolution • Measures of Merit • Point Spread Function (PSF) • Modulation Transfer Function (MTF) at NyquistFrequency • Relative Edge Response (RER)

7. Modulation Transfer Function-MTF • MTF is a parameter described in the spatial frequency domain • Mathematically allows you to model the imaging process by multiplication instead of convolution • Not physically intuitive • Evaluated in two separate orthogonal directions consistent with the along track and cross track of the image • MTF is defined as the magnitude of the OTF (Optical Transfer Function) • OTF is defined as the Fourier Transform of the PSF

8. Edge Response MTF Line Spread Function Differentiate Fourier Transform MTF Estimation

9. 3 examples of undersampled edge responses measured across the tilted edge  – edge tilt angle  – pixel index x – pixel’s distance from edge (in GSD) Problem: Digital cameras undersample edge target Solution: Image tilted edge to improve sampling Superposition of 24 edge responses shifted to compensate for the tilt Tilted Edge Technique DN Pixels DN Distance/GSD

10. Ringing Overshoot 1.0 Region where mean slope is estimated Edge Response 0 Ringing Undershoot -2.0 -1.0 1.0 2.0 Pixels Relative Edge Response-RER • Another measure of spatial resolution is a difference of normalized edge response values at points distanced from the edge by -0.5 and 0.5 GSD • Relative Edge Response is one of the engineering parameters used in the General Image Quality Equation to provide predictions of imaging system performance expressed in terms of the National Imagery Interpretability Rating Scale 0.0

11. GSD Meaning of RER in Remote Sensing Radiance measured for each pixel is assumed to come from the Earth’s surface area represented by that pixel. However, because of many factors, actual measurements integrate radiance L from the entire surface with a weighting function provided by a system’s point spread function (PSF): A simple example: Box PSF Width = 2 GSD ER(0.5) - ER(-0.5) = 0.75 - 0.25 = 0.50 RER = 0.50 Part of radiance that originates in the pixel area is given by: Relative Edge Response squared (RER2) can be used to assess the percentage of the measured pixel radiance that actually originates from the Earth’s surface area represented by the pixel: RER2 = 0.25 means that 25% of information collected with the pixel PSF (blue square) comes from the actual pixel area (shadowed square) Source: Blonski, S., 2005. Spatial resolution characterization for QuickBird image products: 2003-2004 season. In Proceedings of the 2004 High Spatial Resolution Commercial Imagery Workshop, USGS, Reston, VA, Nov 8–10, 2004

12. MTF vs. RER MTF and RER can be related to each other through Fourier analysis

13. Local Laboratory/Observatory (Roof)

14. Data Acquisition System • Max resolution 3456 x 2304 • CMOS Bayer Array • Manual mode • Raw data • Pixel size 6.3 micron Canon EOS Rebel 8 Megapixel Camera

15. High Spatial Resolution Data Measured building GSD = 1.2 cm

16. Initial Image Chip

17. e.g. AVIRIS, Hyperion etc. High SNR, High Spatial Resolution Multispectral Imagery High SNR High Spatial Res. Hyperspectral Imagery Spectral Band Synthesis Band-to-Band Registration • Simulations based on spectral and spatial degradation of higher-resolution hyperspectral images acquired with existing remote sensing instruments MTF Transfer Function Resampling e.g. LDCM, Sentinel-2 Coarser Spatial Resolution Multispectral Imagery Data Quantization Noise Simulation Image Simulation using the Applications Research Toolbox (ART)

18. Image Variation with GSD MTF = 0.3 GSD = 18 cm GSD = 12 cm GSD = 4.8 cm

19. Image Variation with MTF MTF = 0.1 MTF = 0.5 GSD = 4.8 cm

20. Image Variation with MTF MTF = 0.1 MTF = 0.5 GSD = 12 cm

21. Image Variation with MTF MTF = 0.1 MTF = 0.5 GSD = 18 cm

22. Simulated Images MTF = 0.5 MTF = 0.4 MTF = 0.3 MTF = 0.2 MTF = 0.1 GSD = 4.8 cm GSD = 12 cm GSD = 18 cm

23. Initial Image Chip

24. Simulated Images MTF = 0.5 MTF = 0.4 MTF = 0.3 MTF = 0.2 MTF = 0.1 GSD = 4.8 cm GSD = 12 cm GSD = 18 cm

25. Spatial Resolution Validation • Laboratory measurements • Vendor provided prior to delivery • Operational field measurements • Validate image quality over life of instrument • Typically require engineered targets whose contrast should strive to maximize the dynamic range of the sensor being evaluated • Point source targets • Edge targets • Pulse targets • Contrast transfer targets (tri-bars and radial targets)

26. 3.7 deg 20 m 10 m 10 m 20 m Standard Methods of Validation • Validation of spatial resolution is typically performed using specially designed edge targets • Deployable: Radiometric tarp edges • Permanent: Painted concrete edge targets QuickBird Imagery Panchromatic Imagery Feb 17 2002 Tarp Edge Concrete Edge Concrete Edge QuickBird Imagery Panchromatic Imagery Nov 14 2002 National Aeronautics and Space Administration 26

27. Traditional Engineered Spatial Resolution Targets These types of targets however, will not generally be available in the imagery to validate spatial resolution Deployable targets at South Dakota State University Pong Hu, Taiwan Fort Huachuka tri-bar target Causeway bridge over Lake Pontchartrain Finnish Geodetic Institute Sjökulla Site Digital Globe provided satellite imagery

28. Problem… • Most commonly used spatial resolution estimation techniques require engineered targets (deployed or fixed), which are not always available or convenient • Target size scales with GSD • Edge targets are typically uniform edges 10-20 pixels long and ~10 pixels tilted a few degrees relative to pixel grid (improve sampling) • Increasing GSD increases difficulty • Moderate resolution systems such as Landsat use pulse targets

29. Spatial Resolution Estimation Using In-Scene Edges • Exploit edge features in nominal imagery • Edge response estimation is performed without dedicated engineered targets • Appropriate for high spatial resolution Imagery • Automated processes exist that can • Identify edges and screen them • Construct resulting edge response • Calculate MTF and RER Rooflines Building Shadows

30. Summary • Spatial Resolution is the minimum distance between two adjacent features or the minimum size of a feature, that can be detected by a remote sensing system • In addition to GSD, spatial resolution depends on a system’s PSF (blur) • Spatial Resolution is often quantified/specified in terms of MTF at Nyquist or RER • Spatial Resolution should be monitored throughout a system’s lifetime • For more information… Pagnutti, M., S. Blonski, M. Cramer, D. Helder, K. Holekamp, E. Honkavaara, R.E. Ryan. 2010. Targets, methods, and sites for assessing the in-flight spatial resolution of electro-optical data products, Canadian Journal of Remote Sensing, 36:(5) 583-601.