1. 1 K. Clint Slatton, Melba M. Crawford, Larry Teng Center for Space Research The University of Texas at Austin http://www.csr.utexas.edu {slatton, crawford, teng}@csr.utexas.edu Landcover-Dependent Fusion of SRTM Data and Airborne LIDAR Data This work was supported by NIMA and NASA

2. 2 Introduction: DEMs for Hydrologic Modeling Goals –Improve Digital Elevation Models (DEMs) for hydrologic modeling Runoff, flood-risk assessment, and transport of non-point source pollution and sediment –Develop capability for mapping and updating topography using multiple sensors Difficulties –Resolution/Coverage tradeoffs: DEMs with sufficient coverage often have insufficient resolution [Pickup and Marks, 2001] –Medium resolution DEMs can be derived from airborne Interferometric Synthetic Aperture Radar (INSAR) sensors but data dropouts are common –High resolution DEMs can be derived from laser altimetry (LIDAR) sensors but coverage is limited –Multi-sensor acquisitions have different extents, resolutions, and measurement errors Approaches –Application partitioning [Pickup and Marks, 2001] –Large-scale mosaics of high-resolution DEMs [Gibeaut, Gutierrez, Smyth, Crawford, Slatton, and Neuenschwander, 1999] –Fuse DEMs acquired from multiple sensors [Slatton, Crawford, Evans, 2001]

3. 3 Goals –Smooth noisy INSAR data –Combine data using formal mathematical framework to account for process dynamics and measurement errors Potential approaches –Wavelet denoising Provides multiresolution analysis and local smoothing, but Not suited to multiple input/multiple output (MIMO) models Not suited to indirect measurements –Weighted least squares estimation Not robust to data dropouts Stochastic process variability ignored –Multiscale Kalman filter Allows multiresolution analysis and MMSE smoothing Handles MIMO models Handles indirect measurements Provides error measure automatically Introduction: Data Fusion Approaches..

4. 4 Outline Introduction Data fusion methodology –Kalman filter for data fusion –Multiscale Kalman smoother Results Conclusions

5. 5 State Space Dynamic Model Use state-space approach –Can model any random process having rational spectral density function with finite state dimension  applicable to a large class of problems –Can estimate internal variables not directly observed [block diagram] [block diagram] –Able to track non-stationary and sparse data Use discrete formulation –Data from sampled (imaged) continuous process w and v assumed uncorrelated and have vector valued autocorrelations of a white noise sequence

6. 6 Kalman filter is widely used to estimate stochastic signals –Linear, time-varying filter –Implemented in time domain by a recursive algorithm –Requires prior model for filter parameters { , Q, H, R} Bounded estimate error covariance P k|k Reach steady state if { , H} are constant and {w, v} are WSS Kalman Filter Algorithm input output

7. 7 Motivation –Captures multiscale character of natural processes or signals –Combines signals or measurements having different resolutions Various methods –Fine-to-coarse transformations of spatial models –Direct modeling on multiscale data structures, e.g. quadtree [MKS model] [MKS model] [Chou, Willsky, & Benveniste, 1994] Multiscale Data Fusion Multiscale signal modeling has been studied extensively in recent years Multiscale Kalman Smoother (MKS) algorithm –Use fractional Brownian motion data model for self-similar processes like topography [Fieguth, Karl, Willsky, & Wunsch, 1995] [stochastic data model] [stochastic data model] Merge data of different resolutions Fill in all data dropouts INSAR LIDAR

8. 8 INSAR and LIDAR Imaging INSAR (nominal) –Side-looking –Single-pass interferometry –Space-based –Fixed illumination –C-band - 6 cm wavelength –RMS vertical accuracy ~10 m –30 m pixel spacing –Tens of km-scale swaths LIDAR (nominal) –Downward-looking –Airborne –Scanning illumination –1  m wavelength –RMS vertical accuracy ≥ 0.1 m –  1-5 m pixel spacing (gridded) –cm-scale footprint Large coverage area: primary sensor complementary sensor NASA Shuttle Radar Topography Mission (SRTM) UT LIDAR (Optech ALTM) imaging swath >>10 km

9. 9 Problem: no direct measurement of z g in presence of vegetation –INSAR data provide height of phase scattering center z S –Cannot distinguish surface elevation z g from vegetation elevation z v –Neglecting noise, z S = z g for bare surfaces Proposed solution: –Estimate z g and  z v from INSAR data using electromagnetic scattering model –Incorporate additional high-resolution measurements (LIDAR) Measuring Topography with INSAR z g < z S < z v z g = ground height  z v = vegetation height z S = scattering center height (measured height) zvzv

10. 10 Empirical statistical relationships –Most common approach to date –Relate NICC to backscattering coefficient  o using regression [Wegmuller & Werner, 1995] –Use regression equations to distinguish forest types –Results apply only to training sites used in regression Relate volume scattering to vegetation height –Calculate tree heights from NICC phase [Hagberg, Ulander, & Askne, 1995] –Assume nearly opaque canopy so phase scattering center at tree tops –Heights 50% underestimated when forest not extremely dense Relate z g and  z v directly to INSAR measurements –Use interferometric scattering model M [Treuhaft, Madsen, Moghaddam, & van Zyl, 1996] –No assumptions on vegetation density (  = extinction coefficient) required –Nonlinear optimization (iterative)  research tool for small areas Use LIDAR and Optical data to identify vegetation and modulate R Addressing Vegetation Effects in INSAR

11. 11 Outline Introduction Data fusion methodology Results: DEMs for urban floodplain mapping –Fuse SRTM data with dense LIDAR coverage over region of interest –Fuse SRTM data with sparse LIDAR coverage for larger areas Conclusions

12. 12 Portion of Single SRTM Tile Subset coverage (20 km  20 km) with 20 m pixel spacing (m) City of Austin, TX (downtown) Data voids in lakes and rivers Distributed as single image No local error information (nominal distribution) ftp://edcsgs9.cr.usgs.gov/pub/data/srtm/GDPS/ NASA/NIMA mission

13. 13 Portion of Single TOPSAR Swath TOPSAR (19 km  10 km) with 10 m grid spacing (m) NASA/JPL sensor Acquired in single swath (60 km) Look direction

14. 14 Gridded LIDAR Bare-Surface DEM LIDAR (12 km  8 km) with 5 m grid spacing (m) Data voids in urban areas and steep slopes Intensive acquisition requiring multiple flight lines Local error information readily computed

15. 15 Lower Colorado River Basin Color IR aerial photography acquired over entire state of Texas –DOQQ Colorado River Barton Creek Residential development

16. 16 Determining H Determine H for LIDAR, TOPSAR, and SRTM –H parameter acts as a data mask –Scan for data voids and assign zero weight

17. 17 Determining R Determine R for SRTM –No height error measure provided in standard distribution from EDC ftp://edcsgs9.cr.usgs.gov/pub/data/srtm/GDPS/ –Assume uniform value for R according to stated accuracy –Next step: incorporate NDVI from Landsat image (similar scale) Determine R for TOPSAR –Compute INSAR height error from coherence Determine R for LIDAR –Many ways to compute R –Standard deviation of pulses in each grid cell –Differential: z v - z g

18. 18 Coarse-Scale Data Use SRTM as coarse data input to MKS framework Channels poorly resolved and vegetation contributions (m)

19. 19 Fine-Scale Data Use LIDAR as detail data input to MKS framework Determination of bare surface DEMDetermination Data voids present in bare surface DEM Bridges not removed in this data set (m)

20. 20 Fused DEM and Error Measure Data voids and no-coverage areas filled in Retain high-resolution (5 m) where LIDAR data available Obtain estimate of DEM error at every pixel Mean absolute error relative to LIDAR: 6.3 m (SRTM) and 0.43 m (fused)

21. 21 Fused Results at Coarse Scales Due to multiscale framework, also obtain fused DEMs and error maps at each scale in quadtree, including SRTM scale (20 m) The fused DEM at 20 m retains some of the LIDAR information –Opens possibility to distribute improved DEMs at coarse resolutions for large-scale applications

22. 22 Fused Results Using Sparse LIDAR Data To achieve greater coverage with LIDAR data, sparse acquisitions (high altitude and/or slow scan rates) might be acquired Can still achieve significant improved fine-scale and coarse-scale DEMs using sparse LIDAR E.g. With only 50% LIDAR coverage, MAE: 6.3 m to 0.62 m (at fine scale)

23. 23 Conclusions DEMs with different spatial and vertical resolutions are required for different applications –Space-based INSAR suitable for general channel mapping in moderate relief areas –Airborne INSAR suitable for mapping floodplains and channel topography –Airborne LIDAR suitable for high-resolution mapping (urban, stream networks) Multiscale Kalman smoother provides robust framework for fusing DEMs –Obtain estimates and estimate error variance at every pixel –Input data may have different resolution, coverage (data drop outs), and error characteristics –Estimates produced at different scales can be used for improved hydrologic modeling and to reduce memory/storage requirements –Estimation error decreases as add observation data sets [Slatton, Crawford, Teng, 2002]

24. 24 Future Work Develop alternate methods for estimating vegetation contribution in z S for SRTM. –Inverting microwave scattering models is feasible with certain kinds of airborne INSAR data [Slatton, 2001], but not with SRTM data –Investigate use of NDVI derived from Landsat imagery to modulate SRTM “error” –Investigate use of LIDAR data to quantify vegetation “error” signal in SRTM and classification to extrapolate that correction for simple set of landcover archetypes Continue ongoing work on spatially adaptive MKS fusion –Detect suboptimal filter performance via innovations correlation method [Slatton, 2001] –Develop sets of Kalman model parameters for generalized terrain types, e.g. forest and grassland (multi-model approach) –Derive data-dependent metrics to indicate required resolutions for different terrain types

25. 25 End of main presentation

26. 26 Bare Earth Detector Components Minimum Grid Square Average Filter  + - Lower Envelope Follower Threshold Gradient Flood Fill Building Detection Long/Short Range Removal Bridge Removal Ground Mask Image LIDAR Last Return Generate ground surface mask to classify LIDAR data [Weed, Crawford, Neuenschwander, Gutierrez, 2002] –Remove long and short range errors –Minimum grid data –Find general topography with average filter and subtract –Apply lower envelope follower and threshold image [lower envelope detector] –Detect flat areas using gradient flood fill –Remove false positives (buildings and bridges)

27. 27 Kalman filter is widely used to estimate stochastic signals [1][1] –Implemented in time domain in a recursive algorithm –Requires prior model for filter parameters { , Q, H, R} K is Kalman gain [1][1] H reduces to binary indicator function –INSAR and LIDAR data transformed into estimates of z g and  z v prior to fusion –H=I where observations are available Kalman Filter

28. 28 Scalar Multiscale Stochastic Data Model Many natural processes exhibit statistical self-similarity in scale –Can me modeled with 1/f  noise (fractional Brownian motion) –Variance increases as resolution decreases –Gaussian statistics [statistics] Specify downward state transition and downward process noise variance –Power spectra describes variance (power) across scales, so match power spectrum of process model to data –Use  =  0 2 (1-  )m/2,  > 1:  decreases monotonically [Fieguth, Karl, Willsky, and Wunsch, 1995] –Use  = 1 so all variation comes from   = slope Self-similar process [Wornell, 1993] –Statistics invariant to scaling of bases within an amplitude factor Power spectrum is piecewise linear on log-log scale –Integrability preserved at high frequencies by discretization of image data –Integrability preserved at dc by divergence of physical processes from model