Airborne LiDAR System (ALS) Ranging and Georeferencing

Transcription

1 Airborne LiDAR System (ALS) Ranging and Georeferencing R O D P I C K E N S C H I E F S C I E N T I S T, C N S S I E R R A N E V A D A C O R P O R A T I O N F R I D A Y M A R C H 3 1,

2 Topics to cover Remote Sensing with LiDAR Airborne LiDAR Systems Ranging methods for full-waveform LiDAR Georeferencing LiDAR point cloud Conclusion Referencess

3 Remote Sensing with LiDAR

4 LiDAR data NSF LiDAR data

5 Airborne LiDAR System: Overview System Controller Position and Orientation (POS) GPS IMU Ranging Subsystem Laser Tx Laser Rx Pointing System *NGA.SIG.0004 Storage Processing - Range Extraction - Georegistration Scene

6 Pointing System Controller Position and Orientation (POS) GPS IMU Ranging Subsystem Laser Tx Laser Rx Pointing System *NGA.SIG.0004 Storage Processing - Range Extraction - Georegistration Scene

7 LiDAR Pointing Mechanisms LiDAR Scanner: Flying Spot Scannerless: Time-of-Flight Camera Advanced Scientific Concepts: FLASH Lidar Avalanche Photo Diode: Photo by Radovan Blazek

8 Range Extraction System Controller Position and Orientation (POS) GPS IMU Ranging Subsystem Laser Tx Laser Rx Pointing System *NGA.SIG.0004 Storage Processing - Range Extraction - Georegistration Scene

9 Approaches to Range Extraction Discrete returns (hardware based) Full-waveform returns (software based)

10 Time-of-Flight Imaging Technische Universtat Munhchen

11 Processing System Controller Position and Orientation (POS) GPS IMU Ranging Subsystem Laser Tx Laser Rx Pointing System *NGA.SIG.0004 Storage Processing - Range Extraction - Georegistration Scene

12 Full-waveform Range Extraction

13 Full-waveform Range Extraction Discrete returns (hardware based) Full-waveform returns (software based)

14 Some Methods of Range Extraction Gaussian Decomposition Hofton et al. 2000, Persson et al. 2005, Expectation-Maximization Deconvolution Parrish et al 2007, Figueiredo and Nowak 2003 Wiener Deconvolution and Decomposition Jutzi and Silla 2006 Other methods Matched filtering B-Splines Approach Roncat et al Average Square Difference Function Wagner et al 2007

15 Gaussian Decomposition

16 Gaussian Decomposition Each LiDAR waveform is a linear combination of Gaussian components. N y t = i=1 α i exp 1 2σ i 2 t μ i 2 α i = amplitude of ith component σ i = width of ith component μ i = position of ith component Sources: References 4 and 5

17 Functional Diagram of Gaussian Decomposition wave form Smoothing Filter Non-negative Least Squares σ i μ i Flag Important Returns A A Add Gaussian Levenberg Marquardt σ i μ i No Done Yes Hofton: Reference 3 and 4

18 Expectation Maximization Deconvolution

19 Deconvolution: Determine x[n] Given input y n which is the received full waveform: y n = h n x n + η[n] where x n is the full waveform representation of scene h n is system impulse response (optics, electronics, atmosphere) η[n] is white Gaussian noise estimate via deconvolution x n which is the signal of interest.

20 Expectation Maximization (1/5) Maximum Likelihood Expectation maximization (hidden variables h i ) መθ = argmax θ I log Pr x i θ i=1 መθ = argmax θ I log න Pr x i, h i θ dh i i=1 Pr x i θ = න Pr x i, h i θ dh i

21 EM and Full-waveform (2/5) Apply EM to Mixture of Gaussians Source: Prince

22 Expectation Maximization (3/5) መθ = argmax θ I log න Pr x i, h i θ dh i i=1 Set a lower bound to the above log likelihood, A, as follows: A I i=1 q i (h i )log න Pr x i, h i θ q i (h i ) dh i I log න Pr x i, h i θ dh i i=1 A

23 Expectation Maximization (4/5) Set q i h i with hidden parameters h i as follows E-step: q i h i = P h i x i, θ [t] = Pr x i h i, θ t Pr(h i θ t ) Pr(x i ) and maximize for θ as follows M-step: መθ [t+1] = argmax θ I q i (h i )log න Pr x i, h i መθ [t] i=1 dh i

24 Range Extraction with EM (5/5) E step: z Ƹ (t) n = x (t) n + h n y n h n x (t) n M step: x (t+1) n = max z Ƹ (t) n 2 2 τσ η z Ƹ (t) n x (t) n is estimate of signal at nth iteration z Ƹ (t) n is estimate of missing data

25 Wiener Deconvolution and Decomposition

26 Deconvolution Given input y n which is the received full waveform: and y n = h n x n + η[n] x n is the full waveform representation of scene h n is system response (optics, electronics, atmosphere) η[n] is white Gaussian noise estimate via deconvolution x n which is the signal of interest

27 Wiener Deconvolution y n = h n x n + η[n] y n = h n x n y n Fourier Y Wiener Filter X Inverse Fourier Estimate of x[n] x n A Wiener Filter = H H H+α NSR NSR noise to signal ratio

28 Decomposition Y X Inverse Fourier x n A Levenberg Marquardt < az, el, r > i=1:n Deconvolution (previous slide) Decomposition

29 Sensor Coordinates to Georeferenced Coordinates < X, Y, Z > L TO < L A T, L O N, A L T > W G S 8 4

30 LiDAR data: Georeferencing <lat, lon, height> NSF LiDAR data

31 LiDAR data: Georeferencing r L <lat, lon, height> NSF data

32 Quadcopter and Geometry z M M = Local Level Map Coordinates r INS,M r L,M y M r o,m x M

33 Object in LiDAR Sensor Coordinates INS GPS z M x INS LiDAR Mapping Equation y INS zins b L,INS x L r o,m =r INS,M + R M INS(R INS L r L + b L,INS ) z L y L r INS,M r L y M r o,m x M

34 Sensor: Spherical to Cartesian z φ x = r sin θ cos φ y = r sin θ sin φ z = r cos θ θ y x r L r L = r, θ, φ L = x, y, z L Source: Velodyne Inc.

35 Object in LiDAR Sensor Coordinates INS GPS z M x INS LiDAR Mapping Equation y INS zins b L,INS x L r o,m =r INS,M + M R INS ( INS R L r L + b L,INS ) z L y L r INS,M r L y M r o,m x M

36 Local Level (Map) and ECEF Local Level (MAP) (ENU) Earth Centered Earth Fixed (ECEF)

37 Local Level (Map) to ECEF Local Level (MAP) (ENU) Earth Centered Earth Fixed (ECEF) <x,y,z> r o,ecef = ECEF f M (r 0,M,r origin,m ) Diagram: Wang, Huynh, Williamson

38 ECEF to Geodetic (Lat, Lon, Alt) Geodetic Coordinates <Lat, Lon, Height> r o,lla = LLA f ECEF (r 0,ECEF, Datum) Diagram: Wang, Huynh, Williamson

39 LiDAR data: Georeferenced <34.5 N, 115W, 245 m> NSF data

40 LiDAR Range Extraction and Georeferencing Utilizes Estimation and Detection theory Methods of optimal detection Wonderful application of Statistics, probability, and linear algebra Involves Geodesy Mappings between world referenced coordinate systems

41 References 1) Airborne Topographic Lidar Manual, Michael Renslow, Editor 2) Elements of Photogrammetry, Wolf and DeWitt 3) Full-wave topographic lidar: State-of-the-art; Clement Mallet and Frederic Bretar, ISPRS Journal of Photogrammetry and Remote Sensing, 64 (2009) ) Empirical Comparison of Full-Waveform Lidar Algorithms: Range Extraction and Discrimination Performance; Photogrammetric Engineering and Remote Sensing; Christopher E. Parrish, Inseong Jeong, Robert Nowak, and R. Smith; August ) Decomposition of laser altimeter waveforms; M.A. Hofton, J.B. Minster, and J.B. Blair; IEEE Transactions of Geoscience and Remote Sensing, 38(4): ) 3D vegetation mapping using small-footprint full-waveform airborne laser scanners. Available from: [accessed 19 Mar, 2017] 7) An EM Algorithm for Wavelet-Based Image Restoration; Mario Figueiredo and Robert Novak, IEEE Transactions on Image Processing, Vol 12, No 8, August ) Retrieval of the Backscatter Cross-section in Full-Waveform LIDAR data using B-Splines; A. Roncat, G. Bergauer, N. Pfeifer, IAPRS, Vol. XXXVIII, Part 3B, Saint Mande, France, September 1-3, ) Range determination with waveform recornding laser systems using a Wiener Filter; Boris Jutzi and Uwe Stilla, ISPRS Journal of Photogrammetry & Remote Sensing, 61, 2006, ) Gaussian Decomposition and calibration of a novel small-footprint full-waveform digitizing airborne laser scanner; Wolfgang Wagner, Andreas Ullrich, Vesna Ducic, Thomas Melzer, Nick Studnicka, ISPRS Journal of Photogrammetery and Remote Sensing 60 (2006) ) Computer Vision: Models, Learning, and Inference, Simon J.D. Prince, Cambridge University Press