Using Hierarchical Warp Stereo for Topography. Introduction

Transcription

1 Using Hierarchical Warp Stereo for Topography Dr. Daniel Filiberti ECE/OPTI 531 Image Processing Lab for Remote Sensing Introduction Topography from Stereo Given a set of stereoscopic imagery, two perspective views of a three-dimensional object, we can determine elevation differences in the terrain using stereo triangulation. Stereoscopic parallax or disparity is the difference in position of an imaged ground feature from one photo to the next overlapping photo. Parallax differences, the change in disparity due to a change in relief of the terrain being imaged, are used to determine relative elevations to generate a DEM HWS Topography 2 1

2 Imaging Geometry Overlapping pair of vertical aerial photographs Parallax equation h A = H! B "f p a #h = H! h 1 p 2 #p HWS Topography 3 Numerical Example H = 10,000 ft, B = 8 mi, f = 4 in, h = 30 ft p = f!b # 42, 240 = H " h 10, 000 " 30 = 1.41 This is a 1.41 pixel disparity difference on 1 foot imagery Note that the air base, B, determines the sensitivity to changes in elevation HWS Topography 4 2

3 Reference Photo (Cuprite, NV) HWS Topography 5 Overlap Extraction HWS Topography 6 3

4 Stereo Region Reference Target HWS Topography 7 Stereo Region (Cont.) Reference Target HWS Topography 8 4

5 Finding Disparity Types of Stereo Algorithms Computer vision algorithms extract and match features such as edges, contours, and shapes to find a coarse disparity map on a non-uniform grid Correlation-based algorithms match a local area around a point (target template) into a larger search area to find a disparity at every point, producing a dense and uniform grid of samples HWS Topography 9 HWS Algorithm Hierarchical Warp Stereo (Quam, 1984) Correlation-based approach Uses multiresolution image pyramid to match from coarse to fine spatial resolution Disparities propagate as estimates to higher resolutions, reducing the necessary search area (correlation window) size HWS Topography 10 5

6 HWS Processing Matching results in disparity image which is expanded and used as an initial estimate at next level Further processing must usually be done to convert pixel disparities to a digital elevation map HWS Topography 11 Image Pyramid Level 0 is full spatial resolution image Resolution decreases as level increases Reduction can be done in spatial or Fourier domain Scale factor is typically HWS Topography 12 6

7 Pyramid Construction Multiresolution Hierarchical Representation Image pyramid generated by Where REDUCE() performs a downsample and filter operation on the previous level Using a simple weighting function is common, P / (i, j ) = N " N " W (m,n)p l!1 (2i + m,2j + n) m=! N P / = REDUCE(P l! 1 ) n=! N HWS Topography 13 Weight Selection Properties of a good generating kernel (Burt, 1983) Separable, W(m,n) = w(m)w(n) Normalized, weights sum to one Symmetric, w(m) = w(-m) Equal contribution, all nodes at a given level must contribute the same total weight to nodes at next level Use a 5x5 Burt kernel Let W(0) = a, W(1) = W(-1) = b, and W(2) = W(-2) = c Equal contribution requires a + 2c = 2b Constraints satisfied when W(0) = a W(1) = W(-1) = 1/4 W(2) = W(-2) = 1/4 a/2 HWS Topography 14 7

8 Characteristic Functions HWS Topography 15 Equivalent Weighting Functions (a=0.4) W1 in two dimensions HWS Topography 16 8

9 Area Matching Define a match score operator, C(i, j ) = # # ref (m,n)!tgt(m " i,n " j ) m n C(i, j ) ACF(i, j ) = [# # ref 2 (m,n)] m n Improved performance in matching has been shown when the ACF is weighted by a Gaussian function favoring low disparity changes, or a smooth disparity surface The ACF is a normalized, Gaussian weighted crosscorrelation 1/ 2 HWS Topography 17 Match Location Best match point is found by subpixel approximation Fit a parabola to the ACF peak and its nearest neighbors Problem: this approximation generates ripple artifacts when coupled with the image quantization Match Confidence Issues Disparity out of range Multiple ACF peaks Anomaly Detection After finding the ACF peak, estimate the distance between the peak and center of mass of the ACF Match is considered valid if the distance meets a threshold HWS Topography 18 9

10 HWS Example Apply to Cuprite, NV stereo pair HWS Parameters Correlation Window Size of 13x13 pixels Search area of 17x17 pixels Maximum disparity of +-8 pixels per pyramid level Anomaly detection used to mark holes Holes filled using interpolation by bisection (cubic spline) HWS Topography 19 HWS Example (Cont.) Hand digitized contours are interpolated for truth HWS Topography 20 10

11 HWS Results Truth HWS HWS Topography 21 HWS Results (Cont.) HWS Topography 22 11

12 Application: Shaded Relief Assumptions Lambertian surface Nadir view No atmospheric scattering No path radiance L sensor = A!cosi +C HWS Topography 23 Shaded Relief Equations Find cos(i) using surface gradient E, N components from DEM Rotatation for component along direction of solar irradiance p! = f (x i +1,y i ) "f (x i "1,y i ) 2d q! = f (x i,y i +1 ) " f (x i,y i "1 ) 2d p s =! sin" s cot( # 2! $ s ) q s =! cos" s cot( # 2! $ s ) Take the normalized dot product of the two gradient vectors, cosi = 1+ p! p s + q! q s p! + q! 1+ p s + q s HWS Topography 24 12

13 Shaded Relief Aerial Photo, 193 az, 34 zn Aribitrary, 140 az, 66 zn HWS Topography 25 Application: HFM Fusion HWS Topography 26 13

14 HFM Results HWS Topography 27 Further Reading Text R.A. Schowengerdt, Remote sensing, models and methods for image processing, 2nd ed Topographic Distortion Image Resolution Pyramids High-Resolution DEM and Hierarchical Warp Stereo 8.5 Multi-image Fusion HWS Topography 28 14