1 howard schultz, edward m. riseman, frank r. stolle computer science department university of...
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Howard Schultz, Edward M. Riseman, Frank R. StolleComputer Science Department
University of Massachusetts, USA
Dong-Min WooSchool of Electrical EngineeringMyongji University, South Korea
Error Detection and DEM Error Detection and DEM Fusion Using Self-ConsistencyFusion Using Self-Consistency
7th IEEE International Conference onComputer Vision
September 20-27, 1999 Kerkrya, Greece
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Long-Term Objectives Generate 3D terrain models from multiple,
overlapping images (including video sequences) Accurate - Photogrammetric applications Robust with respect to:
– Widely spaced cameras– Oblique viewing– Occlusions– Non-lambertian surface patches
Automatic Efficient
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Long-Term Objectives Terrain models include an estimate of geospatial
uncertainty Detect unreliable elevation estimates associated with
blunders, occlusions, shadows, false matches,... Estimate the RMS elevation errors
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Environmental Monitoring
Wide-angle video: 1 meter per pixels covers a 3/4 km swath Zoom Video: 10 cm pixels covers a 75 meter swath GPS, IMU & laser altimetery continuously recorded
Wide-angleWide-angle ZoomZoom
Reducing the forest to a simple model of Reducing the forest to a simple model of poles and circlespoles and circles
Biomass Estimation from Counting Trees
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Real World Problems
Need reliable estimates of accuracy Almost impossible to get sufficient ground
truth Even 1 blunder in 1,00,000 is problematic
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Work in object space to enable the fusion of multiple DEMs generated from multiple image pairs
Use Laclerc’s Self-Consistency measure to detect unreliable elevation estimates
General Approach
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Elevation estimates result from two types of correspondences True correspondences, characterized by small,
normally distributed errors that result from– Surface micro structure– Geometric misalignment – Optical distortion
False correspondences (outliers), characterized by large errors resulting from
– random, unrealistic texture matches - Large effects
Small effects
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We use the UMass Terrain reconstruction system Terrest, which is an implementation of a hierarchical, texture matching algorithm
Terrest produces a set of pixel correspondences, which are stored in a disparity map DRT R denotes the reference image T denotes the target image
The pixels (i,j) in R and (i+D(i,j)) in T view the same surface spot
The process is not symmetric with respect to the reference
and target images, DAB DBA
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Correspondences
ComputedDEM
TrueDEM
Error
The computed DEM is the sum of the true surface structure and an error term
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Two ways to compute a DEM from 2 images (A and B). A is the Reference and B is the Target
B is the Reference and A is the Target
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The intra-frame difference
ZAB-ZBA = AB-BA
Depends only on the computed DEMs
Taking the standard deviation of both sides
(ZAB-ZBA) = (AB-BA)
The distribution (ZAB-ZBA) provides a means to
separate reliable from unreliable elevation estimates
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If are normally distributed, except for a small number of outliers, and
computed
AB ,BA dependent
AB ,BA independent0 < < 1
uncertaintygeospatial
intra-frame standard deviation
describes the amount of statistical independence depends on surface geometry, viewing geometry, sensor type, optics,
...
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The tails of the distribution are dominated by unreliable points.
We need a method to estimate (ZAB-ZBA) when the distribution is polluted by unreliable points
Fit the histogram of (ZAB-ZBA) to a Gaussian plus a constant
The numbers hmax, dz0, , h0 are parameters of the fit
,...2,1,0,
2exp 02
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max
kh
dzdzh k
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Consider ZAB and ZBA to be unreliable if
|ZAB-ZBA| > n n is a threshold Small values of n pass more points which are less
self-consistent Larger values of n pass fewer points which are
more self-consistent The threshold can be set based on consistency or
the number of points passed
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A simple algorithm to estimate the optimal DEM Accumulate elevations that have an intra-frame difference less than the threshold.
Keep ZAB and ZBA if ZAB-ZBA n Compute the mean surface Z Go back and add in the elevations close to the mean surface, keep ZAB if Z-ZAB n
re-compute the mean surface Z
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Z12-Z21
Z13-Z31
Z14-Z41
Z23-Z32
Z24-Z42
Z34-Z43
4 images 6 intra-frame differences
ZAB-ZBA
-1.0 0.0 +1.0
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Z12-Z21
Z13-Z31
Z14-Z41
Z23-Z32
Z24-Z42
Z34-Z43
Intra-frame differences after removing unreliable elevations
ZAB-ZBA
-1.0 0.0 +1.0
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Rendered View
No. of consistent points0123456789 101112
157
0
17
41
84
296
782
2087
5997
19139
74096
288430
926778
DEM
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DEM Ortho-image
Tree Counting
Group 1: for every bump in the DEM looked for a tree in the ortho-image Group 2: for every tree in the Ortho-image looked for a bump in the DEM 95% agreement
Another Example
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Verification Using Photo-realistic Simulation
Comprehensive analysis requires ground truth, which is impossible to collect
Instead use photo-realistic synthetic images Enables analysis from any view point Allows for changes in lighting and surface
texture
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Start with a previously generated DEM and ortho-image (pseudo ground truth)
Define the viewing geometry Use a photo-realistic rendering program to
generate synthetic images of the pseudo ground truth
Recover the DEM and ortho-image and compare to the pseudo ground truth
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Self-consistency and geospatial error statistics as a function of viewing geometry base-to-height ratio (b/h) incidence angle ()
B/h A B (ZAB–ZBA) % Inliers2 cutoff
(Z*–ZAB) (Z*–ZBA)
0.277 0 15 0.451189 91.90 0.332601 0.244706 0.2136850.293 15 30 0.486813 92.50 0.344480 0.330056 0.2606980.575 15 -15 0.311553 91.36 0.163137 0.213822 0.1314430.868 -15 30 0.203503 89.40 0.157535 0.194275 0.1523261.230 30 -30 0.167713 84.24 0.155302 0.188295 0.155993
(Z*–Z)–
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Reliable Point Mask
A= -30°B= +30°
A= 0°B= +15°
No. ofReliable Points
DEM
RMS error: 17cmElevation range: 762.7 - 885.7mGSD: 35cm 2 consistent point:99.54%
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Future Directions
Develop models that predict the geospatial uncertainty () from the distribution of self-consistency (ZAB-ZBA)
Use the DEM fusion techniques to generate terrain models from digital video sequences