using hierarchical warp stereo for topographydial/ece531/hierarchicalwarpstereo.pdf · using...
TRANSCRIPT
1
ECE/OPTI 531 – Image Processing Lab for Remote Sensing Fall 2005
Using Hierarchical WarpUsing Hierarchical WarpStereo for TopographyStereo for Topography
Dr. Daniel FilibertiDr. Daniel Filiberti
Fall 2005HWS Topography 2
Introduction
• Topography from Stereo– Given a set of stereoscopic imagery, two perspective
views of a three-dimensional object, we can determineelevation differences in the terrain using stereotriangulation.
– Stereoscopic parallax or disparity is the difference inposition of an imaged ground feature from one phototo the next overlapping photo.
• Parallax differences, the change in disparity dueto a change in relief of the terrain being imaged,are used to determine relative elevations togenerate a DEM
2
Fall 2005HWS Topography 3
Imaging Geometry
• Overlapping pair ofvertical aerialphotographs
• Parallax equation
hA= H !
B "f
pa
#h =H ! h
1
p2
#p
Fall 2005HWS Topography 4
Numerical Example
• H = 10,000 ft, B = 8 mi, f = 4 in, h = 30 ft
• This is a 1.41 pixel disparity difference on 1 footimagery
• Note that the air base, B, determines thesensitivity to changes in elevation
p =f !B
H "h=0.333 # 42,240
10, 000 " 30= 1.41
3
Fall 2005HWS Topography 5
Reference Photo (Cuprite, NV)
Fall 2005HWS Topography 6
Overlap Extraction
4
Fall 2005HWS Topography 7
Stereo Region
Reference Target
Fall 2005HWS Topography 8
Stereo Region (Cont.)
Reference Target
5
Fall 2005HWS Topography 9
Finding Disparity
• Types of Stereo Algorithms– Computer vision algorithms extract and match features
such as edges, contours, and shapes to find a coarsedisparity map on a non-uniform grid
– Correlation-based algorithms match a local areaaround a point (target template) into a larger searcharea to find a disparity at every point, producing adense and uniform grid of samples
Fall 2005HWS Topography 10
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
6
Fall 2005HWS Topography 11
HWS Processing
• Matching results indisparity image which isexpanded and used as aninitial estimate at nextlevel
• Further processing mustusually be done to convertpixel disparities to a digitalelevation map
Fall 2005HWS Topography 12
0
1
2
3
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 0.5
7
Fall 2005HWS Topography 13
Pyramid Construction
• Multiresolution Hierarchical Representation– Image pyramid generated by
– Where REDUCE() performs a downsample and filteroperation on the previous level
– Using a simple weighting function is common,
P/(i, j ) = W(m,n)P
l !1n= !N
N
"m= !N
N
" (2i +m,2j + n)
P/= REDUCE(P
l!1)
Fall 2005HWS Topography 14
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
8
Fall 2005HWS Topography 15
Characteristic Functions
Fall 2005HWS Topography 16
• W1 in two dimensions0.0025 0.0125 0.0200 0.0125 0.00250.0125 0.0625 0.1000 0.0625 0.01250.0200 0.1000 0.1600 0.1000 0.02000.0125 0.0625 0.1000 0.0625 0.01250.0025 0.0125 0.0200 0.0125 0.0025
Equivalent Weighting Functions (a=0.4)
9
Fall 2005HWS Topography 17
Area Matching
• Define a match score operator,
– Improved performance in matching has been shownwhen the ACF is weighted by a Gaussian functionfavoring low disparity changes, or a smooth disparitysurface
– The ACF is a normalized, Gaussian weighted cross-correlation
C(i, j ) = ref (m,n) !tgt(m " i ,n " j )n#
m#
ACF(i, j ) =C(i, j )
ref 2 (m,n)n#
m#[ ]
1/ 2
Fall 2005HWS Topography 18
Match Location
• Best match point is found by subpixelapproximation– 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
10
Fall 2005HWS Topography 19
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)
Fall 2005HWS Topography 20
HWS Example (Cont.)
• Hand digitized contours are interpolated fortruth
11
Fall 2005HWS Topography 21
HWS Results
Truth HWS
Fall 2005HWS Topography 22
HWS Results (Cont.)
12
Fall 2005HWS Topography 23
Application: Shaded Relief
• Assumptions– Lambertian surface– Nadir view– No atmospheric scattering– No path radiance
Lsensor
= A!cosi +C
Fall 2005HWS Topography 24
Shaded Relief Equations
• Find cos(i) using surface gradient– E, N components from DEM– Rotatation for component along direction of solar
irradiance
• Take the normalized dot product of the twogradient vectors,
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
ps= !sin"
scot(
#
2! $
s)
qs= !cos"
scot(
#
2!$
s)
cosi =1+ p
!p
s+q
!q
s
1+ p!
2
+ q!
2 1+ ps
2
+ qs
2
13
Fall 2005HWS Topography 25
Shaded Relief
Aerial Photo,193°az, 34° zn
Aribitrary,140°az, 66° zn
Fall 2005HWS Topography 26
Application: HFM Fusion
14
Fall 2005HWS Topography 27
HFM Results
Fall 2005HWS Topography 28
Further Reading
• Text R.A. Schowengerdt, “Remote sensing, modelsand methods for image processing”, 2nd ed.– 3.9.7 Topographic Distortion– 6.5.1 Image Resolution Pyramids– 8.4.2 High-Resolution DEM and Hierarchical Warp Stereo– 8.5 Multi-image Fusion