Post on 21-Mar-2016
description
Locally adaptive template sizes for matching repeat images of Earth surface mass movements
Misganu Debella-Giloa and Andreas Kääbb
a, bInstitute of Geosciences, University of Oslo, P. O. Box 1047, Oslo, Norway
a m.d.gilo@geo.uio.no
ContentsIntroduction
Methods
Results
Conclusion
Introduction Repeat optical images are often used to monitor the displacement of Earth
surface masses (e.g. glacier flow, permafrost creep, rock slide, etc)
Independently ortho-rectified and co-registered images are matched using
certain similarity (dissimilarity) measure
Most commonly the normalized cross-correlation (NCC) is used
Image subset (template) from reference image (usually older) is taken and
its conjugate is searched in the target image (usually newer)
The distance between the central pixels of the reference and the search
templates is comupted as the horizontal displacement
Compute cross-correlation coefficientLocate the peak
Compute displacement
The issue …what template size is appropriate? Small templates lack adequate signal variance for the matching …. Ambiguity (noise) problem
Large templates may contain within template displacement gradient… geometric distortion
There is a need to compromise between ambiguity and geometric distortion
Noise and distortion levels may vary spatially
Need for spatially adaptive template sizes
Ideal template:
Contains optimum SNR,
Contains no geometric distortion, and
Is able to identify distinct feature when encountered
Its true match exists with optimized correlation coefficient
The study presents an algorithm which tries to meet these characteristics
A B C
Template size vs. SNR SNR=σ2s/ σ2n
Noise variance is computed using Immerkær’s (1996) method where the difference
between two Laplacian masks is used to convolve the image
To explore the relationship between SNR and template size:
Syntethic image containing distinct feature of 61 by 61 pixels which repeat itself
was created
The SNR was then computed for varying template sizes starting from 3 by 3 pixels
up to a maximum size set depending on the spatial resolution of the image and mass
movement type
The computation was then conducted on real images
Image sections of good contrast and poor contrast are included
SNR
Template (window) size
For small templates the noise variance is
very high while the signal variance is low
therefore the SNR is very low….. Poor
information content
As the size increases, the SNR increases.
If edge is encountered the SNR rises
sharply, and then decreases after crossing
the edge
The first encountered peak shows some
kind of feature boundary
It can also be saturation of signal
61
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
20000
0 50 100 150
Inte
nsity
var
ianc
e
Window size (pixels by pixels)
A
B
C
0
500
1000
1500
2000
2500
3000
3500
0 20 40 60 80 100 120 140
Noi
se v
aria
nce
Window size (pixels by pixels)
A
B
C
59
6137
0
2000
4000
6000
8000
10000
12000
14000
16000
18000
0 20 40 60 80 100 120 140
Sign
al-to
-noi
se ra
tio
Window size (pixels by pixels)
A
B
C
A
B
C
0
500
1000
1500
2000
2500
3000
3500
0 50 100 150
Inte
nsity
var
ianc
e
Window size (pixels by pixels)
Aerial (Rockglacier)
Shadow
A
0
100
200
300
400
500
600
700
0 50 100 150
Noi
se v
aria
nce
Window size (pixels by pixels)
Aerial (rockglacier)
Shadow
B
39
0
200
400
600
800
1000
1200
1400
0 50 100 150
Sign
al to
Noi
se ra
tio
Window size (pixels by pixels)
Aerial (rockglacier)
Shadow
C
Table 1
0
10
20
30
40
50
60
70
0 50 100 150
Inte
nsity
var
ianc
e
Window size (pixels by pixels)
Snow (landsat)
Smooth rockglacier (Aerial)
A
0
100
200
300
400
500
600
700
0 50 100 150
Noi
se v
aria
nce
Window size (pixels by pixels)
Snow (Landsat)
Smooth Rockglacier (Aerial)
B
29
0
5
10
15
20
25
0 50 100 150
Sign
al-t
o-no
ise ra
tio
Window size (pixels by pixels)
Snow (Landsat)
Smooth rockglacier (aerial)
C
•Thus SNR peak can be
used to identify matchable
templates
•But the matable template
may be occluded or changed
unrecognizably
•But the NCC needs to be
computed to know if the size
is optimum and if the
template has a match
Template size and NCC To know the effect of template size on NCC peak, NCC peak is computed for varying template
sizes
For small templates, the maximum NCC is very high but ambiguous due to inadequate signal variance
B1
B2
B3
B40.820.840.860.880.900.920.940.960.981.00
0 20 40 60 80 100
Max
. Cor
rela
tion
Coeffi
cien
t
Template size (pixels by pixels)B
C1
C2
C3
0
20
40
60
80
100
0 20 40 60 80 100
Horiz
onta
l disp
lace
men
t (p
ixel
)
Template size (pixels by pixels)C
0.00
0.20
0.40
0.60
0.80
1.00
0 20 40 60 80 100 120 140
Max
imum
cor
rela
tion
coeffi
cien
t
Template size(pixels by pixels)
020406080
100120140160180
0 50 100 150
Horiz
onta
l disp
lace
men
t (p
ixel
s)
Template size(pixels by pixels)
A
C B A
The presence or absence of the peak of the SNR can help in selecting
matchable templates and excluding unmatchable ones
The presence or absence of the peak of the NCC maxima can help in
determining optimum template sizes (which have true matches with optimized
correlation-coefficient) and in excluding occluded templates
The algorithm tries to satisfy these conditions at each location
Method• Procedures:
• Take central pixels at intervals
• Compute SNR until it attains the first peak
• If it attains a peak within the set maximum value, take the template and its size (Tw),
• If no peak is attained, reject that central pixel
• For the central pixels that passed the SNR test, compute the NCC using the template sizes ranging beteen half Tw and twice Tw
• If the NCC attained a peak and the matching position is fixed over 3 consecutive template sizes, take that size as optimum and record the matching positions and compute the displacements
• The algorithm is applied and evaluated on:
• artificially deformed image: a glacier image subset was deformed artificially with full pixel displacement and Gaussian noise was added to model bi-temporal images
• Landsat PAN image pair of Baltoro glacier (Himalaya) with one year apart,
• Radarsat2 intensity image pair of Cronebreen glacier (Svalbard) with 25 days apart
Evaluation Visual: ….looking at the pattern of the computed displacement vectors
Mean Absolute Difference (MAD) between the computed and actual displacement for the artificially deformed images
SNR gain of reconstructing the reference image from the deformed image
Compute the global correlation coefficient (ρg) between the reference and the reconstructed
SNR =(ρg)/(1- ρg)
SNRgain=SNR (reconstructed)-SNR(origional)
Both the MAD and SNR gain are compared to that of different globally (image-wide) fixed template sizes
ResultsArtificially deformed images
D
B
C
A
Displacement vectors
computed using globally
fixed template sizes of 11
pixels (A), 61 pixels (B)
and the locally adaptive
algorithm (C) together
with the histogram of the
template sizes of the
locally adaptive algorithm
(D) for the noisy test
image.
Mean absolute error of displacement (MAEd) of the globally fixed template sizes (dotted line) and the locally adaptive algorithm (horizontal line) for the noise-free (left) and noisy (right) test images
Global correlation coefficients between the original reference image and the search image before (dashed horizontal lines), after reconstructing using the globally fixed (dotted lines) and the locally adapted (smooth horizontal lines) template sizes for the noise-free (left) and the noisy (right) test images
Statistics
Statistic Actual displacement data
61 pixels 11 pixel
Locally adapted
Minimum 0 0 1 0 Maximum 37 35.90 96.88 36.67 Mean 16.04 15.17 (1.76) a 27.62 (7.49) a 16.05 (0.65) a Standard deviation 9.18 8.84 22.90 9.16
aThe numbers in the brackets are the corresponding MAEd. Notice that by using the locally adaptive algorithm, the MAEd of the large template size is reduced by about 63% while that of the small template size is reduced by about 91%.
Table 1. Displacement statistics for the small, large and locally adapted template sizes for the central pixel of their respective templates of the noisy test image.
Real glacier images: Baltoro
Real glacier images: Cronebreen
Conclusions A new algorithm for locally adaptive template sizes in Normalized Cross-
Correlation (NCC)-based image matching for displacement measurement of Earth surface mass movements is tested and evaluated.
The algorithm performs better than globally fixed template sizes in its accuracy of matching and displacement estimation
It removes the mismatches due to ambiguity (noise) in small template sizes and reduces the errors of misrepresentation due to displacement gradient in large template sizes
Errors due to geometric distortion remain only where high noise level or lack of good signal variance necessitate the use of large template sizes.
The algorithm discards most of the templates which lack sufficient SNR and occluded templates (i.e. templates whose matches do not exist).
Pushes one step towards automation The computational efficiency of the algorithm is low and needs to be
improved.
Thank you!
•This study was supported by The Research Council of Norway (NFR) through the CORRIA project (no. 185906/V30),
Acknowledgements