i a f m 2 0 0 6 martin j. moene e.h. van tol-homan p.v. ruijgrok t.h. oosterkamp j.w.m. frenken m.j....
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![Page 1: I A f M 2 0 0 6 Martin J. Moene E.H. van Tol-Homan P.V. Ruijgrok T.H. Oosterkamp J.W.M. Frenken M.J. Rost Kamerlingh Onnes Laboratory Image Processing](https://reader035.vdocuments.net/reader035/viewer/2022070306/55174bdd550346a3338b4874/html5/thumbnails/1.jpg)
Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Image Processing forVideo-rate Scanning Probe Microscopy
Martin Moene Interface Physics Leiden University The Netherlands
graphic by Prof.Dr. Richard Berndt, Kiel University
50 x 49 nm 300 K Au(110)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Scanning Probe Microscopy
• 1981 Scanning Tunneling Microscope (STM) [1]
• 1986 Atomic Force Microscope (AFM)• Other variants…
graphic by Prof. Dr. Richard Berndt, Kiel University
[1] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57 (1982).
20 x 13 nm 300 K Si(111)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
40s per Image
1024 x 1024
90 x 90 nm
Si(111)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
27 IMAGES per second (64 x 64 pixels2)
[2] M.J. Rost, L. Crama, P. Schakel, E. van Tol et al.; Rev. Sci. Instrum. 76 (2005) 053710
Zoom
Rotate
Pan
27 Hz
r e a l t i m
e
80 Hz
Au(110) HOPG
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Feedback
Drivers
Scan Generator
ADCs
LeidenProbeMicroscopy.com
STM Head
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Stabilizing and Comparing Images
thermal drift
50 x 49 nm 300 K Au(110)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
pixels
AU
Apply Image Stabilisation to:
• Stay Focused• Enable Quantitative Analysis (comparing images)
A tool for both• Image Stabilisation and• Quantitative Analysis
heightlin
e
1st Solution: Normalized Cross-correlation (NCC)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
What is Cross-correlation (CC) ?
Simplifiednano wire orsingle-atom row0
20
40
60
80
100
120
140
x
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
What is Cross-correlation (CC) ?
Simplified crystal surface
0
20
40
60
80
100
120
140
x
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
0
20
40
60
80
100
120
140
where f is the image and the sum is over x under the window containing the feature t positioned at c: x = c..c+w
Cross-correlation
CC(c) = x f(x) t(x − c)0
10000
20000
30000
40000
50000
60000
70000
c
What is Cross-correlation (CC) ?
“error”
CC depends on offset and amplitude
x
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
- 60
- 40
- 20
0
20
40
60
80
100
120
Mean subtracted
Better Correlate Signal Form
Cross-correlation
CC(c) = x f’(x) t’(x − c)- 50000
- 40000
- 30000
- 20000
- 10000
0
10000
20000
30000
40000
where f is the image and the sum is over x under the window containing the feature t positioned at c: x = c..c+w
-0.4
-0.2
0
0.2
0.4
0.6
0.8
Normalized Cross-correlation
[-1,+1]
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Symmetric Computation
CC(c) = N-1x=0 f(c + x − N/2) t(x)
The usual notation to compute symmetrically around the column at hand
Values required that are outside the signal
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Values required that are outside the image
Boundary ConditionsC
C(c
) =
N-1 x
=0 f
(c +
x −
N/2
) t(
x)
Constant0 0 0 0 00 0 0 0 00 0 1 2 30 0 2 3 40 0 3 4 5
Reflect5 4 3 4 54 3 2 3 43 2 1 2 34 3 2 3 45 4 3 4 5
Extend1 1 1 2 31 1 1 2 31 1 1 2 32 2 2 3 43 3 3 4 5
Periodic3 4 2 3 44 5 3 4 52 3 1 2 33 4 2 3 44 5 3 4 5
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
NCC Application 1: determine shift vector
template
dy
dx
image
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
0
0. 2
0. 4
0. 6
0. 8
1
1. 2
poi nt s
NCC
Normal
0
0. 2
0. 4
0. 6
0. 8
1
1. 2
poi nt s
NCC
Sl ant ed
0
0. 2
0. 4
0. 6
0. 8
1
1. 2
poi nt s
NCC
Normal Sl ant ed
NCC Application 2: compare images
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
• Qualitative: locate ‘a’ at global peak• Quantitative: ‘a’-s can be found at 1• Quantitative: ‘o’-s can be found at 0.7
NCC Application 3: locate feature
1
0.7
templateimage
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Several Ways to Normalise Cross-correlation
[3] J. Martin and J.L. Crowley. Experimental comparison of correlation techniques. In Proc. International Conf. on Intelligent Autonomous Systems, 1995.
energy
zero-mean
image mean under template
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Numerator computed via FFT as a convolution with the template reversed
Fast NCC Implementation [4]
[4] J.P. Lewis. Fast normalized cross-correlation. In Vision Interface, pages 120–123, 1995. [5] H.Huang, D.Dabiri and M.Gharib. On errors of digital particle image velocimetry.
Meas. Sci. Technol. 8 (1997) 1427-1440.
• FFT requires size 2N, pad with zeros• FFT is periodic, prevent errors by padding larger area [5]
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Fast NCC Implementation
Denominator computed from table containing the integral(running sum) of the image square over the search area.
image energy under template
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Fast NCC Implementation: Integral Image
Using the integral image representation one can compute the value of any rectangular sum in constant time.
For example the integral sum inside rectangle D we can compute as:
ii(4) + ii(1) — ii(2) — ii(3)
[6] P. Viola and M. Jones. Robust real-time object detection.Second International Workshop on Statistical and Computational Theories of Vision, 2001.
Def: The integral image at location (x,y), is the sum of the pixel values above and to the left of (x,y), inclusive.
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Results: Timing *)
While Measuring, Registrate (Preliminary)• Decimate image to 64 x 64 pixels2
• Apply Gaussian sub-pixel interpolation [7]
• Background subtraction plus fast NCC: 14 ms
While Analysing, Registrate and Correlate• Spatial Domain NCC: 40 minutes• Fast NCC: 300 ms
*) timing for images of 512 x 512 pixels2 on a PC with an AMD Athlon at 2.8 GHz
[7] J. Bolinder. On the accuracy of a digital particle image velocimetry system. 1999.
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Results: Stabilisation
Au(110)
300 K
39 x 38 nm
26 sec/frame
Au(110)
300 K
52 x 55 nm
3.8 sec/frame
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Summary:• NCC enables finding features• NCC enables quantitatively comparing features &
images• NCC enables tracking to compensate for drift,
there is room for improvement
Future improvement: Lucas-Kanade [8]
• Spatial intensity gradient• Taylor series expansion, iteration• Gaussian Filter ( resolution)• Pyramid of images at different
resolution
[8] B. Lucas and T. Kanade, An iterative image registration technique with an application to stereo vision, in Proc. Imaging Understanding Workshop, 1981, pp. 121—130.
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Recognizing FeaturesCoalescence of Vacancy Islands on Cu(100)
Paul Ruijgrok
200 x 200 nm 300 K Cu(100)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Finding the Vacancy Islands
Paul Ruijgrok
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Leveling the Image
Accuracy:• Data based number of bins• Fit (part of) Gaussian curve
Paul Ruijgrok
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Finding the Vacancy Islands: threshold
Paul Ruijgrok
hthreshold = h0 + sa0 ,
s: 0.1…0.9
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Detecting the Island Edges
Paul Ruijgrok
erosion
Island A Erosion E(A,N4) ∂A = A—E(A,N4)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
-3
-2
-1
0
1
2
3
4
5
-2 -1 0 1 2 3 4 5
y
x
P1(-1,0)
P2(0,1)
P3(1,2)
P4(2,3)
P5(4,1)
-3
-2
-1
0
1
2
3
4
5
-2 -1 0 1 2 3 4 5
b
a
P1
P2
P3
P4
P5
42 2
2
2
22
2 1 1 1 1 1
11111
111
1
11
11
11
1
111111
11
1 1
1 11
11
1111
1
11
Paul Ruijgrok
yi = axi + b
or
b = -xia+ yi
Transform points to curves in parameter
space
a = 1, b = 1 y = x +
1
[9] Duda, R. O. and P. E. Hart, "Use of the Hough Transformation to Detect Lines and Curves in Pictures," Comm. ACM, Vol. 15, pp. 11–15 (January, 1972).
Finding the Vacancy Lines
Hough
Transform
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Finding the Vacancy Lines
Hough Transform
• Slope-intercept representation:unbounded parameters
• Want grid of limited size:
• ρ = x cos(θ) + y sin(θ) , or
• ρ = C cos(θ + δ)
Paul Ruijgrok
rho
theta
x
y
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Summary
Paul Ruijgrok
422
22
22
2 1111111
1111
11
1
11
11
11
1
111111
11
11
111
11
1111
1
Thanks to DIPimage team, Delft University of Technology. DIPimage: a scientific image processing toolbox for MATLAB.
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Thanks To:
www.LeidenProbeMicroscopy.com
Ph.D. Students
drs. K. Schoots (Koen)
Undergraduate Students
P.V. Ruijgrok (Paul)
Technicians
L. Crama (Bert)
E. van Tol-Homan (Els)
R. Koehler (Raymond)
P. Schakel (Peter)
Staff
prof.dr. J.W.M. Frenken (Joost)
dr.ir. T.H. Oosterkamp (Tjerk)
dr. M.J. Rost (Marcel)
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Conclusion
Summary
10.7
templateimage
Hough Transform
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Future ?
The Future: Superresolution ?
10.7
templateimage
Hough Transform
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Introduction | Stabilizing and Comparing Images | Recognizing Features | References
[1] G. Binnig, H. Rohrer, C. Gerber, and E. Weibel, Phys. Rev. Lett. 49, 57 (1982).
[2] M.J. Rost, L. Crama, P. Schakel, E. van Tol et al.; Rev. Sci. Instrum. 76 (2005) 053710
[3] J. Martin and J.L. Crowley. Experimental comparison of correlation techniques. In Proc. International Conf. on Intelligent Autonomous Systems, 1995.
[4] J.P. Lewis. Fast normalized cross-correlation. In Vision Interface, pages 120–123, 1995.
[5] H.Huang, D.Dabiri and M.Gharib. On errors of digital particle image velocimetry.Meas. Sci. Technol. 8 (1997) 1427-1440.
[6] P. Viola and M. Jones. Robust real-time object detection. Second International Workshop on Statistical and Computational Theories of Vision, 2001.
[7] J. Bolinder. On the accuracy of a digital particle image velocimetry system. 1999.
[8] B. Lucas and T. Kanade, An iterative image registration technique with an application to stereo vision, in Proc. Imaging Understanding Workshop, 1981, pp. 121--130.
[9] R. Duda and P. Hart. Use of the Hough transformation to detect lines and curves in pictures. Comm. ACM, Vol. 15, pp. 11–15 (January, 1972).
References
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Introduction | Stabilizing and Comparing Images | Recognizing Features | References
Du-Ming Tsai , Chien-Ta Lin, Fast normalized cross correlation for defect detection, Pattern Recognition Letters, v.24 n.15, p.2625-2631, November 2003
Ian T. Young, Jan. J. Gerbrands and Lucas J. van Vliet. Fundamentals of Image Processing. 1998.
W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery. Numerical Recipes in C: The Art of Scientific Computing, 2nd edition. Cambridge University Press. New York, NY, USA.
Ullrich Köthe. STL-Style Generic Programming with Images. C++ Report Magazine 12(1), pp. 24-30, January 2000.
Leiden Probe Microscopy
Interface Physics at Leiden University
This presentation from author’s web-site
Other Information
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Introduction | Stabilizing and Comparing Images | Recognizing Features | Software
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