Image registration is a process that aligns pixels in two images to correspond to the same point in a scene. It allows images to be combined or focused in a way that improves information extraction. Some applications of image registration include stereo imaging, remote sensing, comparing images over time, and finding where a template matches an image. Template matching is used to find the best match between a template and image by measuring similarity or mismatch between them. Cross-correlation is commonly used as a similarity measure for template matching.

1. Image Registration
Subject: Image Procesing & Computer Vision
Dr. Varun Kumar
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 1 / 10

2. Outlines
1 Image registration
2 Different mismatch or match measures
3 Cross correlation between two images
4 Some application of registration techniques
5 References
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 2 / 10

3. Image registration:
Image registration
⇒ Image registration is a process which makes the pixels in two images
coincide to the same point in the scene.
⇒ Once registered, the image can be combined or focused in a way that
improves information extraction.
Application of image registration:
1 Stereo imaging, where two images are taken from different positions.
2 Remote sensing, where images may be taken from different sensors.
3 Image may be taken at different times.
4 Finding a place in a picture where it matches a given pattern.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 3 / 10

4. Template matching
Objective:
⇒ Best matching of template in a given image.
⇒ Match measure or similarity measure.
⇒ Mismatch measure or dissimilarity measures.
⇒ Best way for matching measurement→ Difference measurement, i.e,
A
max
|f − g|
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 4 / 10

5. Continued–
⇒ Second method (mismatch measure)
A
|f − g| ⇒
i j∈A
[|f (i, j) − g(i, j)|]
⇒ Third method (mismatch measure)
A
(f − g)2
⇒
i j∈A
[|f (i, j) − g(i, j)|]2
Also
A
(f − g)2
=
A
f 2
+
A
g2
− 2
A
fg
⇒ For a given template
A
f 2
remain fixed.
⇒ For a given image
A
g2
remain fixed.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 5 / 10

6. Continued–
⇒
A
fg → match measure/similarity measure.
Cauchy-Schwartz Inequality
fg ≤ f 2 × g2
Let g = cf
For digital image
i,j∈A
f (i, j)g(i, j) ≤
i,j∈A
f (i, j)2 ×
i,j∈A
g(i, j)2
Also
A
f (x, y)g(x + ∆x, y + ∆y)dxdy ≤
A
f (x, y)2dxdy ×
A
g(x + ∆x, y + ∆y)2dxdy
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 6 / 10

7. Example
⇒
∞
−∞
∞
−∞f (x, y)g(x + ∆x, y + ∆y)dxdy → Cross correlation
⇒ We apply the normalized cross correlation
i,j∈A
[g2
(x + ∆x, y + ∆y)]1/2
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 7 / 10

8. Example: Template and Image
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 8 / 10

9. Similarity measure
Similarity measure
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 9 / 10

10. References
M. Sonka, V. Hlavac, and R. Boyle, Image processing, analysis, and machine vision.
Cengage Learning, 2014.
D. A. Forsyth and J. Ponce, “A modern approach,” Computer vision: a modern
approach, vol. 17, pp. 21–48, 2003.
L. Shapiro and G. Stockman, “Computer vision prentice hall,” Inc., New Jersey,
2001.
R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital image processing using
MATLAB. Pearson Education India, 2004.
Subject: Image Procesing & Computer Vision Dr. Varun Kumar (IIIT Surat)Lecture 25 10 / 10