Issues in Image Registration and Image similarity based on mutual information
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The document discusses image registration, particularly focusing on issues related to multimodal acquisition and image super-resolution. It outlines the process and steps involved in image registration, highlights the significance of metrics such as entropy and mutual information in assessing image similarity, and discusses recent approaches in the field. Additionally, it notes the potential for using specific tools and standard image databases in future research.
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![Steps of Image Registration
B. Zitova, J. Flusser[1] introduced basic 4 steps
of image registration.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-5-320.jpg)
![Affine Transformation[1/4]
The affine transformation parameters can be
calculated by coordinates of control points, and then
geometrically transformation may be conducted for
registered image.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-8-320.jpg)
![Affine Transformation[2/4]
(a)
(b)
Fig. 3. (a) Transform of
an image (b) Rotate of
an image, (c) Scaling of
an image
(c)](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-9-320.jpg)
![Affine Transformation[3/4]
(a)
(b)
Fig. 4. (a) Transform of an
image (b) Rotate of an image,
(c) Scaling of an image
(c)](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-10-320.jpg)
![Affine Transformation[4/4]
Fig. 5. Affine Transformation of an image](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-11-320.jpg)
![Entropy[1/7]
A
key measure of information is known as
entropy[2], which is usually expressed by average
amount of information received when the value of
random value X is observed (the average number of
bits needed to store or communicate one symbol in a
message).
Shannon introduced an adopted measure in 1948,
which weights the information per outcome by the
probability of that outcome occurring. Given events
occurring with probabilities
the Shannon entropy is defined as,](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-12-320.jpg)
![Entropy[2/7]
The units for entropy are “nats” when the natural
logarithm is used and “bits" for base 2 logarithms.
When all messages are equally likely to occur, the
entropy is maximal, because you are completely
uncertain which message you will receive.
When one of the messages has a much higher chance of
being sent than the other messages, the uncertainty
decreases.
The amount of information for the individual messages
that have a small chance of occurring is high, but an
average, the information (entropy/ uncertainty ) is lower.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-13-320.jpg)
![Entropy[3/7]
14
Example:1.
Mummy-0.35, daddy-0.2, cat-0.2, cow-0.25
The entropy of child’s language-0.35 log(0.35)-0.2 log(0.2)-0.2 log(0.2)- 0.25
log(0.25)=1.96
Mummy- 0.05, daddy-0.05, cat- 0.02, train-0.02, car0.02, cookie-0.02, telly-0.02, no-0.8
The entropy of child’s language- 1.25
2.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-14-320.jpg)
![Entropy[4/7]
15
Base on the distribution of the grey values of the
image[4], a probability distribution of grey values can be
estimated by counting the number of times each grey
value occurs in the image and dividing those numbers by
the total number of occurrences.
A single intensity of image will have a low entropy; it
contains very little information.
A high entropy value will be yielded by an image with
more or less equal quantities of many different
intensities, which is an image containing a lot of
information.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-15-320.jpg)
![Entropy[5/7]](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-16-320.jpg)
![Entropy[6/7]](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-17-320.jpg)
![Entropy[7/7]
18
Entropy has three interpretations:
1.
The amount of information an event(message, grey value of a
point) gives when it takes place,
2.
The uncertainty about the outcome of an event, and
3.
The dispersion of the probabilities with which the events
take place.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-18-320.jpg)
![Mutual Information[1/3]
Mutual
Information
(transformation)[1]
measures the amount of information that can be
obtained about one random variable by observing
another.
It is important in communication where it can be
used to maximize the amount of information shared
between sent and received signals.
A basic property of the mutual information is that
I(X;Y) = H(X) - H(X|Y)
Mutual information is the amount by which the uncertainty
about Y decrease when X is given: the amount of information
X contains about Y.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-19-320.jpg)
![Mutual Information[2/3]
20
The second form of mutual information is most
closely related to joint entropy.
I(X:Y) = H(X) + H(Y) – H(X,Y)
-H(X,Y) means that maximizing mutual information
is related to minimizing joint entropy.
The advantage of mutual information over joint
entropy per se, is that it includes the entropies of the
separate images.](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-20-320.jpg)
![Mutual Information[3/3]
21
The final form of mutual information is based on Kullback-
Leibler distance[KLD][2]
Where SI (Specific mutual Information) is the point wise
mutual information.
The interpretation of this form is that it measures the distance
between the joint distribution of the images’ grey values p(x,
y) and the joint distribution in case of independence of the
images, p(x)p(y).
It is measure of dependence between two images.
If the testing images are well registered, then the value of KLD
becomes small or is equal to zero[17].](https://image.slidesharecdn.com/rwphd20313-140123035700-phpapp02/85/Issues-in-Image-Registration-and-Image-similarity-based-on-mutual-information-21-320.jpg)
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Issues in Image Registration and Image similarity based on mutual information
- 1. Issues in Image Registration – multimodal image acquisition & image super‐resolution. DARSHANA MISTRY SUPERVISOR:- DR. ASIM BANERJEE-DAIICT CO-SUPTERVISOR:- DR. SHISHIR SHAH, UNIVERSITY OF HOUSTON DPC:- DR ADITYA TATU-DAIICT DR TANISH ZAVERI- NIT, NU
- 2. Outline Introduction of Image Registration(IR) Issues of Image Registration Steps for Image Registration Review Comments on DPC-2 Affine Transformation Entropy Mutual Information
- 3. Introduction Image Registration:-It is a process of overlying of two or more images of the same scene taken at different times, different viewpoints and/or different sensors. Fig. 1. Image Registration
- 4. Issues of Image Registration Multimodal Registration Registration of images of the same scene acquired from different sensors. Viewpoint Registration Registration of images taken from different viewpoints. Temporal Registration Registration of images of same scene taken at different times or under different conditions
- 5. Steps of Image Registration B. Zitova, J. Flusser[1] introduced basic 4 steps of image registration.
- 6. Fig. 2. Four steps of Image Registration (Top row: feature detection, middle row: feature matching, model estimation, bottom right: image resampling and transformation
- 7. Previous Review Comments on DPC-2 (21-Dec. 12) Implement affine transformation and use mutual information and plots its variations. Identify standard image databases that will be used for future work. Identify recent registration approaches reported in literature for future exploration during the next review period.
- 8. Affine Transformation[1/4] The affine transformation parameters can be calculated by coordinates of control points, and then geometrically transformation may be conducted for registered image.
- 9. Affine Transformation[2/4] (a) (b) Fig. 3. (a) Transform of an image (b) Rotate of an image, (c) Scaling of an image (c)
- 10. Affine Transformation[3/4] (a) (b) Fig. 4. (a) Transform of an image (b) Rotate of an image, (c) Scaling of an image (c)
- 11. Affine Transformation[4/4] Fig. 5. Affine Transformation of an image
- 12. Entropy[1/7] A key measure of information is known as entropy[2], which is usually expressed by average amount of information received when the value of random value X is observed (the average number of bits needed to store or communicate one symbol in a message). Shannon introduced an adopted measure in 1948, which weights the information per outcome by the probability of that outcome occurring. Given events occurring with probabilities the Shannon entropy is defined as,
- 13. Entropy[2/7] The units for entropy are “nats” when the natural logarithm is used and “bits" for base 2 logarithms. When all messages are equally likely to occur, the entropy is maximal, because you are completely uncertain which message you will receive. When one of the messages has a much higher chance of being sent than the other messages, the uncertainty decreases. The amount of information for the individual messages that have a small chance of occurring is high, but an average, the information (entropy/ uncertainty ) is lower.
- 14. Entropy[3/7] 14 Example:1. Mummy-0.35, daddy-0.2, cat-0.2, cow-0.25 The entropy of child’s language-0.35 log(0.35)-0.2 log(0.2)-0.2 log(0.2)- 0.25 log(0.25)=1.96 Mummy- 0.05, daddy-0.05, cat- 0.02, train-0.02, car0.02, cookie-0.02, telly-0.02, no-0.8 The entropy of child’s language- 1.25 2.
- 15. Entropy[4/7] 15 Base on the distribution of the grey values of the image[4], a probability distribution of grey values can be estimated by counting the number of times each grey value occurs in the image and dividing those numbers by the total number of occurrences. A single intensity of image will have a low entropy; it contains very little information. A high entropy value will be yielded by an image with more or less equal quantities of many different intensities, which is an image containing a lot of information.
- 16. Entropy[5/7]
- 17. Entropy[6/7]
- 18. Entropy[7/7] 18 Entropy has three interpretations: 1. The amount of information an event(message, grey value of a point) gives when it takes place, 2. The uncertainty about the outcome of an event, and 3. The dispersion of the probabilities with which the events take place.
- 19. Mutual Information[1/3] Mutual Information (transformation)[1] measures the amount of information that can be obtained about one random variable by observing another. It is important in communication where it can be used to maximize the amount of information shared between sent and received signals. A basic property of the mutual information is that I(X;Y) = H(X) - H(X|Y) Mutual information is the amount by which the uncertainty about Y decrease when X is given: the amount of information X contains about Y.
- 20. Mutual Information[2/3] 20 The second form of mutual information is most closely related to joint entropy. I(X:Y) = H(X) + H(Y) – H(X,Y) -H(X,Y) means that maximizing mutual information is related to minimizing joint entropy. The advantage of mutual information over joint entropy per se, is that it includes the entropies of the separate images.
- 21. Mutual Information[3/3] 21 The final form of mutual information is based on Kullback- Leibler distance[KLD][2] Where SI (Specific mutual Information) is the point wise mutual information. The interpretation of this form is that it measures the distance between the joint distribution of the images’ grey values p(x, y) and the joint distribution in case of independence of the images, p(x)p(y). It is measure of dependence between two images. If the testing images are well registered, then the value of KLD becomes small or is equal to zero[17].
- 28. Tools: OpenCV(open source computer vision)2.3/2.4.2 Microsoft Visual Studio 2008/2010 express cMake(cross platform make) 2.8
- 29. Data Set 512 X 512 CT and MRI images a b c d e f
- 30. Conclusion Image similarity is find based on entropy and mutual information. The entropy of an image is a measure of the amount of uncertainty with gray values. Mutual information measures the amount of information, one image that can be obtained about one random variable by observing another. Entropy value is high image similarity is less. Mutual information is maximum then image similarity is high.
- 31. References 1. 2. 3. 4. 5. 6. 7. B.Zitova,J.Flusser,“ Image Registration methods :A survey”, Image and vision computing, vol.21-no.-11,pp977-1000,2003. J. P.W.Pluim, J.B. A. Maintz, and M. A. Viergever, “Mutual Information based registration of medical images: a survey”, IEEE Transactions on Medical Images, Vol.-XX, Issues-Y, 2003. R. M. Gray, “Entropy and Information Theory”, Springr-Verlag, New York, 2009. F. P. M. Oliveira, J. M. R. S. Tavares , “ Medical Image Registration: a Review ”, Computer Methods in Biomechanics and Biomedical Engineering, 2012. A. Sotiras , C. Davatazikos, N. Paragios, “Deformable Medical Image Registration: A Survey”, Research Report n° 7919 September 2012. M.V.Sruthi1, K.Soundararajan, V.Usha Sree , “ Accurate Multimodality Registration of medical images”, Accurate Multimodality Registration of medical images , Volume 1, Issue 3 , PP.33-36 , June 2012 . Q. Xie, S. Kurtek, G. Christensen, Z. Ding, E. Klassen,A. Srivastava, “A Novel Framework for Metric-Based Image Registration”, WBIR2012
- 32. 8. 9. 10. 11. 12. 13. 14. M.V.Wyavahare, P.M.Patil, H.K.Abhyankar,“Image Registration Techniques: An overview”, International Journal of Signal Processing, Image Processing, and PatternReorganization,Vol.2,No.3,2009. J.B.A.Maintz, A.Viegever, “A Survey of Medical Image Registration”, Medical Image Analysis”,Vol.2,No.1,pp(1-37),1998. G.Junbin,G.Xiaosong,W.Wei;P.Pengcheng, “Geometric Global Registration of Parallax Images Based on Wavelet Transform”, International Conference of Electronic Measurement and Instruments, pp 2862-2865,2007. Gang Hong; Yun Zhang, “Combination of feature based and area based image registration technique for high resolution remote sensing image”, International Conference on Geo science and Remote Sensing Symposium, pp 377-380, 2007 Malviya A.; Bhirud,S.G., “Wavelet based image registration using mutual information”, International Conferenceon Emerging Trendsin Electronic and Photonic Devices and Systems (ELECTRO‟09),245-244,2009. HongG.,ZhangY;“Wavelet based image registration technique for high resolution remote sensing image”, Journal of Compute Science and Geosciences 2006. Hui Lin; Peijun Du; Weichang Zhao; Lianpeng Zhang; Huasheng Sun, “Image Registration based on corner detection and affine transformation”, International conference on Image and Signal Processing (CISP), pp2184-2188,2010.
- 33. Y. Yamamura,;H. Kim;J. Tan; S. Yamamura,; Yamamoto, “A method for reducing of computational time on image registration employing wavelet transformation”, International conference on Control Automation and Systems (ICCAS), pp 1286-1291,2007. 16. Y. Pei; H. Wu; J. Yu; G. Cai, “Effective Image Registration based on Improved Harris Corner Detection”, International Conference on Information Networking an Automation (ICINA), V193-V196,2010. 17. R. Gan, J. Wu, A. C.S. Chung, S.C.H. Yu,W.M. Wells, Multiresolution Image Registration Based on Kullback-Leibler Distance”, 7th International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI’04, 2004. 15.