This is my 2nd Doctorate progresses committee presentation in image registration which is explained how do you find image similarity based on Entropy and 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
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4.
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