BMT-Exam 8D030
15-06-2005
1/5
Exam of 8D030:
Medical Image Analysis: Techniques and Applications
15-06-2005
In the exam there are 5 questions. Not all the questions have the same weight.
Q1=2 Q2=1 Q3=2 Q4=3 Q5=2
The questions refer to figures which are in the last pages of the exam.
Keep your answers concise and to the point. Use equations whenever you can to clarify your
answers, and make sure that all variables are described.
If an algorithm or method has to be described, give a step by step and structured solution.
Good luck !
BMT-Exam 8D030
15-06-2005
2/5
Q1. In neurosurgery, there is the need for guidance systems to help surgeons plan the exact
locations for incisions. In order to define the margins of tumors and to precisely identify
locations of neighboring critical structures such as vessels, 3D CT (i.e, Ict[ x ]) and MR (i.e.,
Imr[ x ]) data sets from the same subject are needed. This data is obtained at different
scanners. Therefore, the position, scaling, and rotation of the data sets are different. To
inspect them we need to register the data sets (see figure 1).
We designed a frame adapted to each patient which has a fixed position in relation to the
patient’s head. This frame contains 4 balls with the same radius R and the spatial relationship
as shown in figure 2.
The position of the balls in relation to the head varies from patient to patient. These balls
appear in the CT as well as in the MR data set. Each ball is made from different materials
which give different intensities to each ball in CT as well as in MR. The intensity values of
the balls vary between data sets and can coincide with tissue values. However, we can
assume that the order of the balls according to their intensity is the same for MR and CT. So,
we do not know the exact expected value for Intensity(bi) where i=1…4, but we know that
Intensity(bi)<Intensity(bi+1). Assume that there are no other objects in the brain that are
perfect spheres.
a. Describe a method to extract the balls from Ict[ x ] and Imr[ x ]? Explain which
assumptions are you using for the method you describe.
b. Given the 8 balls, how can you calculate the transformation from one coordinate
frame to the other?
c. How can you apply the transformation to Ict[ x ] and Imr[ x ] such that they get
registered?
Q2. Given the two classes of images and its segmentations shown in the figure 3.
a. Give two features that would allow you to distinguish between these classes. Describe
why these would be good features.
b. What is the computational complexity of calculating these features?
Q3. We want to automatically segment the white matter in 3D MRI data sets obtained with a T1
protocol, see figure 4. The histogram for different data sets is shown in figure 5.
Define a segmentation technique to segment the white matter as automatically as
possible. Explain what assumptions you are making and why you made this choice.
Explain what will be the advantages and disadvantages of using this technique.
BMT-Exam 8D030
15-06-2005
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Q4. We want to distinguish between two states of nature A and B. A appears 3 times more
frequently than B. We calculate two features from which we know are statistically
independent. We also know that each state of nature should have one unique characteristic
value for each class, but due to random noise the actual values differ.
We obtained the following values as training set:
A
B
x1
x2
x1
x2
2.92 2.86 3.15 6.28
4.17 1.85 2.44 4.46
6.09 3.37 1.77 6.08
4.48 2.29 2.57 5.96
4.45 2.31 0.44 7.74
a. Using this information design a classifier. Explain what assumptions are you making.
b. Based on this classifier what would be the state of nature of the feature vectors
(x1,x2)=(3.00, 4.15) and (x1,x2)=(5.97, 3.55)
c. How can we evaluate the performance of this classifier with the information that you
have? What would you be able to tell with the results of this evaluation?
Which assumptions did you need to make if any?
d. Assume that this problem is related to a computer aided diagnoses system and you
want to compare the classifier with the performance achieved nowadays in clinical
practice. What information would you need to gather? How could you make the
comparison?
e. If you are able to recognize that the performance is poor due to the lack of training
data and you know you cannot get more. How could you improve the performance?
Describe which technique would you use and why?
Q5. We want to distinguish between two states of nature A and B which are equally probable to
appear. We know that a good feature that distinguishes these classes is a discrete feature x,
which is known to have a Poisson distribution for both A and B. A Poisson distribution is
given by P( x |  )  e 
x
where  is a parameter.
x!
We know that the cost of the action associated to decide the right state of nature is C. The
costs of deciding A when actually the state of nature is B is 3C and the cost of taking the
decision of B when the state of nature is A is 4C.
a. Design a classifier based on this information.
b. How could you define the error rate or costs of this classifier, assuming that you have
infinite amount of training data?
BMT-Exam 8D030
15-06-2005
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FIGURES ___________________________________________________________________
Figure 1
Figure 2
Pears
Apples
Figure 3
Figure 4
BMT-Exam 8D030
15-06-2005
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Figure 5