Medical Image Analysis: Techniques and Applications

BMT-Exam 8D030 1/5 17-06-2005 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=5 Q2=2 Q3=1 Q4=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 2/5 17-06-2005

Q1. We want to distinguish between malign and benign tumors in mammography. Assume that malign as well as benign tumors appear equally often. Tumor images can be found in figure 1 and its segmentations is shown in the figure 2. The names of benign tumors start with b and malign with m. The malign tumors have been marked with a square. The order of the images is not the same in figure 1 than in figure 2, but they are the same tumors. Notice that the original images have been normalized to a standard size in the figure1 and 2.

a. Define a segmentation technique to segment the tumors of figure 1 to obtain the contours in figure 2 as automatically as possible. Explain what assumptions you are making and why you made this choice. Explain what will be the pros and contras of using this technique. b. Give three features that would allow you to distinguish between these classes. Describe why these can be good features. c. What is the computational complexity of calculating these features? d. Given these features design a classifier. Assume that the cost of misclassifying a malign tumor is 3 times the cost to misclassify a benign. Explain what other assumptions you are making. e. How can we evaluate the performance of this classifier with the information and data 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? f. We want to compare our computer aided diagnoses system with the performance achieved nowadays in clinical practice by radiologists. What information would you need to gather to be able to do the comparison? How could you make the comparison to decide whether the system performs better than the radiologists? g. Imagine that you find out looking at the feature space that each class seems to cluster in more than one location in the feature space. Would that have influence in your choice of the classifier? If you would choose another classifier which one? Which assumptions are you making? Describe how you would implement it? What are the disadvantages of this method? BMT-Exam 8D030 3/5 17-06-2005

Q2. Assume that we are able to produce vertebra prostheses. The prostheses are adapted to each patient, and based in a CT scan of the patient vertebra, figure 3. We have a model of our ideal vertebra based on the segmentation of this CT scan. Once the prosthesis has been generated (figure 4), we also make a CT scan and segment the vertebra in the scan. The shape of the prosthesis usually has some imperfections. We want to use this scan to control the quality of the prosthesis, meaning its similarity to the model. Assume that we checked the volume with relation to the original and it is the same, V. However the same volume can still give different shapes. We consider that the prostheses are correct if the difference in shape, amount of volume that is placed wrongly or is missing in the prosthesis, does not exceed a 10% of the total volume. Describe a method to calculate the shape difference using the segmented data set of the vertebra (i.e., segmented data set of the prosthesis and segmented data set of the patient vertebra).

Q3. We want to distinguish between two states of nature A and B. A appears 2 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 also know that the distribution of the noise for each feature is the same for both classes. We obtained the following values as training set: A B x1 x2 x1 x2 1.92 1.44 2.55 6.43 4.70 2.65 2.19 9.51 3.41 -0.57 0.48 6.44 4.50 0.13 0.91 5.56 3.32 1.66 2.12 4.49

a. Using this information design a classifier. Explain what assumptions you are making. b. Based on this classifier what would be the state of nature of the feature vectors (x1,x2)=(1.97, 2.18) and (x1,x2)=(3.13, 4.61)

Q4. We want to distinguish between two states of nature A and B. Class A appears 3 times more often than class B. 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 l x distribution is given by P( x |l ) = e-l where l is a parameter. We also know a priory x!

that the probability density of the parameter l for class A, pA (l ) , is a normal distribution

with mean mA and standard deviation s A , N(mA , s A ) . For class B, pB(l )= N ( m B , s B ) a. Design a classifier based on this information. Assume you have as many training data as you need b. What will be the error of this classifier, assuming that you have an infinite amount of data to train it? BMT-Exam 8D030 4/5 17-06-2005 FIGURES______

Figure 1 BMT-Exam 8D030 5/5 17-06-2005

Figure 2 BMT-Exam 8D030 6/5 17-06-2005

Figure 3 Figure 4