1. DTU Informatics Introduction to Medical Image Analysis Rasmus R. Paulsen DTU Informatics rrp@imm.dtu.dk http://www.imm.dtu.dk/courses/02511 TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: A A AA A A A A A A A A AA

2. DTU Informatics 1/4/2009Introduction to Medical Imaging 2 DTU Informatics, Technical University of Denmark Lecture 9 – Pixel Classification 9.00Lecture Exercises 12.00 – 13.00Lunch break 13.00Lecture ? Exercises

3. DTU Informatics 1/4/2009Introduction to Medical Imaging 3 DTU Informatics, Technical University of Denmark What can you do after today? Describe the concept of pixel classification Use Matlab to select pixel training data Compute the pixel value ranges in a minimum distance classifier Implement and use a minimum distance classifier Describe how a pixel value histogram can be approximated using a Gaussian distribution Describe how the pixel value ranges can be selected in a parametric classifier Implement and use a parametric classifier Explain the concept of Bayesian classification

4. DTU Informatics 1/4/2009Introduction to Medical Imaging 4 DTU Informatics, Technical University of Denmark Classification Take a measurement and put it into a class ? Wheels: 2 HP: 50 Weight: 200 Bike Truck Car Motorbike Train Bus MeasurementClasses Classifier

5. DTU Informatics 1/4/2009Introduction to Medical Imaging 5 DTU Informatics, Technical University of Denmark General Classification Multi-dimensional measurement Pre-defined classes –Can also be found automatically – can be very difficult!

6. DTU Informatics 1/4/2009Introduction to Medical Imaging 6 DTU Informatics, Technical University of Denmark Pixel Classification Classify each pixel –Independent of neighbours Also called labelling –Put a label on each pixel We look at the pixel value and assign them a label Labels already defined CT scan of human head Background Soft-Tissue Trabecular Bone Hard Bone Quiz: Two class classification with background and object?

7. DTU Informatics 1/4/2009Introduction to Medical Imaging 7 DTU Informatics, Technical University of Denmark Pixel Classification – formal definition Pixel value (the measurement) k classes Classification rule

8. DTU Informatics 1/4/2009Introduction to Medical Imaging 8 DTU Informatics, Technical University of Denmark Pixel Classification – example Pixel value Set of 4 classes Classification rule How do we construct a classification rule?

9. DTU Informatics 1/4/2009Introduction to Medical Imaging 9 DTU Informatics, Technical University of Denmark Pixel classification rule background soft-tissue trabeculae bone How do we do this?

10. DTU Informatics 1/4/2009Introduction to Medical Imaging 10 DTU Informatics, Technical University of Denmark Pixel classification rule – manual inspection background soft-tissue trabeculae bone Looking at some few pixels

11. DTU Informatics 1/4/2009Introduction to Medical Imaging 11 DTU Informatics, Technical University of Denmark Pixel classification rule – manual inspection background soft-tissue trabeculae bone Looking at some few pixels New pixel – where do we put it?

12. DTU Informatics 1/4/2009Introduction to Medical Imaging 12 DTU Informatics, Technical University of Denmark Pixel classification rule – manual inspection background soft-tissue trabeculae bone Looking at some few pixels New pixel – where do we put it? Measure the “distance” to the other classes Select the closest class Minimum distance classification

13. DTU Informatics 1/4/2009Introduction to Medical Imaging 13 DTU Informatics, Technical University of Denmark Pixel classification rule Minimum Distance Classification background soft-tissue trabeculae bone The possible pixel values are divided into ranges Here the distance to “background” is equal to “soft-tissue” Background range soft-tissue range Trabecular range Bone range

14. DTU Informatics 1/4/2009Introduction to Medical Imaging 14 DTU Informatics, Technical University of Denmark Pixel classification rule Minimum Distance Classification background soft-tissue trabeculae bone Background range soft-tissue range Trabecular range Bone range

15. DTU Informatics 1/4/2009Introduction to Medical Imaging 15 DTU Informatics, Technical University of Denmark Pixel classification rule For all pixel in the image do

16. DTU Informatics 1/4/2009Introduction to Medical Imaging 16 DTU Informatics, Technical University of Denmark Pixel Classification example Background Soft-Tissue Trabecular Bone Hard Bone CT scan of human head

17. DTU Informatics 1/4/2009Introduction to Medical Imaging 17 DTU Informatics, Technical University of Denmark Better range selection Guessing range values is not a good idea Better to use “training data” Start by selecting representative regions from an image Annotation –To mark points, regions, lines or other significant structures

18. DTU Informatics 1/4/2009Introduction to Medical Imaging 18 DTU Informatics, Technical University of Denmark Classifier training - annotation An “expert” is asked how many different tissue types that are possible Then the expert is asked to mark representative regions of the selected tissue types Background Soft-Tissue Trabecular Bone Hard Bone

19. DTU Informatics 1/4/2009Introduction to Medical Imaging 19 DTU Informatics, Technical University of Denmark Classifier training – region selection Many tools exist Matlab tool roipoly –Select closed regions using a piecewise polygon Training is only done once! Optimally, the training can be used on many pictures that contains the same tissue types

20. DTU Informatics 1/4/2009Introduction to Medical Imaging 20 DTU Informatics, Technical University of Denmark Initial analysis - histograms Gaussian

21. DTU Informatics 1/4/2009Introduction to Medical Imaging 21 DTU Informatics, Technical University of Denmark Initial analysis - histograms Class separation

22. DTU Informatics 1/4/2009Introduction to Medical Imaging 22 DTU Informatics, Technical University of Denmark Simple pixel statistics Calculate the average (mean) and the standard deviation of each class Average Standard deviation

23. DTU Informatics 1/4/2009Introduction to Medical Imaging 23 DTU Informatics, Technical University of Denmark

24. DTU Informatics 1/4/2009Introduction to Medical Imaging 24 DTU Informatics, Technical University of Denmark Minimum distance classification Any objections? The pixel value ranges are not always in good correspondence with the histograms?

25. DTU Informatics 1/4/2009Introduction to Medical Imaging 25 DTU Informatics, Technical University of Denmark Exam question 09.15

26. DTU Informatics 1/4/2009Introduction to Medical Imaging 26 DTU Informatics, Technical University of Denmark Parametric classification Describe the histogram using a few parameters Gaussian/Normal distribution –Average –Standard deviation Trabecular bone Only two values needed

27. DTU Informatics 1/4/2009Introduction to Medical Imaging 27 DTU Informatics, Technical University of Denmark Parametric classification Trabecular bone Training pixel values Estimated average Estimated standard deviation

28. DTU Informatics 1/4/2009Introduction to Medical Imaging 28 DTU Informatics, Technical University of Denmark Parametric classification Fit a Gaussian to the training pixels for all classes What do we see here? What is the difference between the two classes? Trabeculae has much higher variation in the pixel values

29. DTU Informatics 1/4/2009Introduction to Medical Imaging 29 DTU Informatics, Technical University of Denmark Parametric classification New pixel with value 78 –Is it soft-tissue or trabecular bone? Minimum distance classifier? –Soft-tissue Is that fair? –Soft-tissue Gaussian says “Extremely low probability that this pixel is soft-tissue”

30. DTU Informatics 1/4/2009Introduction to Medical Imaging 30 DTU Informatics, Technical University of Denmark Parametric classification – repeat the question New pixel with value 78 –Is it soft-tissue or trabecular bone? –Most probably trabecular bone Where should we set the limit? –Where the two Gaussians cross!

31. DTU Informatics 1/4/2009Introduction to Medical Imaging 31 DTU Informatics, Technical University of Denmark Parametric classification – ranges The pixel value ranges depends on –The average –The standard deviation Compared to the minimum distance classifier –Only the average Soft-tissue Trabecular bone

32. DTU Informatics 1/4/2009Introduction to Medical Imaging 32 DTU Informatics, Technical University of Denmark Parametric classification – how to Select training pixels for each class Fit Gaussians to each class Use Gaussians to determine pixel value ranges Little bit difficult with the Gaussians

33. DTU Informatics 1/4/2009Introduction to Medical Imaging 33 DTU Informatics, Technical University of Denmark Parametric classifier - ranges We want to compute where they cross Create a lookup table: Run through all 256 possible pixel values Check which Gaussian is the highest Store the [value, class] in the table

34. DTU Informatics 1/4/2009Introduction to Medical Imaging 34 DTU Informatics, Technical University of Denmark Alternatively – analytic solution The two Gaussians Intercept at Piece of cake!

35. DTU Informatics 1/4/2009Introduction to Medical Imaging 35 DTU Informatics, Technical University of Denmark Exam Question 09.2 and 09.19

36. DTU Informatics 1/4/2009Introduction to Medical Imaging 36 DTU Informatics, Technical University of Denmark Exercises ?

37. DTU Informatics 1/4/2009Introduction to Medical Imaging 37 DTU Informatics, Technical University of Denmark Bayesian Classification Area = 1 Pure parametric classifier assumes equal amount of different tissue types

38. DTU Informatics 1/4/2009Introduction to Medical Imaging 38 DTU Informatics, Technical University of Denmark Bayesian Classification Area = 1 Much more soft- tissue than trabecular bone How do we handle that?

39. DTU Informatics 1/4/2009Introduction to Medical Imaging 39 DTU Informatics, Technical University of Denmark Bayesian Classification An expert tells us that a CT scan of a head contains –20% Trabecular bone –50% Soft-tissue Picking a random pixel in the image –20% Chance that it is trabecular bone –50% Chance that it is soft- tissue How do use that?

40. DTU Informatics 1/4/2009Introduction to Medical Imaging 40 DTU Informatics, Technical University of Denmark Bayesian Classification – histogram scaling Parametric classifier Bayesian classifier Scaled with 0.50 Scaled with 0.20 Little change in class border (sometimes significant changes)

41. DTU Informatics 1/4/2009Introduction to Medical Imaging 41 DTU Informatics, Technical University of Denmark Formal definition Given a pixel value What is the probability that the pixel belongs to class Example: If the pixel value is 78, what is the probability that the pixel is bone

42. DTU Informatics 1/4/2009Introduction to Medical Imaging 42 DTU Informatics, Technical University of Denmark Formal definition Constant – ignored from now on

43. DTU Informatics 1/4/2009Introduction to Medical Imaging 43 DTU Informatics, Technical University of Denmark Formal definition The a priori probability (what is known from before) Example: From general biology it is known that 20% of a brain CT scan is trabecular bone. Therefore P(trabecular) = 0.20

44. DTU Informatics 1/4/2009Introduction to Medical Imaging 44 DTU Informatics, Technical University of Denmark Formal definition The class conditional probability Given a class, what is the probability of a pixel with value v Example: If we consider class = soft-tissue. What is the probability that the pixel value is 78? Very low

45. DTU Informatics 1/4/2009Introduction to Medical Imaging 45 DTU Informatics, Technical University of Denmark Formal definition – sum up

46. DTU Informatics 1/4/2009Introduction to Medical Imaging 46 DTU Informatics, Technical University of Denmark Parametric classification – how to Select training pixels for each class Fit Gaussians to each class Ask an expert for the prior probabilities (how much there normally is in total of each type) For each pixel in the image –Compute for each class (the a posterior probability) –Select the class with the highest

47. DTU Informatics 1/4/2009Introduction to Medical Imaging 47 DTU Informatics, Technical University of Denmark When to use Bayesian classification The parametric classifier is good when there are approximately the same amount of all type of tissues Use Bayesian classification if there are very little or very much of some types

48. DTU Informatics 1/4/2009Introduction to Medical Imaging 48 DTU Informatics, Technical University of Denmark Exercises ?