Medical Image Analysis

1. Medical Image Analysis Image Registration Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

2. Image Registration • Atlas • Study the variability of anatomical and functional structures among the subjects • Structural computerized atlas (SCA): CT or conventional MRI. • A model for image segmentation and extraction of a structural volume of interest (VOI) Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

3. Image Registration • Functional computerized atlas (FCA): SPECT, PET, or fMRI. • Understanding the metabolism of functional activity in a specific structural VOI • Image registration methods and algorithms • Transformation of a source image space to the target image space Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

4. Anatomical Reference (SCA) (SCA) Functional Reference (FCA) Functional Reference (FCA) Reference Signatures Reference Signatures PET Image (New Subject) PET Image (New Subject) MR-PET Registration MR-PET Registration MR Image (New Subject) MR Image (New Subject) Analysis Analysis Figure 9.1. A schematic diagram of multi-modality MR-PET image analysis using computerized atlases. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

5. B A f g Figure 9.2. Image registration through transformation. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

6. Image Registration • External markers and stereotactic frames based landmark registration • External markers • Coordinate transformation (rotation, translation and scaling) and interpolation computed from visible markers • Optimizing the mean squared error • Stereotactic frames are usually uncomfortable for the patient Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

7. Image Registration • Rigid-body transformation based global registration • Principal axes transformation • PET-PET, MR-MR, MR-PET • Image feature-based registration • Boundary and surface matching based registration • Edges, boundary and surface information • A geometric transformation is obtained by minimizing a predefined error function between the surfaces

8. Image Registration • Image landmarks and features based registration • Utilize pre-defined anatomical landmarks or features • Bayesian model based probabilistic methods • Neuroanatomical atlases for elastic matching of brain images • Landmark-based elastic matching algorithm • Maximum likelihood estimation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

9. Rigid-Body Transformation • Rigid transformation • : rotation matrix • : translation vector • Translation along -axis by

10. Rigid-Body Transformation • Translation along -axis by • Translation along -axis by

11. Rigid-Body Transformation • Rotation about -axis by • Rotation about -axis by

12. Rigid-Body Transformation Rotation about -axis by

13. Rotation by f Translation of z Translation of y Translation of x Rotation by q Rotation by w Figure 9.3. The translation and rotation operations of a 3-D rigid transformation. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

14. Rigid-Body Transformation Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003. The rotation matrix for the rotational order:

15. Affine Transformation • Affine matrix including the translation, rotation and scaling transformation

16. Principal Axes Registration • Principal axes registration (PAR) • Global matching of two binary volumes • : a binary segmented volume • : centroid of

17. Principal Axes Registration

18. Principal Axes Registration The principal axes of are the eigenvectors of the inertia matrix:

19. Principal Axes Registration

20. Principal Axes Registration • Resolve 6 degrees of freedom • Three rotations and three translations • Equate the normalized eigenvector matrix to the rotation matrix

21. Principal Axes Registration

22. Principal Axes Registration • PAR for two volumes and • 1. Translate the centroid of to the origin • 2. Rotate the principal axes of to coincide with the , and axes • 3. Rotate the , and axes to coincide with the principal axes of • 4. Translate the origin to the centroid of • is scaled to match the volume using the scaling factor

23. Principal Axes Registration • Probabilistic models • Counting the occurrence of a particular binary subvolume that is extracted from the registered volumes corresponding to various images

24. Figure 9.4. A 3-D model of brain ventricles obtained from registering 22 MR brain images using the PAR method. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

25. Figure 9.5. Rotated views of the 3-D brain ventricle model shown in Figure 9.3. Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

26. Iterative Principal Axes Registration • Iterative principal axes registration (IPAR) • Developed by Dhawan et al. • Register MR and PET brain images • Used with partial volumes

27. Iteration 1 (a) Figure 9.6. Three successive iterations of the IPAR algorithms for registration of vol 1 and vol 2: The results of the first iteration (a), the second iteration (b) and the final iteration (c). Vol 1 represents the MR data while the PET image with limited filed of view (FOV) is represented by vol 2.

28. Iteration 2 (b) Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

29. Iteration 3 (c) Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

30. (a) Figures 9.7 a, b and c: Sequential slices of MR (middle rows) and PET (bottom rows) and the registered MR-PET brain images (top row) of the corresponding slices using the IPAR method.

31. (b) Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

32. (c) Figures come from the textbook: Medical Image Analysis, by Atam P. Dhawan, IEEE Press, 2003.

33. Image Landmarks and Features Based Registration • Image landmarks and features based registration • Rigid and non-rigid transformations • Image landmarks (points) and features

34. Similarity Transformation for Point-Based Registration • A non-rigid transformation • : ratation • : scaling • : translation • : the total number of landmarks

35. Similarity Transformation for Point-Based Registration • Algorithm • 1. • 2. Find

36. Similarity Transformation for Point-Based Registration • Singular value decomposition • 3. Compute the scaling factor • 4. Compute

37. Weighted Features Based Registration • , = 1, 2, 3,…, : a set of corresponding data shapes in and spaces

38. Elastic Deformation Based Registration • Elastic deformation • Mimic a manual registration • Map the elastic volume to the reference volume • The elastic volume is deformed by applying external forces such that it matches the reference model • Constraints • Smoothness • incompressibility

39. Elastic Deformation Based Registration • Motion of a deformable body in Lagrangian form • : the force acting on a particle • : the position • : time • : the mass • : the damping constant • : the internal energy of deformation

40. Elastic Deformation Based Registration • Find the displacement vector that maximizes the similarity measure • : metric tensor • : curvature tensor

41. Figure 9.8. Block diagram for the MR image registration procedure.

42. Figure 9.9. Results of the elastic deformation based registration of 3-D MR brain images: The left column shows three images of the reference volume, the middle column shows the respective images of the brain volume to be registered and the right column shows the respective images of the registered brain volume.