1. Image Registration
박성진

2. Surface-based Registration
The 3D boundary of an anatomical object is an intuitive and easily characterized geometrical feature that can be used for registration
Surface-based methods
Determine corresponding surfaces in different images
Find the transformation that best aligns these surfaces
Point-based registration
Aligns generally small number of corresponding points
Surface-based registration
Aligns larger number of points for which correspondence is unavailable

3. Surfaces Skin surface (air-skin interface)
Bone surface (tissue-bone interface)
Representations
Point set (collection of points on the surface)
Faceted surface, e.g., triangle set approximating surface
Implicit surface
Parametric surface, e.g., B-spline surface

4. Surface-based Registration
Disparity function
Given a set of surface points and a surface, find the rigid transformation that minimizes the mean squared distance between the points and the surface

5. Head and Hat Method

6. Iterative Closest Point Method
Initialization:
Iteratively apply the following steps, incrementing k after each loop, until convergence within a tolerance is achieved:
Compute the closest points
Compute the transformation between the initial point set and current set
Apply the transformation to produce registered points
Terminate the iterative loop when

7. Intensity-based registration
Registration based on similarity measures
Uses some measure derived from the intensity of the image directly
Assumes that there is a relationship between the image intensities of both images if the images are registered
Does not require any feature extraction, thus the registration error is not by any errors

8. Generic Intensity-based Registration Procedure
Initial transformation
Calculate cost function
For transformation T
Optimize T by maximizing
cost function C
Update transformation
Final transformation
Is new transformation
an improvement?

9. Intensity-based registration
Registration-based on geometric features is independent of the modalities from which the features have been derived
Registration-based on voxel similarity measures features we must make a distinction between monomodality registration and multimodality registration

10. Monomodality image registration
Sums of Squared Differences (SSD)
Assumes an identity relationship between image intensities in both images
Optimal measure if the difference between both images is Gaussian noise
Sensitive to outliers

11. Monomodality image registration
Robust statistics can be used to reduce the influence of outliers on the registration
Sum of Absolute Differences (SAD)
Assumes an identity relationship between image intensities
Less sensitive to outliers

12. Monomodality image registration
Correlation
Assumes a linear relationship between image intensities
Sensitive to large intensity values

13. Monomodality image registration
Normalized Cross Correlation (CC)
Assumes a linear relationship between image intensities

14. Monomodality image registration
Ratio of Image Uniformity (RIU)
Normalized standard deviation

15. Registration Basis : Image Intensity
Monomodality registration
Image intensities are related by simple function
Identity : SSD, SAD
Linear : CC, RIU
Multimodality registration
Image intensities are related by some unknown function or statistical relationship
Relationship between intensities is not known a priori
Relationship between intensities can be viewed by inspecting a 2D histogram or co-occurrence matrix

16. Multimodality image registration
Partitioned image uniformity (PIU)
Used for MR-PET registration
PIU : Measure the sum of the normalized standard deviation of voxel values in image B for each intensity a in image A

17. Images as Probability Distribution
Images can be viewed as probability distributions p(a)
Marginal probability p(a) of a pixel having intensity a
Joint probability p(a,b) of a pixel having intensity a in one image and intensity b in another image
Probability distribution of an image can be estimated using
Parzen windowing
Histograms
Histograms require “binning”
Usually use 32 to 256 bins per image

18. Images as Probability Distribution

19. Intensity-based on IT Entropy
Describes the amount of information in image A
The information content of an image is maximal if all intensities have equal probability
The information content of an image is minimal if one intensity a has a probability of one

20. Intensity-based on IT Joint Entropy
Describes the amount of information in the combined images A and B
If A and B are totally unrelated, the joint entropy will be the sum of the entropies of A and B
If A and B are related, the joint entropy will be similar
Registration can be achieved by minimizing the joint entropy between both images

21. Intensity-based on IT
Joint Entropy is highly sensitive to the overlap of the two images
Mutual information
Describes how well one image can be explained by another images
Expressed in terms of marginal and joint probability distributions

22. Intensity-based on IT
Mutual information is still sensitive to the overlap of the two images
Normalized mutual information can be shown to be independent of the amount of overlap between images
Registration can be achieved by maximizing (normalized) Mutual Information between both images

23. Registration using Similarity Measures
Some similarity measures assume a functional relationship between intensities
Identity : SSD, SAD
Linear : CC, RIU
Nonlinear : PIU, CR
Other similarity measures only assume a statistical relationship
Joint entropy
(Normalized) Mutual Information
All similarity measures can be calculated from a 2D histogram of the images