Image Registration 박성진

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

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

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

Head and Hat Method

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

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

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?

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

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

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

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

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

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

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

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

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

Images as Probability Distribution

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

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

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

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

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