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 s

urface 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

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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

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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 transformationCalculate cost functionFor transformation T

Optimize T by maximizing cost function C

Is new transformation an improvement?

Update transformation

Final transformation

Intensity-based registration Registration-based on geometric features is independ

ent 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 fun

ction or statistical relationship Relationship between intensities is not known a pri

ori 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 st

andard 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 ima

ge 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