Lec16: Medical Image Registration (Advanced): Deformable Registration
Image Registration
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Image Registration
박성진
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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
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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
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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
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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
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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
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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
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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
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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
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Monomodality image registration Correlation
Assumes a linear relationship between image intensities
Sensitive to large intensity values
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Monomodality image registration Normalized Cross Correlation (CC)
Assumes a linear relationship between image intensities
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Monomodality image registration Ratio of Image Uniformity (RIU)
Normalized standard deviation
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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
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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
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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
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Images as Probability Distribution
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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
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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
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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
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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
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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