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Image Registration I

Comp 254Spring 2002Guido Gerig

Motivation for Image Registration

• Combine images from different modalities (multi-modality registration), e.g. CT&MRI, MRI&PET, MRI&fMRI, post-mortem&MRI, structural and functional images.

• Definition of a standard coordinate system (stereotaxic coordinates for neurosurgery, comparative analysis of corresponding regions in in neurosciences).

• Construction of atlases and normative databases.• Atlas matching for segmentation and interpretation.• Arithmetic and/or statistical operations on images

(averaging, statistical parametric mapping, deformations).• Register serial scans in temporal studies (development,

follow-up, tracking).

Image Registration: Motivation

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MRA / PET FDGMRA / PET H2O

Motivation: Anatomo-functional correlation

Image Registration: Motivation

Courtesy of D. Vandermeulen, KUL

Motivation: Merge of PET and MRI

Three-dimensional data visualization of MRI and PET datasets for two patients: pre-symptomatic SCA1 (upper row) and sporadic OPCA (lower row). http://www.pet.med.va.gov:8080/demos.html

Copyright 1997PET CenterMinneapolis Veterans Affairs Medical Center

Image Registration: Motivation

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Motivation: Construction of Atlases, Normative Databases

Image Registration: Motivation

SPM Software Package (K. Friston): canonical MRI images (probability maps) obtained by averaging 152 registered individual MRI.

Brain Bench: Virtual tools forstereotactic frame surgery

Image Registration: Motivation

http://www.krdl.org.sg/RND/biomed/publications/dextroscope/papers/MIA/BrainBench-1.html

Luis Serra, Wieslaw L. Nowinski, Tim Poston, et al.

3D Talairach-Tournoux atlas (left) andSchaltenbrand-Wahren atlas (right).

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1 2 3

4 5 6

MS, MR T2, time points 1-6

Intra-patient registration over time for studying MS lesion evolution

Image Registration: Temporal Studies

Courtesy of D. Vandermeulen, KUL

Time 1

Time 2

Time series images: MS lesion development

(European BIOMORPH Project)

Image Registration: Temporal Studies

Courtesy of D. Vandermeulen, KUL

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Challenges for Registration

• Multi-modal image data carrying different information (morphological and functional).

• Combination of images with different resolution and non-isotropic voxel dimensions, sometimes distortions.

• Different “photometric” properties of multiple images (intensity differences for tissue, bone, fluid, lesion).

• Intra-patient registration (often rigid), inter-patient registration (normative databases, rigid and elastic), and atlas to patient registration (rigid with prob.atlas, elastic).

• From rigid towards elastic registration (dealing with natural and pathological variability).

Image Registration: Challenges

Combining information from multiple images requires the geometric relationship between them to be known...

T ?

Concept of Registration

T = affine transformation(3D rotation, translation, scale, skew)

Image Registration: Concept

Courtesy of D. Vandermeulen, KUL

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T !aligned

Concept of Registration ctd.Image Registration: Concept

misaligned

Courtesy of D. Vandermeulen, KUL

Registration Strategies

Points:anatomical orgeometrical features

– interactive– correspondence

Surfaces:objects

– segmentation– correspondence

Voxels:difference imageintensity correlationhistogram dispersion

– unimodal– linear relationship– mutual information

External markers: – non retrospective

Image Registration: Strategies

Courtesy of D. Vandermeulen, KUL

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Types of 3D TransformationsImage Registration: Transformation Types

Examples of transformations to a regular mesh (top left): rigid (top right) for position orientation differences, affine (bottom left) for scaling differences andspline (elastic) (bottom right) for local and complex differences (illustration Ph.Thirion, INRIA)

3D Affine Transformation (non-elastic)

Image Registration: Affine Transformation

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Short Excurse: Homogeneous Coordinates: A general view

• Acknowledgement: Greg Welch, Gary Bishop, Siggraph 2001 Course Notes (Tracking).

Series of Transformations

2D Object: Translate, scale, rotate, translate again

E Problem: Rotation, scaling, shear are multiplicative transforms, but translation is additive.

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Solution: Homogeneous Coordinates

• In 2D: add a third coordinate, w

• Point [x,y]T expanded to [x,y,w]T

• Scaling: force w to 1 by [x,y,w]T/w → [x/w,y/w,1]T

• Any two sets of points [x1,y1,w1]T and [x2,y2,w2]T

represent the same point if one is multiple of the other.

2D homogeneous coordinate space

• Every 2D point [x,y]T in 3D space represents point along a line that passes through [x,y,w]T, where we want [x1,y1,1]T.

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Resulting Transformations

new:

before:

3D Space: 4-element vector

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Affine Transformation

Image Registration: Affine Transformation

General case: 12 parameters define 3D affine transformation(translation (3), rotation (3), scaling (3), shear (3)).

Affine Transformation ctd.Affine Transformations can be decomposed:

3D Translation

3D Rotation about z axis,similarly about y and x

Combined 3D Transformation (here only rigid body: Translation and Rotation ⇒ 6 parameters)

Image Registration: Affine Transformation

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Procedure:• user selects pairs of corresponding landmarks in two 3D

images (minimum number of landmarks appropriate to degree of freedom)

• choose type of transformation (rigid body, RTS, affine)• calculation of transformation parameters by least squares

fit (normal equation system)• transform images using interpolation (nearest neighbor, tri-

linear, cubic)

Affine Transformation ctd.Image Registration: Affine Transformation