Image Registration I

Transcription

1 Image Registration I Comp 254 Spring 2002 Guido Gerig Image Registration: Motivation 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). 1

2 Image Registration: Motivation Motivation: Anatomo-functional correlation MRA / PET H2O MRA / PET FDG Courtesy of D. Vandermeulen, KUL Image Registration: Motivation Motivation: Merge of PET and MRI Copyright 1997 PET Center Minneapolis Veterans Affairs Medical Center Three-dimensional data visualization of MRI and PET datasets for two patients: pre-symptomatic SCA1 (upper row) and sporadic OPCA (lower row). 2

3 Image Registration: Motivation Motivation: Construction of Atlases, Normative Databases SPM Software Package (K. Friston): canonical MRI images (probability maps) obtained by averaging 152 registered individual MRI. Image Registration: Motivation Brain Bench: Virtual tools for stereotactic frame surgery Luis Serra, Wieslaw L. Nowinski, Tim Poston, et al. 3D Talairach-Tournoux atlas (left) and Schaltenbrand-Wahren atlas (right). 3

4 Image Registration: Temporal Studies Intra-patient registration over time for studying MS lesion evolution MS, MR T2, time points Courtesy of D. Vandermeulen, KUL Image Registration: Temporal Studies Time 1 Time series images: MS lesion development (European BIOMORPH Project) Time 2 Courtesy of D. Vandermeulen, KUL 4

5 Image Registration: Challenges Challenges for Registration Multi-modal image data carrying different information (morphological and functional). Combination of images with different resolution and nonisotropic 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). T? Image Registration: Concept Concept of Registration Combining information from multiple images requires the geometric relationship between them to be known... T = affine transformation (3D rotation, translation, scale, skew) Courtesy of D. Vandermeulen, KUL 5

6 Image Registration: Concept Concept of Registration ctd. misaligned aligned T! Courtesy of D. Vandermeulen, KUL Image Registration: Strategies Registration Strategies External markers: Points: anatomical or geometrical features Surfaces: objects Voxels: difference image intensity correlation histogram dispersion non retrospective interactive correspondence segmentation correspondence unimodal linear relationship mutual information Courtesy of D. Vandermeulen, KUL 6

7 Image Registration: Transformation Types Types of 3D Transformations Examples of transformations to a regular mesh (top left): rigid (top right) for position orientation differences, affine (bottom left) for scaling differences and spline (elastic) (bottom right) for local and complex differences (illustration Ph.Thirion, INRIA) Image Registration: Affine Transformation 3D Affine Transformation (non-elastic) 7

8 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 Problem: Rotation, scaling, shear are multiplicative transforms, but translation is additive. 8

9 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 [x 1,y 1,w 1 ] T and [x 2,y 2,w 2 ] 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 [x 1,y 1,1] T. 9

10 Resulting Transformations new: before: 3D Space: 4-element vector 10

11 Image Registration: Affine Transformation Affine Transformation General case: 12 parameters define 3D affine transformation (translation (3), rotation (3), scaling (3), shear (3)). Image Registration: Affine Transformation 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) 11

12 Image Registration: Affine Transformation Affine Transformation ctd. 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, trilinear, cubic) 12