Introduction to Medical Imaging Regis Introduction to Medical Imaging Registration Alexandre Kassel Course

Topics Rigid Registration Non-rigid Registration Multi-modal Registration

Registration : definitions Image registration is the process of transforming different sets of data into one coordinate system (Wikipedia) Image registration is the process of overlaying two or more images of the same scene taken at different times, from different viewpoints, and/or by different sensors. It geometrically aligns two images—the reference and sensed images. (Barbara Zitova, Image registration methods: a survey)

A mathematical definition

Registration Herve Lombaert,

Registrations types (Subject) Intra-subject Registration Inter-subject Registration Subject/Atlas Registration

Intra-subject Registration

Inter-subject Registration X-Ray CT Patient 1 Patient 2

Subject/Atlas Registration

Registrations types (data set) Image based Segmentation based Landmarks based Feature Image based

Image based Registration

Feature Image based (e.g: edges) MRIX-Ray CT Registration Edges :

Segmentation based

Landmark based

Registrations types (spatial transformation) Rigid - Translation and Rotation - Affine Non-rigid - Elastic - Fluid

Rotation and Translation Preserves lengths and angles y x 1 y x 2

Registration (Translation) We can find translation using Cross-correlation

Phase Correlation The process is faster using FFT. The cross-power spectrum of two signal is the Inverse Fourier Transform of the cross-correlation

Phase Correlation Resilient to noise Resilient to occlusion Very limited transformation Extendable to rotation with a 3D correlation function and a 3D Power Spectrum (Castro & Morandi)

Affine Transformation x y x Includes: Translation Rotation Scale Shear

Affine Transformation y x 1 y x 2

A Linear Transformation : y x 1 y x 2

Affine Transformation Computing the parameters with Landmark Points, using Least Squares y x 1 y x 2

Affine Transformation Least Squares Reformulating :

Affine Transformation Least Squares Solving by pseudo inverse : The more Landmark points we have, the more accurate and resilient to errors the registration is.

Affine Transformation RANSAC 1)Choose Randomly a group of matched points 2)Compute the spatial transformation (using LS) with those points 3)For every pair of points, compute the error in respect to the transformation 4)Select “in-liners”, pairs with low error in respect to the transformation. 5)Repeat 2-4 with a the new transformation based on those in-liners, until the cluster is large enough 6)Keep the transformation based on the largest cluster

Affine Transformation RANSAC Slower than LS More effective in case of wrongly matched points, by throwing out outliners.

Non rigid Registration Needed for matching two different object (Inter-subject registration, Atlas Registration, Distortion correction) Allows more flexibility than rigid transform Non-linear

Elastic Transformation We define and compute a displacement filed

Elastic Transformation Regularisation The model alone is too much flexible and the problem is ill posed We need regularisation Regularisation Similarity measure

Elastic Transformation Regularisation Simplest exemple We minimize by Gradient Descent We can use different regularizer and different features images Smoothness Accuracy

Fluid Registration We compute a velocity field We regularize and minimize by gradient descent

Multi-modal Registration MRI to CT registration CT, MR, Registered MR, Droske, Marc, and Martin Rumpf. "A variational approach to nonrigid morphological image registration." SIAM Journal on Applied Mathematics 64.2 (2004):

CT-PET Li et al : Multiscale registration of medical images based on edge preserving scale space with application in image-guided radiation therapy

CT-PET medicine

Change detection By superimposing two images we can easily detect changes fMRI is based on change of blood flow

Augmented reality in surgery

Stereotactic surgery

Easy Registration from image to world coordinates, based on the needle No complex optimization needed Useful for breast and brain surgery (biopsy, ablation, stimulation,etc …. Modern devices can also automatically find organs or tumors based on Atlas.