MIA_Registration

When we need non-rigid registration in neuroimaging?

Motion: Compensation for tissue deformation à Brain deformation during neurosurgery / Fusion of functional and anatomical information (MR/PET, etc.) Atlas based studies: Segmentation via atlas propagation Longitudinal or cross-sectional studies: Quantification of change over time (brain growth/ atrophy) Quantification of differences between populations (voxel based -, deformation-based morphometry

What are the two different types of non-rigid transformation? (Name the types and some examples to each type)

Parametric transformation: (#DOF << # Voxels) Affine transformation Polynomial transformation (linear, quadratic, cubic) Spline-based transformation Non-parametric transformations: (#DOF = # Voxels) Optical flow type registration (e.g., demons) Elastic registration Fluid or geodesic registration

What are splines in the mathematic context?

Splines are a tool used to approximate or interpolate function from scattered data 1D: Curves 2D: Surfaces 3D: Volumes

What are the advantages and disadvantages of Thin-plate splines?

Advantages: Control points can have arbitrary (willkürlich, beliebig) spatial distribution Disadvantages: Control points have global influence since the radial basis function have infinite support

What is the basic idea of interpolating spinec?

Basic idea: identify a set of points ϕi in image A identify the corresponding set of points ϕi’ in image B find a spline transformation which interpolates the displacement field at the points and produces a smoothly varying displacement field between the points points are either: anatomical or geometrical landmarks/ pseudo landmarks or control points

How can thin plate splines defined?

Thin-plate splines can be defined as a linear combination of radial basis functions θ:

Name another spline transformation, which is used in computer graphics for modelling 3D deformable objects:

-       Free-Form Deformation (FFD) are a common technique in Computer Graphics for modelling 3D deformable objects (B-splines)

What is the main idea of Free-Form Deformation (FFD)?

FFDs deform an underlying object by manipulating a mesh of control points control point can be displaced from their original location control points provide a parameterization of the transformation

How can we express FFD based on B-splines?

FFDs based on B-splines can be expressed as a 3D tensor product of 1D B-splines:

What is non-rigid image registration used for?

Motion: To compensate for tissue deformation such as lung movement when breathing. Longitudinal or cross-sectional studies: - For quantification of change over time, such as brain growth. For quantification of differences btw populations. Atlas based studies: For segmentation via atlas propagation.

What are the types of non-rigid transformation?

Parametric transformation: affine transformation polynomial transformations (cubic, bi- and linear) spline-based transformations Non-parametric transformations: optical flo type registration, elastic registration, fluid or geodesic registration

What are splines in a mathematical meaning?

Tools, used to approximate or interpolate functions from scatteres data. (1D: cruves, 2D: surfaces, 3D: volumes)

What stands FFD for?

Free-Form Deformation

What forces is elastic deformation governed by?

internal forces, caused by deformation of the elastic body. internal = 0 if body is in equilibrium external forces, acts on the elastic body and causes the body to deform away from the equilibrium

What are the three main motivations for registration?

-       Necessity: Minimization of difference measure can only be ill-posed. Modeling: Regularization can be used to include prior knowledge, for example about underlying tissue properties. Practical Reasons: Without regularization there are a high number of local minima in the energy function (bad for optimization).