non-rigid registration
DESCRIPTION
Non-Rigid Registration. Why Non-Rigid Registration. In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject: tissue deformation Inter-subject: anatomical variability across individuals Fast-Moving area: Non-rigid. - PowerPoint PPT PresentationTRANSCRIPT
Non-Rigid Registration
Why Non-Rigid Registration
In many applications a rigid transformation is sufficient. (Brain)
Other applications:
Intra-subject: tissue deformation
Inter-subject: anatomical variability across individuals
Fast-Moving area: Non-rigid
Registration Framework
In terms of L.Brown.(1992)– Feature Space– Transformation– Similarity Measure– Search Strategy (Optimization)
Rigid vs. Non-rigid in the framework
Feature Space
Geometric landmarks:
Points
Edges
Contours
Surfaces, etc.Intensities:
Raw pixel values23 35
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Transformation
Transformation
Rigid transformation:
3DOF (2D)
6 DOF (3D)Affine transformation:
12 DOF
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Transformation
Additional DOF.Second order polynomial-30 DOF
Higher order:
third-60, fourth-105,fifth-168Model only global shape changes
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Transformation
For each pixel (voxel), one 2d(3d) vector to describe local deformation.
Parameters of non-rigid >> that of rigid
Similarity Measure
Point based
---The distance between features, such as points,curves,or surfaces of corresponding anatomical structure.
--- Feature extraction.Voxel based
---Absolute Difference, Sum of squared differences, Cross correlation, or Mutual information
Search Strategy
Registration can be formulated as an optimization problem whose goal is to minimize an associated energy or cost function.
General form of cost function: C = -Csimilarity+Cdeformation
Search Strategy
Powell’s direction set methodDownhill simplex methodDynamic programmingRelaxation matching
Combined withMulti-resolution techniques
Registration Scheme
Non-rigid Registration
Feature-based– Control Points: TPS– Curve/Edge/Contour– Surface
Intensity-based– Elastic model– Viscous fluid model– Others
Thin-plate splines (TPS)
Come from Physics: TPS has the property of minimizing the bending energy.
TPS (cont.)
Splines based on radial basis functions
Surface interpolation of scattered data
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Description of the Approach
1. Select the control points in the images.
2. Calculate the coefficients for the TPS.
3. Apply the TPS transformation on the whole image.
Synthetic Images
T1 T2
TPS-Results(1)
TPS-Results(2)
Rigid and non-rigid registration
Rigid Registration as pre-processing (global alignment)
Non-rigid registration for local alignment
Next time
Affine-mapping technique