Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is...
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Transcript of Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is...
![Page 1: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/1.jpg)
Non-Rigid Registration
![Page 2: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/2.jpg)
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
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Registration Framework
In terms of L.Brown.(1992)– Feature Space– Transformation– Similarity Measure– Search Strategy (Optimization)
Rigid vs. Non-rigid in the framework
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Feature Space
Geometric landmarks:
Points
Edges
Contours
Surfaces, etc.Intensities:
Raw pixel values23 35
24 56
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Transformation
![Page 6: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/6.jpg)
Transformation
Rigid transformation:
3DOF (2D)
6 DOF (3D)Affine transformation:
12 DOF
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![Page 7: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/7.jpg)
Transformation
Additional DOF.Second order polynomial-30 DOF
Higher order:
third-60, fourth-105,fifth-168Model only global shape changes
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![Page 8: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/8.jpg)
Transformation
For each pixel (voxel), one 2d(3d) vector to describe local deformation.
Parameters of non-rigid >> that of rigid
![Page 9: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/9.jpg)
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
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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
![Page 11: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/11.jpg)
Search Strategy
Powell’s direction set methodDownhill simplex methodDynamic programmingRelaxation matching
Combined withMulti-resolution techniques
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Registration Scheme
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Non-rigid Registration
Feature-based– Control Points: TPS– Curve/Edge/Contour– Surface
Intensity-based– Elastic model– Viscous fluid model– Others
![Page 14: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/14.jpg)
Thin-plate splines (TPS)
Come from Physics: TPS has the property of minimizing the bending energy.
![Page 15: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/15.jpg)
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.
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Synthetic Images
T1 T2
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TPS-Results(1)
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TPS-Results(2)
![Page 20: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/20.jpg)
Rigid and non-rigid registration
Rigid Registration as pre-processing (global alignment)
Non-rigid registration for local alignment
![Page 21: Non-Rigid Registration. Why Non-Rigid Registration In many applications a rigid transformation is sufficient. (Brain) Other applications: Intra-subject:](https://reader030.fdocuments.us/reader030/viewer/2022032800/56649d405503460f94a199a6/html5/thumbnails/21.jpg)
Next time
Affine-mapping technique