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Image Registration with Image Registration with Hierarchical B-SplinesHierarchical B-Splines
Z. Xie and G. Farin
SupportSupport
Arizona Alzheimer Disease Research Center
MotivationMotivation
Image FusionImage ComparisonImage SegmentationPattern Recognition
ClassificationClassification
Landmark based methods– Point based method– Curve based method– Surface based method
Intensity based methods
Free Form Deformation (FFD)Free Form Deformation (FFD)
FFD with Hierarchical B-SplinesFFD with Hierarchical B-Splines
r
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j
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kkjikji zNyNxNbzyxf
0 0 0
333,, )()()(),,(
1. Putting the object into the B-Spline hyperpatchs.
2. Moving the B-Spline control points to deform the object.
3. Refining the control points related to complex regions.
4. Adjusting the refined control points for detail deformation.
Point based registrationPoint based registration
This problem naturally breaks down into two scattered data approximation problems. The least squares solution of this problem can be found by solving the linear systems.
,...,n.,iq) f(p RRf:CA
niR,q), p,q(pn
ii
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1with function n :Output
.,...,1, points of pairs :Input220
2
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How does it work?How does it work?•Local refinement by knot insertion.
•Recomputing related control points.
Why hierarchical B-Splines?Why hierarchical B-Splines?
EfficiencyGlobal to local influence
Example of point based registrationExample of point based registration
Source Target Deformed Source
Surface based registrationSurface based registration
Together with the Iterative Closest Point (ICP) approach, this problem can be converted into a scattered data approximation problem.
minimized. is and between
distance thesuch that rmation A transfo :Output
. surface target theofset point the
and surface source theofset point The :Input
ts
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Iterative Closest PointIterative Closest Point
Distance TransformDistance Transform
Hierarchical Deformation with Hierarchical Deformation with
Hierarchical B-SplinesHierarchical B-Splines
Initialize: Rigid Transformation Linear matching: Iterative Affine Deformation Nonlinear matching: Hierarchical Cubic B-Splines
– Increase level of detail iteratively
AdvantageAdvantage
Validity. Right matching between individual points by matching big shape feature first, then refine the detail gradually.
Efficiency. Only pay attention to complex regions. Precision. Enough of degrees of freedom for
matching detail.
Example of 2-D registrationExample of 2-D registration
Example of 3D matchingExample of 3D matching
Movie of 3D DeformationMovie of 3D Deformation
Intensity-based registrationIntensity-based registration
Together with optic flow, this problem can be converted into scattered data approximation problem.
(f(p)).I(p) I
RRf
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(p)I
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such that
:mation transforspatialA :Output
intensity. tolocation from
mapping are and Both image
target theand image source The :Input
33
Optic flowOptic flow
Optic flow is a visual displacement flow field associated with the variation in an image sequence. It can be used as an estimator of the displacement of one pixel on the source image to its matching pixel on target image.
Hierarchical Deformation vs. Hierarchical Deformation vs. multi-resolution data representationmulti-resolution data representation
Example of intensity based registrationExample of intensity based registration
Source Target Deformed source
Movie of intensity based registrationMovie of intensity based registration
Future WorkFuture Work
Multi-resolution surface representationMore robust displacement estimator for
intensity based registration.Multi-modal intensity based registration
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