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

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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.

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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.

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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.

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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