ITK Deformable Registration B-Splines Free-Form. Deformable Registration

ITK Deformable Registration

B-SplinesFree-Form

Deformable Registration

Deformable Transforms

BSplines

Deformable Transformation

Fixed Image

Transform

Moving Image

Deformable Transformation

Fixed Image

Transform

Moving Image

Deformable Transformationy

Image Resampling

FixedImage

MovingImage

Transform

Interpolator

ResampleImageFilter

DeformedImage

BSplineTransform

Deformable Transforms

BSplines in

Geometrical Terms

BSplines

-2 -1 1 20

Order Zero

BSplines

-2 -1 1 20

Order Zero Piece-Wise

BSplinesConvolution

-2 -1 1 20

BSplinesArea under the

product curve

-2 -1 1 20

BSplines

-2 -1 1 20

BSplinesOrder One

-2 -1 1 20

BSplinesOrder One

-2 -1 1 20

Piece-Wise

Y = ( 1 - X )Y = ( X + 1 )

BSplinesConvolution

-2 -1 1 20

BSplinesConvolution

-2 -1 1 20

BSplinesOrder Two

-2 -1 1 20

BSplinesOrder Two

-2 -1 1 20

Piece-Wise

Y = ( X – 3/2 )2 / 2

Y = ( 1 – 2 X2 )

Y = ( X + 3/2 )2 / 2

BSplinesConvolution

-2 -1 1 20

BSplinesConvolution

-2 -1 1 20

BSplinesOrder Three

-2 -1 1 20

BSplinesOrder Three

-2 -1 1 20

Piece-Wise

Y = ( 3X3 - 6X2 + 4 )/6

Y = (2-X)3 / 6Y = (2+X)3 / 6

Y = ( - 3X3 - 6X2 + 4 )/6

BSplines

Interpolating

BSplines

BSplines Interpolation

-2 -1 1 20

Zero Order Nearest Neighbor

-2 -1 1 20

First Order Linear Interpolation

-2 -1 1 20

First Order Linear Interpolator

-2 -1 1 20

Second Order Quadratic Interpolation

-2 -1 1 20

Second Order Quadratic Interpolator

-2 -1 1 20

Third Order Cubic Interpolation

-2 -1 1 20

Third Order Cubic Interpolator

BSplines

Cubic BSplines

Two Dimensions

BSplines in 2DTensor Product

BSplines in 2DTensor Product Separable

BSplines in 2DSupport Nodes in Region

of Influence

#Nodes = 4N

BSplines in 2DInterpolation

BSplineGrid

ResamplingGrid

BSplines in 2DInterpolation

BSplineGrid

ResamplingGrid

Sampling Gridy

BSpline Gridy

BSplineGrid

ResamplingGrid

BSplines Grid & Image Grid

BSplineGrid

ValidRegion

BSplineGrid

ValidRegion

Interpolating

Vectors

Interpolating Vectorsy

BSplineGrid

ResamplingGrid

BSplineGrid

ResamplingGrid

XCompo-nents

BSplineGrid

ResamplingGrid

XCompo-nents

BSplineGrid

ResamplingGrid

YCompo-nents

BSplineGrid

ResamplingGrid

XCompo-nents

Feeding the BSpline Transform

BSpline

Transform

Dimension N

Grid…..

Input Point

Output Point

Array of Parameters

BSpline

Transform

Input Point

Output Point

Array of Parameters

BSpline

Transform

Input Point

Output Point

x1 x2 x3 x4 x5... y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….…

BSpline

Transform

Input Point

Output Point

x1 x2 x3 x4 x5... y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….…

x1y1z1 x2y2z2 x3y3z3 x4y4z4 …. xNyNzN Input File

Parameters Array

Image Resampling

BSpline Warping

Image Resampling

FixedImage

MovingImage

Transform

Interpolator

ResampleImageFilter

DeformedImage

Original Lena

Deformed with BSpline Transform

Original LenaDeformed Lena

Deformable Registration

Image Registration

BSpline Transform

Image Registration Framework

FixedImage

MovingImage

Metric

Transform

Interpolator Optimizer

Parameters Array

BSplines Deformable Registration

Deformed with BSpline Transform

Registered with BSpline Transform

Original Lena

Difference After Registration

Difference Before Registration

Enjoy ITK !

ITK Deformable Registration B-Splines Free-Form. Deformable Registration

Documents

Deformable Registration with Spatially Varying Degrees of Freedom

Deformable Registration

Deformable Registration of 3D Vessel Structures to a Single ...campar.in.tum.de/pub/zikic2008deformable/zikic2008...Deformable Registration of 3D Vessel Structures to a Single Projection

Recurrent Registration Neural Networks for Deformable Image Registration · 2020-02-13 · deformable image registration can be very large and the training of deep reinforcement learning

Lecture 9 Registration with ITK

Automatic Rigid and Deformable Medical Image Registration€¦ · Automatic Rigid and Deformable Medical Image Registration by Hongliang Yu A Dissertation Submitted to the Faculty

Deformable Image Registration Methods and Clinical Endpoints · 2008. 8. 6. · Deformable Image Registration Methods and Clinical Endpoints Marc L Kessler, PhD 1 Deformable Image

Stereoscopic Video Overlay with Deformable Registration

Applications of deformable image registration: automatic ...digitool.library.mcgill.ca/thesisfile106480.pdf · Applications of deformable image registration: automatic segmentation

Geometric Registration for Deformable Shapesresources.mpi-inf.mpg.de/deformableShapeMatching... · Eurographics 2010 Course – Geometric Registration for Deformable Shapes “Thin

Deformable Image Registration, Contour Propagation and ...amos3.aapm.org/abstracts/pdf/77-22594-311436-91622.pdf · Deformable Image Registration, Contour Propagation and Dose Mapping:

ITK Deformable Registration Demons Methods. Deformable Registration

Overview: ITK Registration Methods - pudn.comread.pudn.com/.../309973/RegistrationMethodsOverview.pdfSPIE2004: Medical Image Segmentation and Registration With ITK, February 14, 2004

INVERSE CONSISTENT DEFORMABLE IMAGE REGISTRATION · 2014-08-02 · Inverse consistent deformable image registration has been an active subject of study in the literature. There has

ITK The Insight Segmentation & Registration Toolkit

NOVEL APPLICATIONS OF 2D AND 3D DEFORMABLE REGISTRATION IN IMAGE

Deformable Registration of Pre-Operative MR, Pre-Resection

CLARET: A Fast Deformable Registration Method Applied to ...midag.cs.unc.edu/pubs/papers/chou_miccai_pulm2011.pdfCLARET: A Fast Deformable Registration Method Applied to Lung Radiation

Regularization in Deformable Registration

Deformable Image Registration in Radiation Oncologyamos3.aapm.org/abstracts/pdf/99-28329-359478-112905... · 2015-07-21 · Sarah Geneser, Yale University 4 Deformable Image Registration