Date post: | 27-Mar-2015 |
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ITK Deformable Registration
B-SplinesFree-Form
Deformable Registration
Deformable Registration
Deformable Transforms
BSplines
Deformable Transformation
y
Fixed Image
Transform
x
y
Moving Image
x
Deformable Transformation
y
Fixed Image
Transform
x
y
Moving Image
x
Deformable Transformationy
x
Deformable Transformationy
x
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
Y = 1
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
with
BSplines
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolator
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolator
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolator
BSplines
Cubic BSplines
in
Two Dimensions
BSplines in 2DTensor Product
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
x
BSpline Gridy
x
BSplineGrid
ResamplingGrid
BSplines Grid & Image Grid
BSplines Grid & Image Grid
BSplineGrid
BSplines Grid & Image Grid
BSplineGrid
ValidRegion
BSplines Grid & Image Grid
BSplineGrid
BSplines Grid & Image Grid
BSplineGrid
ValidRegion
BSplines Interpolation
Interpolating
Vectors
Interpolating Vectorsy
x
BSplineGrid
ResamplingGrid
Interpolating Vectorsy
x
BSplineGrid
ResamplingGrid
XCompo-nents
Interpolating Vectorsy
x
BSplineGrid
ResamplingGrid
XCompo-nents
Interpolating Vectorsy
x
BSplineGrid
ResamplingGrid
YCompo-nents
Interpolating Vectorsy
x
BSplineGrid
ResamplingGrid
XCompo-nents
X
Grid
Feeding the BSpline Transform
x
BSpline
Transform
Dimension N
N
Grid
Y
Grid…..
Z
Grid
Input Point
Output Point
Array of Parameters
Feeding the BSpline Transform
x
BSpline
Transform
Input Point
Output Point
Array of Parameters
Feeding the BSpline Transform
x
BSpline
Transform
Input Point
Output Point
x1 x2 x3 x4 x5... y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….…
Feeding the BSpline Transform
x
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
BSplines Interpolation
Image Resampling
BSpline Warping
Image Resampling
FixedImage
MovingImage
Transform
Interpolator
ResampleImageFilter
DeformedImage
BSplines Interpolation
Original Lena
BSplines Interpolation
Deformed with BSpline Transform
BSplines Interpolation
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
BSplines Deformable Registration
Registered with BSpline Transform
BSplines Deformable Registration
Original Lena
BSplines Deformable Registration
Difference After Registration
Difference Before Registration
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