CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004
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Transcript of CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004
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CSci 6971: Image Registration Lecture 26: BSpline Transforms
April 20, 2004
Prof. Chuck Stewart, RPIDr. Luis Ibanez, Kitware
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Image Registration Lecture 26 2
Deformable Registration
Deformable Registration
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Image Registration Lecture 26 3
Deformable Transforms
BSplines
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Image Registration Lecture 26 4
Deformable Transformation
y
Fixed Image
Transform
x
y
Moving Imagex
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Image Registration Lecture 26 5
Deformable Transformation
y
Fixed Image
Transform
x
y
Moving Imagex
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Image Registration Lecture 26 6
Deformable Transformation
y
x
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Image Registration Lecture 26 7
Deformable Transformation
y
x
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Image Registration Lecture 26 8
Image Resampling
FixedImage
MovingImage
Transform
Interpolator
ResampleImageFilter
DeformedImage
BSplineTransform
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Image Registration Lecture 26 9
Deformable Transforms
BSplines in Geometrical Terms
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Image Registration Lecture 26 10
BSplines
-2 -1 1 20
Order Zero
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Image Registration Lecture 26 11
BSplines
-2 -1 1 20
Order Zero Piece-Wise
Y = 1
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Image Registration Lecture 26 12
BSplines
Convolution
-2 -1 1 20
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Image Registration Lecture 26 13
BSplines
Area under the product curve
-2 -1 1 20
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Image Registration Lecture 26 14
BSplines
-2 -1 1 20
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Image Registration Lecture 26 15
BSplines
Order One
-2 -1 1 20
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Image Registration Lecture 26 16
BSplines
Order One
-2 -1 1 20
Piece-Wise
Y = ( 1 - X )Y = ( X + 1 )
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Image Registration Lecture 26 17
BSplines
Convolution
-2 -1 1 20
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Image Registration Lecture 26 18
BSplines
Convolution
-2 -1 1 20
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Image Registration Lecture 26 19
BSplines
Order Two
-2 -1 1 20
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Image Registration Lecture 26 20
BSplines
Order Two
-2 -1 1 20
Piece-Wise
Y = ( X – 3/2 )2 / 2
Y = ( 1 – 2 X2 )
Y = ( X + 3/2 )2 / 2
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Image Registration Lecture 26 21
BSplines
Convolution
-2 -1 1 20
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Image Registration Lecture 26 22
BSplines
Convolution
-2 -1 1 20
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Image Registration Lecture 26 23
BSplines
Order Three
-2 -1 1 20
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Image Registration Lecture 26 24
BSplines
Order 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
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Image Registration Lecture 26 25
BSplines
Interpolatingwith
BSplines
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Image Registration Lecture 26 26
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
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Image Registration Lecture 26 27
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
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Image Registration Lecture 26 28
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
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Image Registration Lecture 26 29
BSplines Interpolation
-2 -1 1 20
Zero Order Nearest Neighbor
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Image Registration Lecture 26 30
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
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Image Registration Lecture 26 31
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
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Image Registration Lecture 26 32
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolation
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Image Registration Lecture 26 33
BSplines Interpolation
-2 -1 1 20
First Order Linear Interpolator
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Image Registration Lecture 26 34
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
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Image Registration Lecture 26 35
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
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Image Registration Lecture 26 36
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolation
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Image Registration Lecture 26 37
BSplines Interpolation
-2 -1 1 20
Second Order Quadratic Interpolator
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Image Registration Lecture 26 38
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
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Image Registration Lecture 26 39
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
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Image Registration Lecture 26 40
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolation
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Image Registration Lecture 26 41
BSplines Interpolation
-2 -1 1 20
Third Order Cubic Interpolator
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Image Registration Lecture 26 42
BSplines
Cubic BSplinesin
Two Dimensions
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Image Registration Lecture 26 43
BSplines in 2D
Tensor Product
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Image Registration Lecture 26 44
BSplines in 2D
Tensor Product
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Image Registration Lecture 26 45
BSplines in 2D
Tensor Product Separable
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Image Registration Lecture 26 46
BSplines in 2D
Support Nodes in Region of Influence
#Nodes = 4N
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Image Registration Lecture 26 47
BSplines in 2D
Interpolation
BSplineGrid
ResamplingGrid
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Image Registration Lecture 26 48
BSplines in 2D
Interpolation
BSplineGrid
ResamplingGrid
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Image Registration Lecture 26 49
Sampling Grid
y
x
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Image Registration Lecture 26 50
BSpline Grid
y
x
BSplineGrid
ResamplingGrid
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Image Registration Lecture 26 51
BSplines Grid & Image Grid
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Image Registration Lecture 26 52
BSplines Grid & Image Grid
BSplineGrid
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Image Registration Lecture 26 53
BSplines Grid & Image Grid
BSplineGrid
ValidRegion
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Image Registration Lecture 26 54
BSplines Grid & Image Grid
BSplineGrid
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Image Registration Lecture 26 55
BSplines Grid & Image Grid
BSplineGrid
ValidRegion
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Image Registration Lecture 26 56
BSplines Interpolation
InterpolatingVectors
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Image Registration Lecture 26 57
Interpolating Vectors
y
x
BSplineGrid
ResamplingGrid
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Image Registration Lecture 26 58
Interpolating Vectors
y
x
BSplineGrid
ResamplingGrid
XCompo-
nents
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Image Registration Lecture 26 59
Interpolating Vectors
y
x
BSplineGrid
ResamplingGrid
XCompo-
nents
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Image Registration Lecture 26 60
Interpolating Vectors
y
x
BSplineGrid
ResamplingGrid
YCompo-
nents
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Image Registration Lecture 26 61
Interpolating Vectors
y
x
BSplineGrid
ResamplingGrid
XCompo-
nents
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Image Registration Lecture 26 62
X Grid
Feeding the BSpline Transform
x
BSplineTransform
Dimension N
NGrid
YGrid
…..Z
Grid
Input Point
Output Point
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Image Registration Lecture 26 63
Array of Parameters
Feeding the BSpline Transform
x
BSplineTransform
Input Point
Output Point
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Image Registration Lecture 26 64
Array of Parameters
Feeding the BSpline Transform
x
BSplineTransform
Input Point
Output Point
x1 x2 x3 x4 x5... y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….…
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Image Registration Lecture 26 65
Feeding the BSpline Transform
x
BSplineTransform
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
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Image Registration Lecture 26 66
BSplines Interpolation
Image Resampling
BSpline Warping
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Image Registration Lecture 26 67
Image Resampling
FixedImage
MovingImage
Transform
Interpolator
ResampleImageFilter
DeformedImage
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Image Registration Lecture 26 68
BSplines Interpolation
Original Lena
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Image Registration Lecture 26 69
BSplines Interpolation
Deformed with BSpline Transform
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Image Registration Lecture 26 70
BSplines Interpolation
Original LenaDeformed Lena
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Image Registration Lecture 26 71
Deformable Registration
Image Registration
BSpline Transform
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Image Registration Lecture 26 72
Image Registration Framework
FixedImage
MovingImage
Metric
Transform
Interpolator Optimizer
Parameters Array
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Image Registration Lecture 26 73
BSplines Deformable Registration
Deformed with BSpline Transform
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Image Registration Lecture 26 74
BSplines Deformable Registration
Registered with BSpline Transform
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Image Registration Lecture 26 75
BSplines Deformable Registration
Original Lena
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Image Registration Lecture 26 76
BSplines Deformable Registration
Difference After Registration
Difference Before Registration
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Image Registration Lecture 26 77
End
Enjoy ITK !