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Registration: Spatial Image Definitions

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Outline

  • Image Resampling
  • Registration Overview
  • Registration Framework

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Image Resampling

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Image Origin and Spacing

Origin (Ox,Oy)

Spacing (Sy)

Spacing (Sx)

x

y

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Image Sampling Grid

Origin (Ox,Oy)

Spacing (Sy)

Spacing (Sx)

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Image Pixel

Spacing (Sy)

Pixel Value

Pixel Region

Origin (Ox,Oy)

Spacing (Sx)

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Image Indices

Spacing (Sy)

Spacing (Sx)

Origin (Ox,Oy)

[0,0]

[1,0]

[2,0]

[3,0]

[4,0]

[5,0]

[0,1]

[0,2]

[0,3]

[0,4]

[0,5]

[4,7]

[0,6]

[0,7]

Pixel Index

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Index to Physical Coordinates

Spacing (Sy)

Spacing (Sx)

Origin (Ox,Oy)

[0,0]

[1,0]

[2,0]

[3,0]

[4,0]

[5,0]

[0,1]

[0,2]

[0,3]

[0,4]

[0,5]

[4,7]

[0,6]

[0,7]

Pixel Index

P[0] = Index[0] x Spacing[0] + Origin[0]

P[1] = Index[1] x Spacing[1] + Origin[1]

Index[0] = floor( ( P[0] - Origin[0] ) / Spacing[0] + 0.5 )

Index[1] = floor( ( P[1] - Origin[1] ) / Spacing[1] + 0.5 )

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Image Region

Spacing (Sy)

Pixel Value

Pixel Region

Origin (Ox,Oy)

Spacing (Sx)

Image Region

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Image Region

Spacing (Sy)

Pixel Value

Pixel Region

Origin (Ox,Oy)

Spacing (Sx)

Image Region

Starting Index

Region Size

[2,3]

[3,5]

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Axes directions

Origin (Ox,Oy)

[0,0]

[1,0]

[2,0]

[3,0]

[4,0]

[5,0]

[0,1]

[0,2]

[0,3]

[0,4]

[0,5]

[4,7]

[0,6]

[0,7]

Pixel Index

x (1,0,0)

y (0,1,0)

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Axes directions

Origin (Ox,Oy)

[0,0]

[1,0]

[2,0]

[3,0]

[4,0]

[5,0]

[0,1]

[0,2]

[0,3]

[0,4]

[0,5]

[4,7]

[0,6]

[0,7]

Pixel Index

x (0.866,0.5,0)

y (-0.5, 0.866,0)

30° rotation

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Axes directions

Origin (Ox,Oy)

[0,0]

[1,0]

[2,0]

[3,0]

[4,0]

[5,0]

[0,1]

[0,2]

[0,3]

[0,4]

[0,5]

[4,7]

[0,6]

[0,7]

Pixel Index

x (-1,0,0)

y (0,1,0)

x axis flip

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Basic Resampling

  • Resampling Trivial Cases

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Image Pixel

Spacing (Sy)

Origin (Ox,Oy)

Spacing (Sx)

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Sub-Sampling by Half

Spacing (Sy)

Origin (Ox,Oy)

Spacing (Sx)

Image Region

Spacing

( 2 x Sy )

Spacing ( 2 x Sx )

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Sub-Sampling by Half

New Origin

(O’x,O’y)

New Spacing

S’y

New Spacing

S’x

Origin (Ox,Oy)

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Image Pixel

Spacing (Sy)

Origin (Ox,Oy)

Spacing (Sx)

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Super-Sampling by Double

Spacing (Sy)

Origin (Ox,Oy)

Spacing (Sx)

Image Region

Spacing ( Sy/2 )

Spacing ( Sx/2 )

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Super-Sampling by Double

Origin (Ox,Oy)

New Spacing

S’x

New Spacing

S’y

New Origin

(O’x,O’y)

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Resampling in ITK

  • itk.ResampleImageFilter
    • Object oriented interface
  • itk.resample_image_filter
    • Functional-style interface

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Resampling in ITK

Transform

Interpolator

Origin

Spacing

Region Start

Region Size

Resample Filter

Input Image

Output Image

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Coordinate System Conversions

Image Grid

j

i

y

x

Physical Coordinates

Image Grid

j

i

Space Transform

y’

x’

Physical Coordinates

x

y

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Things I will not do…

I will not register images in pixel space

I will not register images in pixel space

I will not register images in pixel space

I will not register images in pixel space

I will not register images in pixel space

I will not register images in pix

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Fixed Image & Moving Image

y

x

Physical Coordinates

Space Transform

y’

x’

Physical Coordinates

x

y

y

x

Physical Coordinates

Image Grid

j

i

Image Grid

j

i

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Selecting Moving & Fixed Images

  • In principle, the denomination of Fixed Image & �Moving Image is arbitrary

​

  • In practice, the moving image is the one that will be resampled �into the fixed image coordinate system
  • Yet, the spatial transform maps from the fixed image to the moving image. This avoid "holes" in the image when resampling.�

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Registration Frameworks in ITK

Registration Optimization Framework

PDE Deformable Registration (Demons)

FEM Registration

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Registration Optimization Framework

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Parameteric Spatial Transforms

  • Translation
  • Scaling
  • Rotation
  • Rigid3D
  • Rigid2D
  • Affine
  • BSplines
  • Splines:
    • Thin plate spline
    • Elastic body spline
  • Dense displacement vector field
  • Time-varying velocity field

​

​

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Enjoy ITK !