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ITK Deformable Registration

Published byKayla Harrison Modified over 10 years ago

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Presentation on theme: "ITK Deformable Registration"— Presentation transcript:

1 ITK Deformable Registration
B-Splines Free-Form

2 Deformable Registration

3 Deformable Transforms
BSplines

4 Deformable Transformation
y y Transform x x Fixed Image Moving Image

5 Deformable Transformation
y y Transform x x Fixed Image Moving Image

6 Deformable Transformation
y x

7 Deformable Transformation
y x

8 Image Resampling Interpolator Fixed Image Resample Image Moving Image
Filter Moving Image BSpline Transform Deformed Image Transform

9 Deformable Transforms
BSplines in Geometrical Terms

10 BSplines Order Zero -2 -1 1 2

11 BSplines Order Zero Piece-Wise Y = 1 -2 -1 1 2

12 BSplines Convolution -2 -1 1 2

13 BSplines Area under the product curve -2 -1 1 2

14 BSplines -2 -1 1 2

15 BSplines Order One -2 -1 1 2

16 BSplines Order One Piece-Wise Y = ( X + 1 ) Y = ( 1 - X ) -2 -1 1 2

17 BSplines Convolution -2 -1 1 2

18 BSplines Convolution -2 -1 1 2

19 BSplines Order Two -2 -1 1 2

20 BSplines Order Two Piece-Wise Y = ( 1 – 2 X2 ) Y = ( X + 3/2 )2 / 2
-2 -1 1 2

21 BSplines Convolution -2 -1 1 2

22 BSplines Convolution -2 -1 1 2

23 BSplines Order Three -2 -1 1 2

24 BSplines Order Three Piece-Wise Y = ( - 3X3 - 6X2 + 4 )/6
-2 -1 1 2

25 Interpolating with BSplines

26 BSplines Interpolation
Zero Order Nearest Neighbor -2 -1 1 2

27 BSplines Interpolation
Zero Order Nearest Neighbor -2 -1 1 2

28 BSplines Interpolation
Zero Order Nearest Neighbor -2 -1 1 2

29 BSplines Interpolation
Zero Order Nearest Neighbor -2 -1 1 2

30 BSplines Interpolation
First Order Linear Interpolation -2 -1 1 2

31 BSplines Interpolation
First Order Linear Interpolation -2 -1 1 2

32 BSplines Interpolation
First Order Linear Interpolation -2 -1 1 2

33 BSplines Interpolation
First Order Linear Interpolator -2 -1 1 2

34 BSplines Interpolation
Second Order Quadratic Interpolation -2 -1 1 2

35 BSplines Interpolation
Second Order Quadratic Interpolation -2 -1 1 2

36 BSplines Interpolation
Second Order Quadratic Interpolation -2 -1 1 2

37 BSplines Interpolation
Second Order Quadratic Interpolator -2 -1 1 2

38 BSplines Interpolation
Third Order Cubic Interpolation -2 -1 1 2

39 BSplines Interpolation
Third Order Cubic Interpolation -2 -1 1 2

40 BSplines Interpolation
Third Order Cubic Interpolation -2 -1 1 2

41 BSplines Interpolation
Third Order Cubic Interpolator -2 -1 1 2

42 Cubic BSplines in Two Dimensions

43 BSplines in 2D Tensor Product

44 BSplines in 2D Tensor Product

45 BSplines in 2D Tensor Product Separable

46 Nodes in Region of Influence
BSplines in 2D Support Nodes in Region of Influence #Nodes = 4N

47 BSplines in 2D Interpolation BSpline Grid Resampling Grid

48 BSplines in 2D Interpolation BSpline Grid Resampling Grid

49 Sampling Grid y x

50 BSpline Grid y BSpline Grid Resampling Grid x

51 BSplines Grid & Image Grid

52 BSplines Grid & Image Grid

53 BSplines Grid & Image Grid
Valid Region

54 BSplines Grid & Image Grid

55 BSplines Grid & Image Grid
Valid Region

56 BSplines Interpolation
Interpolating Vectors

57 Interpolating Vectors
y BSpline Grid Resampling Grid x

58 Interpolating Vectors
y BSpline Grid X Compo- nents Resampling Grid x

59 Interpolating Vectors
y BSpline Grid X Compo- nents Resampling Grid x

60 Interpolating Vectors
y BSpline Grid Y Compo- nents Resampling Grid x

61 Interpolating Vectors
y BSpline Grid X Compo- nents Resampling Grid x

62 Feeding the BSpline Transform
Z Grid Y Grid N Grid X Grid ….. Dimension N BSpline Transform Input Point Output Point x

63 Feeding the BSpline Transform
Array of Parameters BSpline Transform Input Point Output Point x

64 Feeding the BSpline Transform
x1 x2 x3 x4 x y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….… Array of Parameters BSpline Transform Input Point Output Point x

65 Feeding the BSpline Transform
x1y1z1 x2y2z2 x3y3z3 x4y4z4 …. xNyNzN Input File Parameters Array x1 x2 x3 x4 x y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….… BSpline Transform Input Point Output Point x

66 BSplines Interpolation
Image Resampling BSpline Warping

67 Image Resampling Interpolator Fixed Image Resample Image Moving Image
Filter Moving Image Deformed Image Transform

68 BSplines Interpolation
Original Lena

69 BSplines Interpolation
Deformed with BSpline Transform

70 BSplines Interpolation
Deformed Lena Original Lena

71 Deformable Registration
Image Registration BSpline Transform

72 Image Registration Framework
Fixed Image Metric Moving Image Interpolator Optimizer Transform Parameters Array

73 BSplines Deformable Registration
Deformed with BSpline Transform

74 BSplines Deformable Registration
Registered with BSpline Transform

75 BSplines Deformable Registration
Original Lena

76 BSplines Deformable Registration
Difference Before Registration Difference After Registration

77 Enjoy ITK !

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