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

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Presentation on theme: "ITK Deformable Registration B-Splines Free-Form. Deformable Registration."— Presentation transcript:

1 ITK Deformable Registration B-Splines Free-Form

2 Deformable Registration

3 Deformable Transforms BSplines

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

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

6 Deformable Transformation y x

7 y x

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

9 Deformable Transforms BSplines in Geometrical Terms

10 BSplines Order Zero

11 BSplines Order Zero Piece-Wise Y = 1

12 BSplines Convolution -2120

13 BSplines Area under the product curve -2120

14 BSplines -2120

15 BSplines Order One -2120

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

17 BSplines Convolution -2120

18 BSplines Convolution -2120

19 BSplines Order Two -2120

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

21 BSplines Convolution -2120

22 BSplines Convolution -2120

23 BSplines Order Three -2120

24 BSplines Order Three Piece-Wise Y = ( 3X 3 - 6X )/6 Y = (2-X) 3 / 6 Y = (2+X) 3 / 6 Y = ( - 3X 3 - 6X )/6

25 BSplines Interpolating with BSplines

26 BSplines Interpolation Zero OrderNearest Neighbor

27 BSplines Interpolation Zero OrderNearest Neighbor

28 BSplines Interpolation Zero OrderNearest Neighbor

29 BSplines Interpolation Zero OrderNearest Neighbor

30 BSplines Interpolation First OrderLinear Interpolation

31 BSplines Interpolation First OrderLinear Interpolation

32 BSplines Interpolation First OrderLinear Interpolation

33 BSplines Interpolation First OrderLinear Interpolator

34 BSplines Interpolation Second OrderQuadratic Interpolation

35 BSplines Interpolation Second OrderQuadratic Interpolation

36 BSplines Interpolation Second OrderQuadratic Interpolation

37 BSplines Interpolation Second OrderQuadratic Interpolator

38 BSplines Interpolation Third OrderCubic Interpolation

39 BSplines Interpolation Third OrderCubic Interpolation

40 BSplines Interpolation Third OrderCubic Interpolation

41 BSplines Interpolation Third OrderCubic Interpolator

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

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 x BSpline Grid Resampling Grid

51 BSplines Grid & Image Grid

52 BSpline Grid

53 BSplines Grid & Image Grid BSpline Grid Valid Region

54 BSplines Grid & Image Grid BSpline Grid

55 BSplines Grid & Image Grid BSpline Grid Valid Region

56 BSplines Interpolation Interpolating Vectors

57 y x BSpline Grid Resampling Grid

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

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

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

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

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

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

64 Array of Parameters Feeding the BSpline Transform x BSpline Transform Input Point Output Point x 1 x 2 x 3 x 4 x 5... y 1 y 2 y 3 y 4 y 5 ….…. z 1 z 2 z 3 z 4….…

65 Feeding the BSpline Transform x BSpline Transform Input Point Output Point x 1 x 2 x 3 x 4 x 5... y 1 y 2 y 3 y 4 y 5 ….…. z 1 z 2 z 3 z 4….… x 1 y 1 z 1 x 2 y 2 z 2 x 3 y 3 z 3 x 4 y 4 z 4 …. x N y N z N Input File Parameters Array

66 BSplines Interpolation Image Resampling BSpline Warping

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

68 BSplines Interpolation Original Lena

69 BSplines Interpolation Deformed with BSpline Transform

70 BSplines Interpolation Original LenaDeformed Lena

71 Deformable Registration Image Registration BSpline Transform

72 Image Registration Framework Fixed Image Moving Image Metric Transform Interpolator Optimizer 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 After Registration Difference Before Registration

77 Enjoy ITK !


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