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CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004

CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004. Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware. Deformable Registration. Deformable Registration. Deformable Transforms. BSplines. Deformable Transformation. y. y. Transform. x. x. Fixed Image.

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CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004

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  1. CSci 6971: Image Registration Lecture 26: BSpline TransformsApril 20, 2004 Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware

  2. Deformable Registration Deformable Registration Lecture 26

  3. Deformable Transforms BSplines Lecture 26

  4. Deformable Transformation y y Transform x x Fixed Image Moving Image Lecture 26

  5. Deformable Transformation y y Transform x x Fixed Image Moving Image Lecture 26

  6. Deformable Transformation y x Lecture 26

  7. Deformable Transformation y x Lecture 26

  8. Image Resampling Interpolator FixedImage Resample Image Filter MovingImage BSpline Transform DeformedImage Transform Lecture 26

  9. Deformable Transforms BSplines in Geometrical Terms Lecture 26

  10. -2 -1 0 1 2 BSplines Order Zero Lecture 26

  11. -2 -1 0 1 2 BSplines Order Zero Piece-Wise Y = 1 Lecture 26

  12. -2 -1 0 1 2 BSplines Convolution Lecture 26

  13. -2 -1 0 1 2 BSplines Area under the product curve Lecture 26

  14. -2 -1 0 1 2 BSplines Lecture 26

  15. -2 -1 0 1 2 BSplines Order One Lecture 26

  16. -2 -1 0 1 2 BSplines Order One Piece-Wise Y = ( X + 1 ) Y = ( 1 - X ) Lecture 26

  17. -2 -1 0 1 2 BSplines Convolution Lecture 26

  18. -2 -1 0 1 2 BSplines Convolution Lecture 26

  19. -2 -1 0 1 2 BSplines Order Two Lecture 26

  20. -2 -1 0 1 2 BSplines Order Two Piece-Wise Y = ( 1 – 2 X2 ) Y = ( X + 3/2 )2 / 2 Y = ( X – 3/2 )2 / 2 Lecture 26

  21. -2 -1 0 1 2 BSplines Convolution Lecture 26

  22. -2 -1 0 1 2 BSplines Convolution Lecture 26

  23. -2 -1 0 1 2 BSplines Order Three Lecture 26

  24. -2 -1 0 1 2 BSplines Order Three Piece-Wise Y = ( - 3X3 - 6X2 + 4 )/6 Y = ( 3X3 - 6X2 + 4 )/6 Y = (2-X)3 / 6 Y = (2+X)3 / 6 Lecture 26

  25. BSplines Interpolatingwith BSplines Lecture 26

  26. -2 -1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26

  27. -2 -1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26

  28. -2 -1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26

  29. -2 -1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26

  30. -2 -1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26

  31. -2 -1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26

  32. -2 -1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26

  33. -2 -1 0 1 2 BSplines Interpolation First Order Linear Interpolator Lecture 26

  34. -2 -1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26

  35. -2 -1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26

  36. -2 -1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26

  37. -2 -1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolator Lecture 26

  38. -2 -1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26

  39. -2 -1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26

  40. -2 -1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26

  41. -2 -1 0 1 2 BSplines Interpolation Third Order Cubic Interpolator Lecture 26

  42. BSplines Cubic BSplinesinTwo Dimensions Lecture 26

  43. BSplines in 2D Tensor Product Lecture 26

  44. BSplines in 2D Tensor Product Lecture 26

  45. BSplines in 2D Tensor Product Separable Lecture 26

  46. BSplines in 2D Support Nodes in Region of Influence #Nodes = 4N Lecture 26

  47. BSplines in 2D Interpolation BSpline Grid Resampling Grid Lecture 26

  48. BSplines in 2D Interpolation BSpline Grid Resampling Grid Lecture 26

  49. Sampling Grid y x Lecture 26

  50. BSpline Grid y BSpline Grid Resampling Grid x Lecture 26

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