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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

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

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**CSci 6971: Image Registration Lecture 26: BSpline**TransformsApril 20, 2004 Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware**Deformable Registration**Deformable Registration Lecture 26**Deformable Transforms**BSplines Lecture 26**Deformable Transformation**y y Transform x x Fixed Image Moving Image Lecture 26**Deformable Transformation**y y Transform x x Fixed Image Moving Image Lecture 26**Deformable Transformation**y x Lecture 26**Deformable Transformation**y x Lecture 26**Image Resampling**Interpolator FixedImage Resample Image Filter MovingImage BSpline Transform DeformedImage Transform Lecture 26**Deformable Transforms**BSplines in Geometrical Terms Lecture 26**-2**-1 0 1 2 BSplines Order Zero Lecture 26**-2**-1 0 1 2 BSplines Order Zero Piece-Wise Y = 1 Lecture 26**-2**-1 0 1 2 BSplines Convolution Lecture 26**-2**-1 0 1 2 BSplines Area under the product curve Lecture 26**-2**-1 0 1 2 BSplines Lecture 26**-2**-1 0 1 2 BSplines Order One Lecture 26**-2**-1 0 1 2 BSplines Order One Piece-Wise Y = ( X + 1 ) Y = ( 1 - X ) Lecture 26**-2**-1 0 1 2 BSplines Convolution Lecture 26**-2**-1 0 1 2 BSplines Convolution Lecture 26**-2**-1 0 1 2 BSplines Order Two Lecture 26**-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**-2**-1 0 1 2 BSplines Convolution Lecture 26**-2**-1 0 1 2 BSplines Convolution Lecture 26**-2**-1 0 1 2 BSplines Order Three Lecture 26**-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**BSplines**Interpolatingwith BSplines Lecture 26**-2**-1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26**-2**-1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26**-2**-1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26**-2**-1 0 1 2 BSplines Interpolation Zero Order Nearest Neighbor Lecture 26**-2**-1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation First Order Linear Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation First Order Linear Interpolator Lecture 26**-2**-1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Second Order Quadratic Interpolator Lecture 26**-2**-1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Third Order Cubic Interpolation Lecture 26**-2**-1 0 1 2 BSplines Interpolation Third Order Cubic Interpolator Lecture 26**BSplines**Cubic BSplinesinTwo Dimensions Lecture 26**BSplines in 2D**Tensor Product Lecture 26**BSplines in 2D**Tensor Product Lecture 26**BSplines in 2D**Tensor Product Separable Lecture 26**BSplines in 2D**Support Nodes in Region of Influence #Nodes = 4N Lecture 26**BSplines in 2D**Interpolation BSpline Grid Resampling Grid Lecture 26**BSplines in 2D**Interpolation BSpline Grid Resampling Grid Lecture 26**Sampling Grid**y x Lecture 26**BSpline Grid**y BSpline Grid Resampling Grid x Lecture 26