Report

ITK Deformable Registration B-Splines Free-Form Deformable Registration Deformable Registration Deformable Transforms BSplines Deformable Transformation y y Transform x Fixed Image x Moving Image Deformable Transformation y y Transform x Fixed Image x Moving Image Deformable Transformation y x Deformable Transformation y x Image Resampling Interpolator Fixed Image Moving Image Resample Image Filter BSpline Transform Transform Deformed Image Deformable Transforms BSplines in Geometrical Terms BSplines Order Zero -2 -1 0 1 2 BSplines Order Zero Piece-Wise Y= 1 -2 -1 0 1 2 BSplines Convolution -2 -1 0 1 2 BSplines Area under the product curve -2 -1 0 1 2 BSplines -2 -1 0 1 2 BSplines Order One -2 -1 0 1 2 BSplines Order One Piece-Wise Y=(X+1) -2 -1 Y=(1-X) 0 1 2 BSplines Convolution -2 -1 0 1 2 BSplines Convolution -2 -1 0 1 2 BSplines Order Two -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 -2 -1 0 1 2 BSplines Convolution -2 -1 0 1 2 BSplines Convolution -2 -1 0 1 2 BSplines Order Three -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 -2 -1 0 1 2 BSplines Interpolating with BSplines BSplines Interpolation Zero Order -2 Nearest Neighbor -1 0 1 2 BSplines Interpolation Zero Order -2 Nearest Neighbor -1 0 1 2 BSplines Interpolation Zero Order -2 Nearest Neighbor -1 0 1 2 BSplines Interpolation Zero Order -2 Nearest Neighbor -1 0 1 2 BSplines Interpolation First Order -2 Linear Interpolation -1 0 1 2 BSplines Interpolation First Order -2 Linear Interpolation -1 0 1 2 BSplines Interpolation First Order -2 Linear Interpolation -1 0 1 2 BSplines Interpolation First Order -2 Linear Interpolator -1 0 1 2 BSplines Interpolation Second Order -2 -1 Quadratic Interpolation 0 1 2 BSplines Interpolation Second Order -2 -1 Quadratic Interpolation 0 1 2 BSplines Interpolation Second Order -2 -1 Quadratic Interpolation 0 1 2 BSplines Interpolation Second Order -2 -1 Quadratic Interpolator 0 1 2 BSplines Interpolation Third Order -2 -1 Cubic Interpolation 0 1 2 BSplines Interpolation Third Order -2 -1 Cubic Interpolation 0 1 2 BSplines Interpolation Third Order -2 -1 Cubic Interpolation 0 1 2 BSplines Interpolation Third Order -2 Cubic Interpolator -1 0 1 2 BSplines Cubic BSplines in Two Dimensions BSplines in 2D Tensor Product BSplines in 2D Tensor Product BSplines in 2D Tensor Product Separable BSplines in 2D Support Nodes in Region of Influence #Nodes = 4N BSplines in 2D Interpolation BSpline Grid Resampling Grid BSplines in 2D Interpolation BSpline Grid Resampling Grid Sampling Grid y x BSpline Grid y BSpline Grid Resampling Grid x BSplines Grid & Image Grid BSplines Grid & Image Grid BSpline Grid BSplines Grid & Image Grid BSpline Grid Valid Region BSplines Grid & Image Grid BSpline Grid BSplines Grid & Image Grid BSpline Grid Valid Region BSplines Interpolation Interpolating Vectors Interpolating Vectors y BSpline Grid Resampling Grid x Interpolating Vectors y BSpline Grid X Components Resampling Grid x Interpolating Vectors y BSpline Grid X Components Resampling Grid x Interpolating Vectors y BSpline Grid Y Components Resampling Grid x Interpolating Vectors y BSpline Grid X Components Resampling Grid x Feeding the BSpline Transform Y X Grid Grid Z Grid ….. N Grid Dimension N Input Point BSpline Transform Output Point x Feeding the BSpline Transform Array of Parameters Input Point BSpline Transform Output Point x Feeding the BSpline Transform x1 x2 x3 x4 x5... y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….… Array of Parameters Input Point BSpline Transform Output Point x Feeding the BSpline Transform x1y1z1 x2y2z2 x3y3z3 x4y4z4 …. xNyNzN Input File Parameters Array x1 x2 x3 x4 x5... Input Point y1 y2 y3 y4 y5 ….…. z1 z2 z3 z4….… BSpline Transform Output Point x BSplines Interpolation Image Resampling BSpline Warping Image Resampling Interpolator Fixed Image Moving Image Resample Image Filter Transform Deformed Image BSplines Interpolation Original Lena BSplines Interpolation Deformed with BSpline Transform BSplines Interpolation Deformed Lena Original Lena Deformable Registration Image Registration BSpline Transform Image Registration Framework Fixed Image Metric Moving Image Interpolator Optimizer Transform Parameters Array BSplines Deformable Registration Deformed with BSpline Transform BSplines Deformable Registration Registered with BSpline Transform BSplines Deformable Registration Original Lena BSplines Deformable Registration Difference Before Registration Difference After Registration Enjoy ITK !