CSci 6971: Image Registration Lecture 26: BSpline Transforms April 20, 2004 Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware Prof. Chuck Stewart, RPI Dr. Luis Ibanez, Kitware
Image RegistrationLecture 26 2 Deformable Registration
Image RegistrationLecture 26 3 Deformable Transforms BSplines
Image RegistrationLecture 26 4 Deformable Transformation y Fixed Image Transform x y Moving Image x
Image RegistrationLecture 26 5 Deformable Transformation y Fixed Image Transform x y Moving Image x
Image RegistrationLecture 26 6 Deformable Transformation y x
Image RegistrationLecture 26 7 Deformable Transformation y x
Image RegistrationLecture 26 8 Image Resampling Fixed Image Moving Image Transform Interpolator Resample Image Filter Deformed Image BSpline Transform
Image RegistrationLecture 26 9 Deformable Transforms BSplines in Geometrical Terms
Image RegistrationLecture BSplines Order Zero
Image RegistrationLecture BSplines Order Zero Piece-Wise Y = 1
Image RegistrationLecture BSplines Convolution -2120
Image RegistrationLecture BSplines Area under the product curve -2120
Image RegistrationLecture BSplines -2120
Image RegistrationLecture BSplines Order One -2120
Image RegistrationLecture BSplines Order One Piece-Wise Y = ( 1 - X )Y = ( X + 1 )
Image RegistrationLecture BSplines Convolution -2120
Image RegistrationLecture BSplines Convolution -2120
Image RegistrationLecture BSplines Order Two -2120
Image RegistrationLecture BSplines Order Two Piece-Wise Y = ( X – 3/2 ) 2 / 2 Y = ( 1 – 2 X 2 ) Y = ( X + 3/2 ) 2 / 2
Image RegistrationLecture BSplines Convolution -2120
Image RegistrationLecture BSplines Convolution -2120
Image RegistrationLecture BSplines Order Three -2120
Image RegistrationLecture 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
Image RegistrationLecture BSplines Interpolating with BSplines
Image RegistrationLecture BSplines Interpolation Zero OrderNearest Neighbor
Image RegistrationLecture BSplines Interpolation Zero OrderNearest Neighbor
Image RegistrationLecture BSplines Interpolation Zero OrderNearest Neighbor
Image RegistrationLecture BSplines Interpolation Zero OrderNearest Neighbor
Image RegistrationLecture BSplines Interpolation First OrderLinear Interpolation
Image RegistrationLecture BSplines Interpolation First OrderLinear Interpolation
Image RegistrationLecture BSplines Interpolation First OrderLinear Interpolation
Image RegistrationLecture BSplines Interpolation First OrderLinear Interpolator
Image RegistrationLecture BSplines Interpolation Second OrderQuadratic Interpolation
Image RegistrationLecture BSplines Interpolation Second OrderQuadratic Interpolation
Image RegistrationLecture BSplines Interpolation Second OrderQuadratic Interpolation
Image RegistrationLecture BSplines Interpolation Second OrderQuadratic Interpolator
Image RegistrationLecture BSplines Interpolation Third OrderCubic Interpolation
Image RegistrationLecture BSplines Interpolation Third OrderCubic Interpolation
Image RegistrationLecture BSplines Interpolation Third OrderCubic Interpolation
Image RegistrationLecture BSplines Interpolation Third OrderCubic Interpolator
Image RegistrationLecture BSplines Cubic BSplines in Two Dimensions
Image RegistrationLecture BSplines in 2D Tensor Product
Image RegistrationLecture BSplines in 2D Tensor Product
Image RegistrationLecture BSplines in 2D Tensor Product Separable
Image RegistrationLecture BSplines in 2D Support Nodes in Region of Influence #Nodes = 4 N
Image RegistrationLecture BSplines in 2D Interpolation BSpline Grid Resampling Grid
Image RegistrationLecture BSplines in 2D Interpolation BSpline Grid Resampling Grid
Image RegistrationLecture Sampling Grid y x
Image RegistrationLecture BSpline Grid y x BSpline Grid Resampling Grid
Image RegistrationLecture BSplines Grid & Image Grid
Image RegistrationLecture BSplines Grid & Image Grid BSpline Grid
Image RegistrationLecture BSplines Grid & Image Grid BSpline Grid Valid Region
Image RegistrationLecture BSplines Grid & Image Grid BSpline Grid
Image RegistrationLecture BSplines Grid & Image Grid BSpline Grid Valid Region
Image RegistrationLecture BSplines Interpolation Interpolating Vectors
Image RegistrationLecture Interpolating Vectors y x BSpline Grid Resampling Grid
Image RegistrationLecture Interpolating Vectors y x BSpline Grid Resampling Grid X Compo- nents
Image RegistrationLecture Interpolating Vectors y x BSpline Grid Resampling Grid X Compo- nents
Image RegistrationLecture Interpolating Vectors y x BSpline Grid Resampling Grid Y Compo- nents
Image RegistrationLecture Interpolating Vectors y x BSpline Grid Resampling Grid X Compo- nents
Image RegistrationLecture X Grid Feeding the BSpline Transform x BSpline Transform Dimension N N Grid Y Grid ….. Z Grid Input Point Output Point
Image RegistrationLecture Array of Parameters Feeding the BSpline Transform x BSpline Transform Input Point Output Point
Image RegistrationLecture 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….…
Image RegistrationLecture 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
Image RegistrationLecture BSplines Interpolation Image Resampling BSpline Warping
Image RegistrationLecture Image Resampling Fixed Image Moving Image Transform Interpolator Resample Image Filter Deformed Image
Image RegistrationLecture BSplines Interpolation Original Lena
Image RegistrationLecture BSplines Interpolation Deformed with BSpline Transform
Image RegistrationLecture BSplines Interpolation Original LenaDeformed Lena
Image RegistrationLecture Deformable Registration Image Registration BSpline Transform
Image RegistrationLecture Image Registration Framework Fixed Image Moving Image Metric Transform Interpolator Optimizer Parameters Array
Image RegistrationLecture BSplines Deformable Registration Deformed with BSpline Transform
Image RegistrationLecture BSplines Deformable Registration Registered with BSpline Transform
Image RegistrationLecture BSplines Deformable Registration Original Lena
Image RegistrationLecture BSplines Deformable Registration Difference After Registration Difference Before Registration
Image RegistrationLecture End Enjoy ITK !