B-spline Grid, Image and Point based Registration (original) (raw)

B-spline registration of two 2D / 3D images or corrsp. points, affine and with smooth b-spline grid.

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Updated16 Mar 2011

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Affine and B-spline grid based registration and data-fitting of two 2D color/grayscale images or 3D volumes or point-data. Registration can be done intensity / pixel based, or landmark / corresponding points based (See OpenSurf), or a combination.

Description Pixel-based registration:
This function is an (enhanced) implementation of the b-spline registration algorithm in D. Rueckert et al. "Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images". Including the smoothness penalty of Rueckert (thin sheet of metal bending energy), and Jacobian (diffeomorphic) function. Also including, localized normalized mutual information as registration error, allowing the images or volumes to be of a different type/modality for instance a MRI T1 and T2 patient scan.

How it works:
A grid of b-spline control points is constructed which controls the transformation of an input image. An error measure is used to measure the registration error between the moving and static image. The quasi newton Matlab optimizer fminlbfgs (also on Mathworks) is used to move the control points to achieve the optimal registration between both images with minimal registration error.

Usage:
- The function image_registration.m is easy to use, and contains examples in the help, and will fit most applications. (If you want to write your own specialized registration code study the registration examples)
- The function point_registration is fast fitting of a b-spline grid to 2D/3D corresponding points, for landmark based registration.
- There is also the function manually_warp_images which allow control grid changes with the mouse, to get better registration.

First, you need to compile mex / C code with compile_c_files.m. (2D registration also works without mex files but will be slower)

The multi-threaded mex code supports Windows, Linux (and Mac OS?)

Some Features:
- 2-D / 3-D Eulerian strain tensor images can be made from the transformations fields. For example to describe cardiac motion in the images.
- Landmarks can be used for already known corresponding points (for example from Sift). Influence of every landmark on the registration process can be adjust.
- It is possible to register a number of movie frames by using the registration grid of previous two images as initial registration grid of the next two images.
- It is possible to mask parts of the images, to decrease or increase the influence of an image structure on the registration result.

Literature:
- D. Rueckert et al. "Nonrigid Registration Using Free-Form Deformations: Application to Breast MR Images".
- Seungyong Lee, George Wolberg, and Sung Yong Shing, "Scattered Data interpolation with Multilevel B-splines"

note:
- B-spline registration is slower and more complex than demon registration see:
http://www.mathworks.fr/matlabcentral/fileexchange/loadFile.do?objectId=21451
- Why still use B-spine registration?, because the resulting transformation-field corresponds better to real-live deformation than transformation fields from fluid registration.

Please report bugs, successes and questions.

Cite As

Dirk-Jan Kroon (2025). B-spline Grid, Image and Point based Registration (https://www.mathworks.com/matlabcentral/fileexchange/20057-b-spline-grid-image-and-point-based-registration), MATLAB Central File Exchange. Retrieved January 14, 2025.

functions/

• backwards2forwards(B)
• backwards2forwards_2d_double(Bx,By,H)
• fminlbfgs.m
• image_difference(V,U,type,Mask,MaskNum)
• imgaussian(I,sigma,siz)
• imresize3d(V,scale,tsize,ntype,npad)
• inversegrid(O_trans,Spacing,sizeI,MaxRef)
• MakeDiffeomorphic(O_trans,Spacing,sizeI)
• make_grid_image(Spacing,sizeI)
• make_init_grid(Spacing,sizeI,M)
• maxNumCompThreads(varargin)
• mutual_histogram_double(I1,I2,Imin,Imax,nbins)
• penalties_smoothness(O,sizeI,Scaling)
• refine_grid(O_trans,Spacing,sizeI)
• showcs3(varargin)
• squared_difference_double(V,U)
• strain(Ux,Uy,Uz)

functions_affine/

• affine_parameter_scaling(sizeI)
• affine_registration_error(par,scale,I1,I2,type,O_trans,Spacing,MaskI1,MaskI2,Points1,Points2,PStrength,mode)
• affine_registration_image(par,scale,I1,I2,type)
• affine_transform(Iin,M,mode)
• affine_transform_2d_double(Iin,M,mode,ImageSize)
• make_transformation_matrix(t,r,s,h)

functions_nonrigid/

• bspline_coefficients(u,v,w)
• bspline_grid_fitting(O,Spacing,D,X)
• bspline_registration_gradient(O_grid,sizes,Spacing,I1,I2,options,MaskI1,MaskI2,Points1,Points2,PStrength)
• bspline_registration_image(O_grid,sizes,Spacing,I1,I2,type)
• bspline_transform(O,I,Spacing,mode)
• bspline_transform_2d_double(Ox,Oy,Iin,dx,dy,mode)
• bspline_trans_points_double(O_trans,Spacing,X,check)
• image_interpolation(Iin,Tlocalx,Tlocaly,Interpolation,Boundary,ImageSize)
• jacobiandet_cost_gradient(O_grid,sizes,O_goal,sizeI,Spacing)
• jacobiandet_error_2d_double(Ox,Oy,sizeI,dx,dy)
• jacobiandet_transform_2d_double(Ox,Oy,Isize,dx,dy)
• movepixels(I1,T,mode)
• movepixels_2d_double(Iin,Tx,Ty,mode)

low_level_examples/