B-spline Grid, Image and Point based Registration: [O_error, O_grad]=jacobiandet_cost_gradient(O_grid,sizes,O_goal,sizeI,Spacing) - File Exchange

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B-spline Grid, Image and Point based Registration

manually_warp_images(varargin) MANUALLY_WARP_IMAGES, is a GUI which shows the controlpoint grid used
showcs3(varargin) Function showcs3(V) will display x,y,z cross sections of the volume V
A=imresize3d(V,scale,tsize,nt... This function resizes a 3D image volume to new dimensions
Dlocal=jacobiandet_transform_... Determinant of the Jacobian of the transformation grid
E=strain(Ux,Uy,Uz) Calculate the Eulerian strain from displacement images
F=backwards2forwards(B) This function will turn a backward transformation field in to a
I3=movepixels(I1,T,mode) This function movepixels, will (backwards) translate the pixels
I=affine_registration_image(p... This function affine_registration_image, uses affine transfomation of the
I=imgaussian(I,sigma,siz) IMGAUSSIAN filters an 1D, 2D color/greyscale or 3D image with an
Igrid=make_grid_image(Spacing... This function creates a uniform 2d or 3D image of grid
Iout=affine_transform(Iin,M,m... Function affine_transform, is a wrapper of the (mex) functions
Iout=affine_transform_2d_doub... Affine transformation function (Rotation, Translation, Resize)
Iout=movepixels_2d_double(Iin... This function movepixels, will translate the pixels of an image
M=make_transformation_matrix(... This function make_transformation_matrix.m creates an affine
O_error=bspline_registration_... Function Registration_image. This function will create
O_trans=bspline_grid_fitting(... calculate which is the closest point on the lattic to the top-left
O_trans=make_init_grid(Spacin... This function creates a uniform 2d or 3D b-spline control grid
W=bspline_coefficients(u,v,w) Calculate influences of all neighborh b-spline knots
[Fx,Fy]=backwards2forwards_2d... This function will turn a backwards transformation field into
[I,T]=bspline_transform(O,I,S... Function bspline_transform, is a wrapper of the mex
[Iout,Tx,Ty]=bspline_transfor... Bspline transformation grid function
[O_error, O_grad]=bspline_reg... Function registration_gradient. This function will calculate a registration
[O_error, O_grad]=jacobiandet... Convert Grid vector to grid matrix
[O_error, O_grad]=jacobiandet... Gradient and error of the Jacobian of the transformation grid
[O_new,Spacing]=refine_grid(O... Refine image transformation grid of 1D b-splines with use of spliting matrix
[O_penalty, O_grad]=penalties... This function calculates the 2D or 3D equivalent of the 2D
[O_trans,Spacing,Xreg]=point_... This function creates a 2D or 3D b-spline grid, which transform space to
[O_trans,Spacing]=MakeDiffeom... This function MakeDiffeomorphic will make the b-spline grid diffeomorphic
[O_trans2,Spacing2]=inversegr... Calculates the (numeric) inverse of the current b-spline grid
[Tlocal,Dlocal]=bspline_trans... If Spacing and points are not an integer, we can not use fast look up tables,
[V1,V2]=get_example_data get_example_data is used to make some rigid and nonrigid transformed
[e,egrad]=affine_registration... This function affine_registration_error, uses affine transfomation of the
[hist12, hist1, hist2]=mutual... This function makes a 2D joint histogram of 1D,2D...ND images
[s_Trans, s_Rotation, s_Scale... This function gives scaling values for different parameters, such as
[t,I]=image_difference(V,U,ty... This function gives a registration error and error image I between the two
[x,fval,exitflag,output,grad]... FMINLBFGS finds a local minimum of a function of several variables.
addpaths.m add all needed function paths
err=squared_difference_double...
image_interpolation(Iin,Tloca... This function is used to transform an 2D image, in a backwards way with an
image_registration(Imoving,Is... This function image_registration is the most easy way to register two
maxNumCompThreads(varargin) maxNumCompThreads returns the number of available CPU cores, works with
compile_c_files.m
example_2d_affine.m
example_2d_nonrigid_1.m
example_2d_nonrigid_2.m
example_2d_nonrigid_3.m
example_3d_affine.m
example_3d_nonrigid.m
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from B-spline Grid, Image and Point based Registration by Dirk-Jan Kroon
B-spline registration of two 2D / 3D images or corrsp. points, affine and with smooth b-spline grid.

[O_error, O_grad]=jacobiandet_cost_gradient(O_grid,sizes,O_goal,sizeI,Spacing)

function [O_error, O_grad]=jacobiandet_cost_gradient(O_grid,sizes,O_goal,sizeI,Spacing)
% Convert Grid vector to grid matrix
O_grid=reshape(O_grid,sizes);

% Delta step used for error gradient
step=0.001;

if(nargout>1)
    if(length(Spacing)==2)
        [O_error1,O_grad1]=jacobiandet_error_2d_double(O_grid(:,:,1),O_grid(:,:,2),sizeI,Spacing(1),Spacing(2));
    else
        [O_error1,O_grad1]=jacobiandet_error_3d_double(O_grid(:,:,:,1),O_grid(:,:,:,2),O_grid(:,:,:,3),sizeI,Spacing(1),Spacing(2),Spacing(3));
    end
else
    if(length(Spacing)==2)
        O_error1=jacobiandet_error_2d_double(O_grid(:,:,1),O_grid(:,:,2),sizeI,Spacing(1),Spacing(2));
    else
        O_error1=jacobiandet_error_3d_double(O_grid(:,:,:,1),O_grid(:,:,:,2),O_grid(:,:,:,3),sizeI,Spacing(1),Spacing(2),Spacing(3));
    end
end

O_org=(O_goal-O_grid).^2;
O_error2=sum(O_org(:))/numel(O_goal);

if(nargout>1)
    if(length(Spacing)==2)
        E_gradpx=(O_goal(:,:,1)-(O_grid(:,:,1)+step)).^2-O_org(:,:,1);
        E_gradpy=(O_goal(:,:,2)-(O_grid(:,:,2)+step)).^2-O_org(:,:,2);
        O_grad2(:,:,1)=E_gradpx/step;
        O_grad2(:,:,2)=E_gradpy/step;
        O_grad2=O_grad2 /numel(O_goal);
    else
        E_gradpx=(O_goal(:,:,:,1)-(O_grid(:,:,:,1)+step)).^2-O_org(:,:,:,1);
        E_gradpy=(O_goal(:,:,:,2)-(O_grid(:,:,:,2)+step)).^2-O_org(:,:,:,2);
        E_gradpz=(O_goal(:,:,:,3)-(O_grid(:,:,:,3)+step)).^2-O_org(:,:,:,3);
        O_grad2(:,:,:,1)=E_gradpx/step;
        O_grad2(:,:,:,2)=E_gradpy/step;
        O_grad2(:,:,:,3)=E_gradpz/step;
        O_grad2=O_grad2 /numel(O_goal);
    end
end

if(nargout>1)
    O_grad=O_grad2 + O_grad1;
end
O_error=O_error2 + O_error1;

Highlights from B-spline Grid, Image and Point based Registration

Highlights from
B-spline Grid, Image and Point based Registration