example_2d_nonrigid_3.m

% Example using lsqnonlin optimizer and registration error image 
% instead of value.

% clean
clear all; close all; clc;

% Add all function paths
addpaths

% Read two greyscale images of Lena
I1=im2double(imread('lenag1.png')); 
I2=im2double(imread('lenag2.png'));

% b-spline grid spacing in x and y direction
Spacing=[32 32];

% Type of registration error used see registration_error.m
type='d';

% Make the Initial b-spline registration grid
[O_trans]=make_init_grid(Spacing,size(I1));

% Convert all values tot type double
I1=double(I1); I2=double(I2); O_trans=double(O_trans); 

% Smooth both images for faster registration
I1s=imfilter(I1,fspecial('gaussian',[20 20],5));
I2s=imfilter(I2,fspecial('gaussian',[20 20],5));

% Optimizer parameters
optim=optimset('Display','iter','MaxIter',40);

% Reshape O_trans from a matrix to a vector.
sizes=size(O_trans); O_trans=O_trans(:);

% Start the b-spline nonrigid registration optimizer
O_trans = lsqnonlin(@(x)bspline_registration_image(x,sizes,Spacing,I1s,I2s,type),O_trans,[],[],optim);

% Reshape O_trans from a vector to a matrix
O_trans=reshape(O_trans,sizes);

% Transform the input image with the found optimal grid.
Icor=bspline_transform(O_trans,I1,Spacing); 

% Make a (transformed) grid image
Igrid=make_grid_image(Spacing,size(I1));
Igrid=bspline_transform(O_trans,Igrid,Spacing); 

% Show the registration results
figure,
subplot(2,2,1), imshow(I1); title('input image 1');
subplot(2,2,2), imshow(I2); title('input image 2');
subplot(2,2,3), imshow(Icor); title('transformed image 1');
subplot(2,2,4), imshow(Igrid); title('grid');