Leo*_*Leo 5 matlab geometry transformation image-processing image-registration
我有一个3D体积和一个2D图像和两者之间的近似映射(没有skwewing的仿射变换,已知缩放,旋转和平移近似已知且需要拟合).因为此映射中存在错误,我想进一步将2D图像注册到3D卷.我之前没有为注册目的编写代码,但由于我找不到任何程序或代码来解决这个问题,我想尝试这样做.我认为注册标准是优化互信息.我认为这也适用于此,因为两幅图像之间的强度不相等.所以我认为我应该为转换创建一个函数,一个用于交互信息的函数和一个用于优化的函数.
基于一篇文章,我确实在两年前的mathworks 线程中找到了一些Matlab代码.OP报告她设法让代码工作,但我不知道她是怎么做到的.另外在matlab的IP包中有一个实现,但我没有那个包,似乎没有相应的八度.SPM是一个使用matlab并已实现注册的程序,但不能处理2d到3d注册.在文件交换机上,存在使用互信息登记两个2D图像的强力方法.
她所做的是将多平面重建函数和相似/误差函数传递给最小化算法.但细节我不太明白.也许最好重新开始:
load mri; volume = squeeze(D);
phi = 3; theta = 2; psi = 5; %some small angles
tx = 1; ty = 1; tz = 1; % some small translation
dx = 0.25, dy = 0.25, dz = 2; %different scales
t = [tx; ty; tz];
r = [phi, theta, psi]; r = r*(pi/180);
dims = size(volume);
p0 = [round(dims(1)/2);round(dims(2)/2);round(dims(3)/2)]; %image center
S = eye(4); S(1,1) = dx; S(2,2) = dy; S(3,3) = dz;
Rx=[1 0 0 0;
0 cos(r(1)) sin(r(1)) 0;
0 -sin(r(1)) cos(r(1)) 0;
0 0 0 1];
Ry=[cos(r(2)) 0 -sin(r(2)) 0;
0 1 0 0;
sin(r(2)) 0 cos(r(2)) 0;
0 0 0 1];
Rz=[cos(r(3)) sin(r(3)) 0 0;
-sin(r(3)) cos(r(3)) 0 0;
0 0 1 0;
0 0 0 1];
R = S*Rz*Ry*Rx;
%make affine matrix to rotate about center of image
T1 = ( eye(3)-R(1:3,1:3) ) * p0(1:3);
T = T1 + t; %add translation
A = R;
A(1:3,4) = T;
Rold2new = A;
Rnew2old = inv(Rold2new);
%the transformation
[xx yy zz] = meshgrid(1:dims(1),1:dims(2),1:1);
coordinates_axes_new = [xx(:)';yy(:)';zz(:)'; ones(size(zz(:)))'];
coordinates_axes_old = Rnew2old*coordinates_axes_new;
Xcoordinates = reshape(coordinates_axes_old(1,:), dims(1), dims(2), dims(3));
Ycoordinates = reshape(coordinates_axes_old(2,:), dims(1), dims(2), dims(3));
Zcoordinates = reshape(coordinates_axes_old(3,:), dims(1), dims(2), dims(3));
%interpolation/reslicing
method = 'cubic';
slice= interp3(volume, Xcoordinates, Ycoordinates, Zcoordinates, method);
%so now I have my slice for which I would like to find the correct position
% first guess for A
A0 = eye(4); A0(1:3,4) = T1; A0(1,1) = dx; A0(2,2) = dy; A0(3,3) = dz;
% this is pretty close to A
% now how would I fit the slice to the volume by changing A0 and examining some similarity measure?
% probably maximize mutual information?
% http://www.mathworks.com/matlabcentral/fileexchange/14888-mutual-information-computation/content//mi/mutualinfo.m
好吧，我希望别人的方法，这可能会比我的方法更好，因为我以前从未做过任何优化或注册。所以我等待克内德尔塞普斯的赏金快结束了。但我确实有一些代码现在可以工作。它将找到局部最优值，因此初始猜测一定是好的。我自己编写了一些函数，按原样从文件交换中获取了一些函数，并从文件交换中广泛编辑了一些其他函数。现在我将所有代码放在一起作为示例，旋转已关闭，将尝试纠正该问题。我不确定示例和我的原始代码之间的代码差异在哪里，一定是在替换某些变量和数据加载方案时犯了拼写错误。
我所做的就是获取起始仿射变换矩阵，将其分解为正交矩阵和上三角矩阵。然后我假设正交矩阵是我的旋转矩阵，因此我从中计算欧拉角。我直接从仿射矩阵中获取平移，并且如问题中所述，我假设我知道缩放矩阵并且没有剪切。因此，我拥有仿射变换的所有自由度，我的优化函数会更改仿射变换并从中构造一个新的仿射矩阵，将其应用于体积并计算互信息。然后，matlab 优化函数patternsearch 最小化 1-MI/MI_max。
当我在我的真实数据（多模态大脑图像）上使用它时，我注意到它在大脑提取图像上效果更好，因此去除了头骨和头骨外部的组织。
%data
load mri; volume = double(squeeze(D));
%transformation parameters
phi = 3; theta = 1; psi = 5; %some small angles
tx = 1; ty = 1; tz = 3; % some small translation
dx = 0.25; dy = 0.25; dz = 2; %different scales
t = [tx; ty; tz];
r = [phi, theta, psi]; r = r*(pi/180);
%image center and size
dims = size(volume);
p0 = [round(dims(1)/2);round(dims(2)/2);round(dims(3)/2)];
%slice coordinate ranges
range_x = 1:dims(1)/dx;
range_y = 1:dims(2)/dy;
range_z = 1;
%rotation
R = dofaffine([0;0;0], r, [1,1,1]);
T1 = ( eye(3)-R(1:3,1:3) ) * p0(1:3); %rotate about p0
%scaling
S = eye(4); S(1,1) = dx; S(2,2) = dy; S(3,3) = dz;
%translation
T = [[eye(3), T1 + t]; [0 0 0 1]];
%affine
A = T*R*S;
% first guess for A
r00 = [1,1,1]*pi/180;
R00 = dofaffine([0;0;0], r00, [1 1 1]);
t00 = T1 + t + ( eye(3) - R00(1:3,1:3) ) * p0;
A0 = dofaffine( t00, r00, [dx, dy, dz] );
[ t0, r0, s0 ] = dofaffine( A0 );
x0 = [ t0.', r0, s0 ];
%the transformation
slice = affine3d(volume, A, range_x, range_y, range_z, 'cubic');
guess = affine3d(volume, A0, range_x, range_y, range_z, 'cubic');
%initialisation
Dt = [1; 1; 1];
Dr = [2 2 2].*pi/180;
Ds = [0 0 0];
Dx = [Dt', Dr, Ds];
%limits
LB = x0-Dx;
UB = x0+Dx;
%other inputs
ref_levels = length(unique(slice));
Qref = imquantize(slice, ref_levels);
MI_max = MI_GG(Qref, Qref);
%patternsearch options
options = psoptimset('InitialMeshSize',0.03,'MaxIter',20,'TolCon',1e-5,'TolMesh',5e-5,'TolX',1e-6,'PlotFcns',{@psplotbestf,@psplotbestx});
%optimise
[x2, MI_norm_neg, exitflag_len] = patternsearch(@(x) AffRegOptFunc(x, slice, volume, MI_max, x0), x0,[],[],[],[],LB(:),UB(:),options);
%check
p0 = [round(size(volume)/2).'];
R0 = dofaffine([0;0;0], x2(4:6)-x0(4:6), [1 1 1]);
t1 = ( eye(3) - R0(1:3,1:3) ) * p0;
A2 = dofaffine( x2(1:3).'+t1, x2(4:6), x2(7:9) ) ;
fitted = affine3d(volume, A2, range_x, range_y, range_z, 'cubic');
overlay1 = imfuse(slice, guess);
overlay2 = imfuse(slice, fitted);
figure(101);
ax(1) = subplot(1,2,1); imshow(overlay1, []); title('pre-reg')
ax(2) = subplot(1,2,2); imshow(overlay2, []); title('post-reg');
linkaxes(ax);
function normed_score = AffRegOptFunc( x, ref_im, reg_im, MI_max, x0 )
t = x(1:3).';
r = x(4:6);
s = x(7:9);
rangx = 1:size(ref_im,1);
rangy = 1:size(ref_im,2);
rangz = 1:size(ref_im,3);
ref_levels = length(unique(ref_im));
reg_levels = length(unique(reg_im));
t0 = x0(1:3).';
r0 = x0(4:6);
s0 = x0(7:9);
p0 = [round(size(reg_im)/2).'];
R = dofaffine([0;0;0], r-r0, [1 1 1]);
t1 = ( eye(3) - R(1:3,1:3) ) * p0;
t = t + t1;
Ap = dofaffine( t, r, s );
reg_im_t = affine3d(reg_im, A, rangx, rangy, rangz, 'cubic');
Qref = imquantize(ref_im, ref_levels);
Qreg = imquantize(reg_im_t, reg_levels);
MI = MI_GG(Qref, Qreg);
normed_score = 1-MI/MI_max;
end
function [ varargout ] = dofaffine( varargin )
% [ t, r, s ] = dofaffine( A )
% [ A ] = dofaffine( t, r, s )
if nargin == 1
%affine to degrees of freedom (no shear)
A = varargin{1};
[T, R, S] = decompaffine(A);
r = GetEulerAngles(R(1:3,1:3));
s = [S(1,1), S(2,2), S(3,3)];
t = T(1:3,4);
varargout{1} = t;
varargout{2} = r;
varargout{3} = s;
elseif nargin == 3
%degrees of freedom to affine (no shear)
t = varargin{1};
r = varargin{2};
s = varargin{3};
R = GetEulerAngles(r); R(4,4) = 1;
S(1,1) = s(1); S(2,2) = s(2); S(3,3) = s(3); S(4,4) = 1;
T = eye(4); T(1,4) = t(1); T(2,4) = t(2); T(3,4) = t(3);
A = T*R*S;
varargout{1} = A;
else
error('incorrect number of input arguments');
end
end
function [ T, R, S ] = decompaffine( A )
%I assume A = T * R * S
T = eye(4);
R = eye(4);
S = eye(4);
%decompose in orthogonal matrix q and upper triangular matrix r
%I assume q is a rotation matrix and r is a scale and shear matrix
%matlab 2014 can force real solution
[q r] = qr(A(1:3,1:3));
R(1:3,1:3) = q;
S(1:3,1:3) = r;
% A*S^-1*R^-1 = T*R*S*S^-1*R^-1 = T*R*I*R^-1 = T*R*R^-1 = T*I = T
T = A*inv(S)*inv(R);
t = T(1:3,4);
T = [eye(4) + [[0 0 0;0 0 0;0 0 0;0 0 0],[t;0]]];
end
function [varargout]= GetEulerAngles(R)
assert(length(R)==3)
dims = size(R);
if min(dims)==1
rx = R(1); ry = R(2); rz = R(3);
R = [[ cos(ry)*cos(rz), -cos(ry)*sin(rz), sin(ry)];...
[ cos(rx)*sin(rz) + cos(rz)*sin(rx)*sin(ry), cos(rx)*cos(rz) - sin(rx)*sin(ry)*sin(rz), -cos(ry)*sin(rx)];...
[ sin(rx)*sin(rz) - cos(rx)*cos(rz)*sin(ry), cos(rz)*sin(rx) + cos(rx)*sin(ry)*sin(rz), cos(rx)*cos(ry)]];
varargout{1} = R;
else
ry=asin(R(1,3));
rz=acos(R(1,1)/cos(ry));
rx=acos(R(3,3)/cos(ry));
if nargout > 1 && nargout < 4
varargout{1} = rx;
varargout{2} = ry;
varargout{3} = rz;
elseif nargout == 1
varargout{1} = [rx ry rz];
else
error('wrong number of output arguments');
end
end
end