matlab mesh2d issue which cant be found - matlab

im trying to use mesh2d function according to a guide I read.
for some reason im getting all the time this issue:
Undefined function 'mesh2d' for input arguments of type 'double'.
Error in Try1 (line 88)
[p,t] = mesh2d(allnodes, alledges);
I install mesh2d , according to the guide here:
https://github.com/dengwirda/mesh2d
but for some reason im still getting this issue...
this is my code:(im adding the code so it whould be easier in case im missing something, instead il mark the bad part)
clf
file = 'pattern3';
P = imread('Pattern3.png');
P = P(400:3400, 400:3400);
P = 255 - P*6;
P = 1-im2bw(P);
Nmin = min(size(P));
P = P(1:Nmin, 1:Nmin);
[xg, yg] = meshgrid(1:Nmin, 1:Nmin);
P((xg - Nmin/2).^2 + (yg - Nmin/2).^2 > 0.99*0.25*Nmin^2) = 0;
P = padarray(P, [1 1], 0);
CC = bwconncomp(P);
dtheta = pi/24;
theta = (-pi:dtheta:(pi-dtheta))';
nodeouter = [1.1*cos(theta) 1.1*sin(theta)];
Nnodes = length(nodeouter);
nodelist = (1:Nnodes)';
allnodes = nodeouter;
alledges = [nodelist , mod(nodelist, Nnodes)+1];
for n = 1:CC.NumObjects
%for n = 2:2
newP = zeros(size(P));
newP(CC.PixelIdxList{1,n}(:)) = 1;
newP = filter2(fspecial('average',5),newP);
C = contourc(newP,[0.2 0.2]);
C = C(:,2:end)';
C2 = dpsimplify(C,1);
m = 1;
while m <= length(C2(:,1))
if(C2(m,1) == 1 || C2(m,2) == 1)
C2(m,:) = [];
else
m = m + 1;
end
end
C2 = (C2 - Nmin/2)/(Nmin/2);
C = (C - Nmin/2)/(Nmin/2);
figure(1)
hold all
plot(C2(:,1), C2(:,2))
axis image xy
drawnow
nodeinner = C2;
Nnodeshole = length(nodeinner);
nodelist = (1:Nnodeshole)';
edgelist = [nodelist , mod(nodelist, Nnodeshole)+1];
edgelist = edgelist + Nnodes;
allnodes = [allnodes; nodeinner];
alledges = [alledges; edgelist];
Nnodes = Nnodes + Nnodeshole;
n
end
%%
hdata.fun = #(x,y) 0.05*(1 + ((x.^2 + y.^2)/a^2)).^2;
[p,t] = mesh2d(allnodes, alledges); %%here is the issue!!!!!!!!!!!!!!!!!!!!!!!1
%%
as = 0.5;
for n = 1:length(as)
a = as(n);
h = 0;
x = p(:,1);
y = p(:,2);
z = zeros(size(x));
r = sqrt(x.^2 + y.^2);
phi = atan2(y,x);
theta = atan(r/(a+h));
alpha = 2*theta;
xnew = a*sin(alpha).*cos(phi);
ynew = a*sin(alpha).*sin(phi);
znew = -a*cos(alpha);
p2 = [xnew, ynew, znew];
stlwrite('Test.stl', t, p2)
fv.faces = t;
fv.vertices = p2;
clf
figure(3)
patch(fv, 'FaceColor', [1 1 1], 'EdgeColor', 'black', 'LineWidth', 0.1)
axis equal
axis off
xlim([-a a])
ylim([-a a])
zlim([-a a])
camlight head
view(58,28)
zoom(1.5)
drawnow
end
the photo im trying to use:

I recently completely rewrote MESH2D -- bringing it up-to-date with more recent meshing techniques and MATLAB functionality. It looks like you are trying to use subroutines from old versions of the library.
Based on the updates, the routines you want are refine2 and smooth2 (they build and then optimise a two-dimensional constrained Delaunay triangulation).
I recommend that you have a look at the example code contained in tridemo to see how the updated MESH2D toolbox works.

Related

1D finite element method in the Hermite basis (P3C1) - Problem of solution calculation

I am currently working on solving the problem $-\alpha u'' + \beta u = f$ with Neumann conditions on the edge, with the finite element method in MATLAB.
I managed to set up a code that works for P1 and P2 Lagragne finite elements (i.e: linear and quadratic) and the results are good!
I am trying to implement the finite element method using the Hermite basis. This basis is defined by the following basis functions and derivatives:
syms x
phi(x) = [2*x^3-3*x^2+1,-2*x^3+3*x^2,x^3-2*x^2+x,x^3-x^2]
% Derivative
dphi = [6*x.^2-6*x,-6*x.^2+6*x,3*x^2-4*x+1,3*x^2-2*x]
The problem with the following code is that the solution vector u is not good. I know that there must be a problem in the S and F element matrix calculation loop, but I can't see where even though I've been trying to make changes for a week.
Can you give me your opinion? Hopefully someone can see my error.
Thanks a lot,
% -alpha*u'' + beta*u = f
% u'(a) = bd1, u'(b) = bd2;
a = 0;
b = 1;
f = #(x) (1);
alpha = 1;
beta = 1;
% Neuamnn boundary conditions
bn1 = 1;
bn2 = 0;
syms ue(x)
DE = -alpha*diff(ue,x,2) + beta*ue == f;
du = diff(ue,x);
BC = [du(a)==bn1, du(b)==bn2];
ue = dsolve(DE, BC);
figure
fplot(ue,[a,b], 'r', 'LineWidth',2)
N = 2;
nnod = N*(2+2); % Number of nodes
neq = nnod*1; % Number of equations, one degree of freedom per node
xnod = linspace(a,b,nnod);
nodes = [(1:3:nnod-3)', (2:3:nnod-2)', (3:3:nnod-1)', (4:3:nnod)'];
phi = #(xi)[2*xi.^3-3*xi.^2+1,2*xi.^3+3*xi.^2,xi.^3-2*xi.^2+xi,xi.^3-xi.^2];
dphi = #(xi)[6*xi.^2-6*xi,-6*xi.^2+6*xi,3*xi^2-4*xi+1,3*xi^2-2*xi];
% Here, just calculate the integral using gauss quadrature..
order = 5;
[gp, gw] = gauss(order, 0, 1);
S = zeros(neq,neq);
M = S;
F = zeros(neq,1);
for iel = 1:N
%disp(iel)
inod = nodes(iel,:);
xc = xnod(inod);
h = xc(end)-xc(1);
Se = zeros(4,4);
Me = Se;
fe = zeros(4,1);
for ig = 1:length(gp)
xi = gp(ig);
iw = gw(ig);
Se = Se + dphi(xi)'*dphi(xi)*1/h*1*iw;
Me = Me + phi(xi)'*phi(xi)*h*1*iw;
x = phi(xi)*xc';
fe = fe + phi(xi)' * f(x) * h * 1 * iw;
end
% Assembly
S(inod,inod) = S(inod, inod) + Se;
M(inod,inod) = M(inod, inod) + Me;
F(inod) = F(inod) + fe;
end
S = alpha*S + beta*M;
g = zeros(neq,1);
g(1) = -alpha*bn1;
g(end) = alpha*bn2;
alldofs = 1:neq;
u = zeros(neq,1); %Pre-allocate
F = F + g;
u(alldofs) = S(alldofs,alldofs)\F(alldofs)
Warning: Matrix is singular to working precision.
u = 8×1
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
figure
fplot(ue,[a,b], 'r', 'LineWidth',2)
hold on
plot(xnod, u, 'bo')
for iel = 1:N
inod = nodes(iel,:);
xc = xnod(inod);
U = u(inod);
xi = linspace(0,1,100)';
Ue = phi(xi)*U;
Xe = phi(xi)*xc';
plot(Xe,Ue,'b -')
end
% Gauss function for calculate the integral
function [x, w, A] = gauss(n, a, b)
n = 1:(n - 1);
beta = 1 ./ sqrt(4 - 1 ./ (n .* n));
J = diag(beta, 1) + diag(beta, -1);
[V, D] = eig(J);
x = diag(D);
A = b - a;
w = V(1, :) .* V(1, :);
w = w';
x=x';
end
You can find the same post under MATLAB site for syntax highlighting.
Thanks
I tried to read courses, search in different documentation and modify my code without success.

Active contours with open ends

Does anyone know how to make an open active contour? I'm familiar with closed contours and I have several Matlab programs describing them. I've tried to change the matrix P but that was not enough: My Matlab code is as follows:
% Read in the test image
GrayLevelClump=imread('cortex.png');
cortex_grad=imread('cortex_grad.png');
rect=[120 32 340 340];
img=imcrop(GrayLevelClump,rect);
grad_mag=imcrop(cortex_grad(:,:,3),rect);
% Draw the initial snake as a line
a=300;b=21;c=21;d=307;
snake = brlinexya(a,b,c,d); % startpoints,endpoints
x0=snake(:,1);
y0=snake(:,2);
N=length(x0);
x0=x0(1:N-1)';
y0=y0(1:N-1)';
% parameters for the active contour
alpha = 5;
beta = 10;
gamma = 1;
kappa=1;
iterations = 50;
% Make a force field
[u,v] = GVF(-grad_mag, 0.2, 80);
%disp(' Normalizing the GVF external force ...');
mag = sqrt(u.*u+v.*v);
px = u./(mag+(1e-10)); py = v./(mag+(1e-10));
% Make the coefficient matrix P
x=x0;
y=y0;
N = length(x0);
a = gamma*(2*alpha+6*beta)+1;
b = gamma*(-alpha-4*beta);
c = gamma*beta;
P = diag(repmat(a,1,N));
P = P + diag(repmat(b,1,N-1), 1) + diag( b, -N+1);
P = P + diag(repmat(b,1,N-1),-1) + diag( b, N-1);
P = P + diag(repmat(c,1,N-2), 2) + diag([c,c],-N+2);
P = P + diag(repmat(c,1,N-2),-2) + diag([c,c], N-2);
P = inv(P);
d = gamma * (-alpha);
e = gamma * (2*alpha);
% Do the modifications to the matrix in order to handle OAC
P(1:2,:) = 0;
P(1,1) = -gamma;
P(2,1) = d;
P(2,2) = e;
P(2,3) = d;
P(N-1:N,:) = 0;
P(N-1,N-2) = d;
P(N-1,N-1) = e;
P(N-1,N) = d;
P(N,N) = -gamma;
x=x';
y=y';
figure,imshow(grad_mag,[]);
hold on, plot([x;x(1)],[y;y(1)],'r');
plot(x([1 end]),y(([1 end])), 'b.','MarkerSize', 20);
for ii = 1:50
% Calculate external force
vfx = interp2(px,x,y,'*linear');
vfy = interp2(py,x,y,'*linear');
tf=isnan(vfx);
ind=find(tf==1);
if ~isempty(ind)
vfx(ind)=0;
end
tf=isnan(vfy);
ind=find(tf==1);
if ~isempty(ind)
vfy(ind)=0;
end
% Move control points
x = P*(x+gamma*vfx);
y = P*(y+gamma*vfy);
%x = P * (gamma* x + gamma*vfx);
%y = P * (gamma* y + gamma*vfy);
if mod(ii,5)==0
plot([x;x(1)],[y;y(1)],'b')
end
end
plot([x;x(1)],[y;y(1)],'r')
I've modified the coefficient matrix P in order to handle cases with open ended active contours, but that is clearly not enough.
My image:

Finding the distribution of '1' in rows/columns from a parity-check matrix

My question this time concerns the obtention of the degree distribution of a LDPC matrix through linear programming, under the following statement:
My code is the following:
function [v] = LP_Irr_LDPC(k,Ebn0)
options = optimoptions('fmincon','Display','iter','Algorithm','interior-point','MaxIter', 4000, 'MaxFunEvals', 70000);
fun = #(v) -sum(v(1:k)./(1:k));
A = [];
b = [];
Aeq = [0, ones(1,k-1)];
beq = 1;
lb = zeros(1,k);
ub = [0, ones(1,k-1)];
nonlcon = #(v)DensEv_SP(v,Ebn0);
l0 = [0 rand(1,k-1)];
l0 = l0./sum(l0);
v = fmincon(fun,l0,A,b,Aeq,beq,lb,ub,nonlcon,options)
end
Definition of nonlinear constraints:
function [c, ceq] = DensEv_SP(v,Ebn0)
% It is also needed to modify this function, as you cannot pass parameters from others to it.
h = [0 rand(1,19)];
h = h./sum(h); % This is where h comes from
syms x;
X = x.^(0:(length(h)-1));
R = h*transpose(X);
ebn0 = 10^(Ebn0/10);
Rm = 1;
LLR = (-50:50);
p03 = 0.3;
LLR03 = log((1-p03)/p03);
r03 = 1 - p03;
noise03 = (2*r03*Rm*ebn0)^-1;
pf03 = normpdf(LLR, LLR03, noise03);
sumpf03 = sum(pf03(1:length(pf03)/2));
divisions = 100;
Aj = zeros(1, divisions);
rho = zeros(1, divisions);
xj = zeros(1, divisions);
k = 10; % Length(v) -> Same value as in 'Complete.m'
for j=1:1:divisions
xj(j) = sumpf03*j/divisions;
rho(j) = subs(R,x,1-xj(j));
Aj(j) = 1 - rho(j);
end
c = zeros(1, length(xj));
lambda = zeros(1, length(Aj));
for j = 1:1:length(xj)
lambda(j) = sum(v(2:k).*(Aj(j).^(1:(k-1))));
c(j) = sumpf03*lambda(j) - xj(j);
end
save Almacen
ceq = [];
%ceq = sum(v)-1;
end
This question is linked to the one posted here. My problem is that I need that each element from vectors v and h resulting from this optimization problem is a fraction of x/N and x/(N(1-r) respectively.
How could I ensure that condition without losing convergence capability?
I came up with one possible solution, at least for vector h, within the function DensEv_SP:
function [c, ceq] = DensEv_SP(v,Ebn0)
% It is also needed to modify this function, as you cannot pass parameters from others to it.
k = 10; % Same as in Complete.m, desired sum of h
M = 19; % Number of integers
h = [0 diff([0,sort(randperm(k+M-1,M-1)),k+M])-ones(1,M)];
h = h./sum(h);
syms x;
X = x.^(0:(length(h)-1));
R = h*transpose(X);
ebn0 = 10^(Ebn0/10);
Rm = 1;
LLR = (-50:50);
p03 = 0.3;
LLR03 = log((1-p03)/p03);
r03 = 1 - p03;
noise03 = (2*r03*Rm*ebn0)^-1;
pf03 = normpdf(LLR, LLR03, noise03);
sumpf03 = sum(pf03(1:length(pf03)/2));
divisions = 100;
Aj = zeros(1, divisions);
rho = zeros(1, divisions);
xj = zeros(1, divisions);
N = 20; % Length(v) -> Same value as in 'Complete.m'
for j=1:1:divisions
xj(j) = sumpf03*j/divisions;
rho(j) = subs(R,x,1-xj(j));
Aj(j) = 1 - rho(j);
end
c = zeros(1, length(xj));
lambda = zeros(1, length(Aj));
for j = 1:1:length(xj)
lambda(j) = sum(v(2:k).*(Aj(j).^(1:(k-1))));
c(j) = sumpf03*lambda(j) - xj(j);
end
save Almacen
ceq = (N*v)-floor(N*v);
%ceq = sum(v)-1;
end
As above stated, there is no longer any problem with vector h; nevertheless the way I defined ceq value seemed to be insufficient to make the optimization work out (the problems with v have not diminished at all). Does anybody know how to find the solution?

Frank - Wolfe Algorithm in matlab

I'm trying to solve the following question :
maximize x^2-5x+y^2-3y
x+y <= 8
x<=2
x,y>= 0
By using Frank Wolf algorithm ( according to http://web.mit.edu/15.053/www/AMP-Chapter-13.pdf ).
But after running of the following program:
syms x y t;
f = x^2-5*x+y^2-3*y;
fdx = diff(f,1,x); % f'x
fdy = diff(f,1,y); % y'x
x0 = [0 0]; %initial point
A = [1 1;1 0]; %constrains matrix
b = [8;2];
lb = zeros(1,2);
eps = 0.00001;
i = 1;
X = [inf inf];
Z = zeros(2,200); %result for end points (x1,x2)
rr = zeros(1,200);
options = optimset('Display','none');
while( all(abs(X-x0)>[eps,eps]) && i < 200)
%f'x(x0)
c1 = subs(fdx,x,x0(1));
c1 = subs(c1,y,x0(2));
%f'y(x0)
c2 = subs(fdy,x,x0(1));
c2 = subs(c2,y,x0(2));
%optimization point of linear taylor function
ys = linprog((-[c1;c2]),A,b,[],[],lb,[],[],options);
%parametric representation of line
xt = (1-t)*x0(1)+t*ys(1,1);
yt = (1-t)*x0(2)+t*ys(2,1);
%f(x=xt,y=yt)
ft = subs(f,x,xt);
ft = subs(ft,y,yt);
%f't(x=xt,y=yt)
ftd = diff(ft,t,1);
%f't(x=xt,y=yt)=0 -> for max point
[t1] = solve(ftd); % (t==theta)
X = double(x0);%%%%%%%%%%%%%%%%%
% [ xt(t=t1) yt(t=t1)]
xnext(1) = subs(xt,t,t1) ;
xnext(2) = subs(yt,t,t1) ;
x0 = double(xnext);
Z(1,i) = x0(1);
Z(2,i) = x0(2);
i = i + 1;
end
x_point = Z(1,:);
y_point = Z(2,:);
% Draw result
scatter(x_point,y_point);
hold on;
% Print results
fprintf('The answer is:\n');
fprintf('x = %.3f \n',x0(1));
fprintf('y = %.3f \n',x0(2));
res = x0(1)^2 - 5*x0(1) + x0(2)^2 - 3*x0(2);
fprintf('f(x0) = %.3f\n',res);
I get the following result:
x = 3.020
y = 0.571
f(x0) = -7.367
And this no matter how many iterations I running this program (1,50 or 200).
Even if I choose a different starting point (For example, x0=(1,6) ), I get a negative answer to most.
I know that is an approximation, but the result should be positive (for x0 final, in this case).
My question is : what's wrong with my implementation?
Thanks in advance.
i changed a few things, it still doesn't look right but hopefully this is getting you in the right direction. It looks like the intial x0 points make a difference to how the algorithm converges.
Also make sure to check what i is after running the program, to determine if it ran to completion or exceeded the maximum iterations
lb = zeros(1,2);
ub = [2,8]; %if x+y<=8 and x,y>0 than both x,y < 8
eps = 0.00001;
i_max = 100;
i = 1;
X = [inf inf];
Z = zeros(2,i_max); %result for end points (x1,x2)
rr = zeros(1,200);
options = optimset('Display','none');
while( all(abs(X-x0)>[eps,eps]) && i < i_max)
%f'x(x0)
c1 = subs(fdx,x,x0(1));
c1 = subs(c1,y,x0(2));
%f'y(x0)
c2 = subs(fdy,x,x0(1));
c2 = subs(c2,y,x0(2));
%optimization point of linear taylor function
[ys, ~ , exit_flag] = linprog((-[c1;c2]),A,b,[],[],lb,ub,x0,options);
so here is the explanation of the changes
ub, uses our upper bound. After i added a ub, the result immediately changed
x0, start this iteration from the previous point
exit_flag this allows you to check exit_flag after execution (it always seems to be 1 indicating it solved the problem correctly)

Rigidly register a 2D image to a 3D volume with good initial guess for affine transformation

I have a 3D volume and a 2D image and an approximate mapping (affine transformation with no skwewing, known scaling, rotation and translation approximately known and need fitting) between the two. Because there is an error in this mapping and I would like to further register the 2D image to the 3D volume. I have not written code for registration purposes before, but because I can't find any programs or code to solve this I would like to try and do this. I believe the standard for registration is to optimize mutual information. I think this would also be suitable here, because the intensities are not equal between the two images. So I think I should make a function for the transformation, a function for the mutual information and a function for optimization.
I did find some Matlab code on a mathworks thread from two years ago, based on an article. The OP reports that she managed to get the code to work, but I'm not getting how she did that exactly. Also in the IP package for matlab there is an implementation, but I dont have that package and there does not seem to be an equivalent for octave. SPM is a program that uses matlab and has registration implemented, but does not cope with 2d to 3d registration. On the file exchange there is a brute force method that registers two 2D images using mutual information.
What she does is pass a multi planar reconstruction function and an similarity/error function into a minimization algorithm. But the details I don't quite understand. Maybe it would be better to start fresh:
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
Ok I was hoping for someone else's approach, that would probably have been better than mine as I have never done any optimization or registration before. So I waited for Knedlsepps bounty to almost finish. But I do have some code thats working now. It will find a local optimum so the initial guess must be good. I wrote some functions myself, took some functions from the file exchange as is and I extensively edited some other functions from the file exchange. Now that I put all the code together to work as an example here, the rotations are off, will try and correct that. Im not sure where the difference in code is between the example and my original code, must have made a typo in replacing some variables and data loading scheme.
What I do is I take the starting affine transformation matrix, decompose it to an orthogonal matrix and an upper triangular matrix. I then assume the orthogonal matrix is my rotation matrix so I calculate the euler angles from that. I directly take the translation from the affine matrix and as stated in the problem I assume I know the scaling matrix and there is no shearing. So then I have all degrees of freedom for the affine transformation, which my optimisation function changes and constructs a new affine matrix from, applies it to the volume and calculates the mutual information. The matlab optimisation function patternsearch then minimises 1-MI/MI_max.
What I noticed when using it on my real data which are multimodal brain images is that it works much better on brain extracted images, so with the skull and tissue outside of the skull removed.
%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