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spm_maff8.m
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spm_maff8.m
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function [M,h] = spm_maff8(varargin)
% Affine registration to MNI space using mutual information
% FORMAT M = spm_maff8(P,samp,fwhm,tpm,M,regtyp)
% P - filename or structure handle of image
% samp - distance between sample points (mm). Small values are
% better, but things run more slowly.
% fwhm - smoothness estimate for computing a fudge factor. Estimate
% is a full width at half maximum of a Gaussian (in mm).
% tpm - data structure encoding a tissue probability map, generated
% via spm_load_priors8.m.
% M - starting estimates for the affine transform (or [] to use
% default values).
% regtype - regularisation type
% 'mni' - registration of European brains with MNI space
% 'eastern' - registration of East Asian brains with MNI space
% 'rigid' - rigid(ish)-body registration
% 'subj' - inter-subject registration
% 'none' - no regularisation
%__________________________________________________________________________
% Copyright (C) 2008-2014 Wellcome Trust Centre for Neuroimaging
% John Ashburner
% $Id: spm_maff8.m 5962 2014-04-17 12:47:43Z spm $
[buf,MG,x,ff] = loadbuf(varargin{1:3});
[M,h] = affreg(buf, MG, x, ff, varargin{4:end});
return;
%==========================================================================
% function [buf,MG,x,ff] = loadbuf(V,samp,fwhm)
%==========================================================================
function [buf,MG,x,ff] = loadbuf(V,samp,fwhm)
if ischar(V), V = spm_vol(V); end;
d = V(1).dim(1:3);
vx = sqrt(sum(V(1).mat(1:3,1:3).^2)); % Voxel sizes
sk = max([1 1 1],round(samp*[1 1 1]./vx));
[x1,x2] = ndgrid(1:sk(1):d(1),1:sk(2):d(2));
x3 = 1:sk(3):d(3);
% Fudge Factor - to (approximately) account for
% non-independence of voxels
s = (fwhm+mean(vx))/sqrt(8*log(2)); % Standard deviation
ff = prod(4*pi*(s./vx./sk).^2 + 1)^(1/2);
% Old version of fudge factor
%ff = max(1,ff^3/prod(sk)/abs(det(V(1).mat(1:3,1:3))));
% Load the image
V = spm_vol(V);
o = ones(size(x1));
d = [size(x1) length(x3)];
g = zeros(d);
spm_progress_bar('Init',d(3),'Loading volume','Planes loaded');
for i=1:d(3)
g(:,:,i) = spm_sample_vol(V,x1,x2,o*x3(i),0);
spm_progress_bar('Set',i);
end;
spm_progress_bar('Clear');
spm_progress_bar('Init',d(3),'Initial Histogram','Planes complete');
mn = min(g(:));
mx = max(g(:));
sf = [mn 1;mx 1]\[1;4000];
h = zeros(4000,1);
for i=1:d(3)
p = g(:,:,i);
p = p(isfinite(p) & (p~=0));
p = round(p*sf(1)+sf(2));
h = h + accumarray(p(:),1,[4000,1]);
spm_progress_bar('Set',i);
end;
spm_progress_bar('Clear');
spm_progress_bar('Init',d(3),'Converting to uint8','Planes complete');
h = cumsum(h)/sum(h);
mn = (find(h>(0.0005),1)-sf(2))/sf(1);
mx = (find(h>(0.9995),1)-sf(2))/sf(1);
sf = [mn 1;mx 1]\[0;255];
if spm_type(V.dt(1),'intt'),
scrand = V.pinfo(1);
rand('seed',1);
else
scrand = 0;
end
cl = cell(1,d(3));
buf = struct('nm',cl,'msk',cl,'g',cl);
for i=1:d(3),
gz = g(:,:,i);
buf(i).msk = isfinite(gz) & gz~=0;
buf(i).nm = sum(buf(i).msk(:));
if scrand, gz = gz + rand(size(gz))*scrand-scrand/2; end
gz = gz(buf(i).msk)*sf(1)+sf(2);
buf(i).g = uint8(max(min(round(gz),255),0));
spm_progress_bar('Set',i);
end;
spm_progress_bar('Clear');
MG = V.mat;
x = {x1,x2,x3};
return;
%==========================================================================
% function [M,h0] = affreg(buf,MG,x,ff,tpm,M,regtyp)
%==========================================================================
function [M,h0] = affreg(buf,MG,x,ff,tpm,M,regtyp)
% Mutual Information Registration
x1 = x{1};
x2 = x{2};
x3 = x{3};
[mu,isig] = spm_affine_priors(regtyp);
mu = [zeros(6,1) ; mu];
Alpha0 = [eye(6,6)*0.00001 zeros(6,6) ; zeros(6,6) isig]*ff;
if ~isempty(M),
sol = M2P(M);
else
sol = mu;
end
sol1 = sol;
ll = -Inf;
krn = spm_smoothkern(4,(-256:256)',0);
spm_plot_convergence('Init','Registering','Log-likelihood','Iteration');
stepsize = 1;
h1 = ones(256,numel(tpm.dat));
for iter=1:200
penalty = 0.5*(sol1-mu)'*Alpha0*(sol1-mu);
T = tpm.M\P2M(sol1)*MG;
%fprintf('%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g\t%g | %g\n', sol1,penalty);
%global st
%st.vols{1}.premul = P2M(sol1);
%spm_orthviews('Redraw')
%drawnow
R = derivs(tpm.M,sol1,MG);
y1a = T(1,1)*x1 + T(1,2)*x2 + T(1,4);
y2a = T(2,1)*x1 + T(2,2)*x2 + T(2,4);
y3a = T(3,1)*x1 + T(3,2)*x2 + T(3,4);
for i=1:length(x3)
if ~buf(i).nm, continue; end
y1 = y1a(buf(i).msk) + T(1,3)*x3(i);
y2 = y2a(buf(i).msk) + T(2,3)*x3(i);
y3 = y3a(buf(i).msk) + T(3,3)*x3(i);
msk = y3>=1;
y1 = y1(msk);
y2 = y2(msk);
y3 = y3(msk);
b = spm_sample_priors8(tpm,y1,y2,y3);
buf(i).b = b;
buf(i).msk1 = msk;
buf(i).nm1 = sum(buf(i).msk1);
end
ll0 = 0;
for subit=1:60
h0 = zeros(256,numel(tpm.dat))+eps;
ll1 = ll0;
ll0 = 0;
for i=1:length(x3),
if ~buf(i).nm || ~buf(i).nm1, continue; end
gm = double(buf(i).g(buf(i).msk1))+1;
q = zeros(numel(gm),size(h0,2));
for k=1:size(h0,2),
q(:,k) = h1(gm(:),k).*buf(i).b{k};
end
sq = sum(q,2) + eps;
if ~rem(subit,4),
ll0 = ll0 + sum(log(sq));
end
for k=1:size(h0,2),
h0(:,k) = h0(:,k) + accumarray(gm,q(:,k)./sq,[256 1]);
end
end
if ~rem(subit,4) && (ll0-ll1)/sum(h0(:)) < 1e-5, break; end
h1 = conv2((h0+eps)/sum(h0(:)),krn,'same');
%figure(9); plot(log(h0+1)); drawnow;
h1 = h1./(sum(h1,2)*sum(h1,1));
end
for i=1:length(x3)
buf(i).b = [];
buf(i).msk1 = [];
end
ssh = sum(h0(:));
ll1 = (sum(sum(h0.*log(h1))) - penalty)/ssh/log(2);
%fprintf('%g\t%g\n', sum(sum(h0.*log2(h1)))/ssh, -penalty/ssh);
spm_plot_convergence('Set',ll1);
if abs(ll1-ll)<1e-5, break; end
if (ll1<ll)
stepsize = stepsize*0.5;
h1 = oh1;
R = derivs(tpm.M,sol,MG);
if stepsize<0.5^8, break; end;
else
stepsize = min(stepsize*1.1,1);
oh1 = h1;
ll = ll1;
sol = sol1;
%spm_plot_convergence('Set',ll1);
end
Alpha = zeros(12);
Beta = zeros(12,1);
for i=1:length(x3)
if ~buf(i).nm, continue; end
gi = double(buf(i).g)+1;
y1 = y1a(buf(i).msk) + T(1,3)*x3(i);
y2 = y2a(buf(i).msk) + T(2,3)*x3(i);
y3 = y3a(buf(i).msk) + T(3,3)*x3(i);
msk = y3>=1;
y1 = y1(msk);
y2 = y2(msk);
y3 = y3(msk);
gi = gi(msk);
nz = size(y1,1);
if nz
mi = zeros(nz,1) + eps;
dmi1 = zeros(nz,1);
dmi2 = zeros(nz,1);
dmi3 = zeros(nz,1);
[b, db1, db2, db3] = spm_sample_priors8(tpm,y1,y2,y3);
for k=1:size(h0,2)
tmp = h1(gi,k);
mi = mi + tmp.*b{k};
dmi1 = dmi1 + tmp.*db1{k};
dmi2 = dmi2 + tmp.*db2{k};
dmi3 = dmi3 + tmp.*db3{k};
end
dmi1 = dmi1./mi;
dmi2 = dmi2./mi;
dmi3 = dmi3./mi;
x1m = x1(buf(i).msk); x1m = x1m(msk);
x2m = x2(buf(i).msk); x2m = x2m(msk);
x3m = x3(i);
A = [dmi1.*x1m dmi2.*x1m dmi3.*x1m...
dmi1.*x2m dmi2.*x2m dmi3.*x2m...
dmi1 *x3m dmi2 *x3m dmi3 *x3m...
dmi1 dmi2 dmi3];
Alpha = Alpha + A'*A;
Beta = Beta - sum(A,1)';
end
end
drawnow;
Alpha = R'*Alpha*R;
Beta = R'*Beta;
% Gauss-Newton update
sol1 = sol - stepsize*((Alpha+Alpha0)\(Beta+Alpha0*(sol-mu)));
end
spm_plot_convergence('Clear');
M = P2M(sol);
return;
%==========================================================================
% function P = M2P(M)
%==========================================================================
function P = M2P(M)
% Polar decomposition parameterisation of affine transform,
% based on matrix logs
J = M(1:3,1:3);
V = sqrtm(J*J');
R = V\J;
lV = logm(V);
lR = -logm(R);
if sum(sum(imag(lR).^2))>1e-6, error('Rotations by pi are still a problem.'); end;
P = zeros(12,1);
P(1:3) = M(1:3,4);
P(4:6) = lR([2 3 6]);
P(7:12) = lV([1 2 3 5 6 9]);
P = real(P);
return;
%==========================================================================
% function M = P2M(P)
%==========================================================================
function M = P2M(P)
% Polar decomposition parameterisation of affine transform,
% based on matrix logs
% Translations
D = P(1:3);
D = D(:);
% Rotation part
ind = [2 3 6];
T = zeros(3);
T(ind) = -P(4:6);
R = expm(T-T');
% Symmetric part (zooms and shears)
ind = [1 2 3 5 6 9];
T = zeros(3);
T(ind) = P(7:12);
V = expm(T+T'-diag(diag(T)));
M = [V*R D ; 0 0 0 1];
return;
%==========================================================================
% function R = derivs(MF,P,MG)
%==========================================================================
function R = derivs(MF,P,MG)
% Numerically compute derivatives of Affine transformation matrix w.r.t.
% changes in the parameters.
R = zeros(12,12);
M0 = MF\P2M(P)*MG;
M0 = M0(1:3,:);
for i=1:12
dp = 0.0000001;
P1 = P;
P1(i) = P1(i) + dp;
M1 = MF\P2M(P1)*MG;
M1 = M1(1:3,:);
R(:,i) = (M1(:)-M0(:))/dp;
end
return;