% =======================================================================================
% function [Dc,rc,dD,dr,d2psi] = SSD(Tc,Rc,omega,m,varargin);
% (c) Jan Modersitzki 2009/03/24, see FAIR.2 and FAIRcopyright.m.
% Sum of Squared Differences based distance measure 
% for usage in a general Gauss-Newton type framework
% computes D(Tc,Rc) = hd*psi(r(Tc)), r = Tc-Rc, psi = 0.5*r'*r 
% and derivatives, dr = dT, d2psi= hd*I, hd = prod(omega./m)
%
% Input: 
%  Tc, Rc     template and reference
%  omega, m   represents domain and discretization
%  varargin   optional parameters, e.g. doDerivative=0
%
% Output:
%  Dc         SSD(Tc,Rc)
%  rc         Tc-Rc
%  dD         dpsi*dr
%  dr         dT
%  d2psi      hd = prod(omega./m)
% =======================================================================================

function [Dc,rc,dD,dr,d2psi] = SSD(Tc,Rc,omega,m,varargin);

Dc  = []; dD = []; rc  = []; dr = []; d2psi = [];
doDerivative = (nargout > 3);

for k=1:2:length(varargin), % overwrite default parameter
  eval([varargin{k},'=varargin{',int2str(k+1),'};']);
end;

hd = prod((omega(2:2:end)-omega(1:2:end))./m); % voxel size for integration
rc = Tc - Rc;              		% the residual
Dc = 0.5*hd * rc'*rc;       	% the SSD
if ~doDerivative, return; end;
dr = 1; 						% or speye(length(rc),length(rc)); 
dD = hd * rc'*dr; 
d2psi = hd;                 

%$=======================================================================================
%$  FAIR: Flexible Algorithms for Image Registration
%$  Copyright (c): Jan Modersitzki
%$  1280 Main Street West, Hamilton, ON, Canada, L8S 4K1
%$  Email: modersitzki@mcmaster.ca
%$  URL:   http://www.cas.mcmaster.ca/~modersit/index.shtml
%$=======================================================================================
%$  No part of this code may be reproduced, stored in a retrieval system,
%$  translated, transcribed, transmitted, or distributed in any form
%$  or by any means, means, manual, electric, electronic, electro-magnetic,
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%$  without the prior explicit written permission of the authors or their 
%$  designated proxies. In no event shall the above copyright notice be 
%$  removed or altered in any way.
%$ 
%$  This code is provided "as is", without any warranty of any kind, either
%$  expressed or implied, including but not limited to, any implied warranty
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%$  who distributed the code be liable for damages or for any claim(s) by 
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%$=======================================================================================
%$  Any use of this code constitutes acceptance of the terms of the above
%$                              statements
%$=======================================================================================

