% est_bilinear                                         Steve Mann, 1992-1993
% (not called est_bilinear2 because the 2 is obvious from ``bi'' in bilinear)
%
% estimate the 8 bilinear parameters from a pair of images
%
% The model is:   u = p1xy + p2x + p3y + p4
%                 v = p5xy + p6x + p7y + p8
%
% Use: p = est_bilinear(A,B);
%  or: [p1,p2,p3,p4,p5,p6,p7,p8] = bilinear_est(A,B);
%  or : est_bilinear(A,B);      % nicely formatted screen output
%
% Example application: pb=est_bilinear(A,B);
%                      pp=bilinear2p(pb);
%                      B2=pchirp2(pp,B);      % now B2 will look alot like A
%                      pb=est_bilinear(A,B2); % residual difference
%                      pp=bilinear2p(pb);
%                      B3=pchirp2(pp,B);      % almost exactly like A by now
%
% relation to pchirp2: p1=-(ah+bg); p2=(a-cg); p3=(b-ch); p4=c;
%                      p5=-(dh+eg); p6=(d-fg); p7=(e-fh); p8=f;
% sign convention: m (or X) down, n (or Y) to right
% properly handles situation when one or both images contain some NaN points
%
% See also: bilinear2p, pchirp2

function [p1,p2,p3,p4,p5,p6,p7,p8]=f(E1,E2);  % two images in, 0,1,or 8 outs

%%%%mask = isnan(E1).*isnan(E2);  % NaN mask: regions where either is undefined
% doesnt work because nanmask makes it still nan

[El,Em,En] = derivatives(E1,E2);
[M,N]= size(El);                    % size of any of the 3 derivative matrices
[n m]=meshdom(1:N,M:-1:1);          % variables ``x'' and ``y''
%disp('est_bilinear: converting from pixels to units on [0,1)')      doesnt work
%m=m/M;    doesnt work
%n=n/N;    doesnt work

DERIVATIVES = ...
 [...
  [sum2nan(m.*n.*Em .*m.*n.*Em) sum2nan(m.*Em .*m.*n.*Em) sum2nan(n.*Em .*m.*n.*Em) sum2nan(Em .*m.*n.*Em)...
   sum2nan(m.*n.*En .*m.*n.*Em) sum2nan(m.*En .*m.*n.*Em) sum2nan(n.*En .*m.*n.*Em) sum2nan(En .*m.*n.*Em)];...
  [sum2nan(m.*n.*Em .*m.*Em)    sum2nan(m.*Em .*m.*Em)    sum2nan(n.*Em .*m.*Em)    sum2nan(Em .*m.*Em)...
   sum2nan(m.*n.*En .*m.*Em)    sum2nan(m.*En .*m.*Em)    sum2nan(n.*En .*m.*Em)    sum2nan(En .*m.*Em)];...
  [sum2nan(m.*n.*Em .*n.*Em)    sum2nan(m.*Em .*n.*Em)    sum2nan(n.*Em .*n.*Em)    sum2nan(Em .*n.*Em)...
   sum2nan(m.*n.*En .*n.*Em)    sum2nan(m.*En .*n.*Em)    sum2nan(n.*En .*n.*Em)    sum2nan(En .*n.*Em)];...
  [sum2nan(m.*n.*Em .*Em)       sum2nan(m.*Em .*Em)       sum2nan(n.*Em .*Em)       sum2nan(Em .*Em)...
   sum2nan(m.*n.*En .*Em)       sum2nan(m.*En .*Em)       sum2nan(n.*En .*Em)       sum2nan(En .*Em)];...
  [sum2nan(m.*n.*Em .*m.*n.*En) sum2nan(m.*Em .*m.*n.*En) sum2nan(n.*Em .*m.*n.*En) sum2nan(Em .*m.*n.*En)...
   sum2nan(m.*n.*En .*m.*n.*En) sum2nan(m.*En .*m.*n.*En) sum2nan(n.*En .*m.*n.*En) sum2nan(En .*m.*n.*En)];...
  [sum2nan(m.*n.*Em .*m.*En)    sum2nan(m.*Em .*m.*En)    sum2nan(n.*Em .*m.*En)    sum2nan(Em .*m.*En)...
   sum2nan(m.*n.*En .*m.*En)    sum2nan(m.*En .*m.*En)    sum2nan(n.*En .*m.*En)    sum2nan(En .*m.*En)];...
  [sum2nan(m.*n.*Em .*n.*En)    sum2nan(m.*Em .*n.*En)    sum2nan(n.*Em .*n.*En)    sum2nan(Em .*n.*En)...
   sum2nan(m.*n.*En .*n.*En)    sum2nan(m.*En .*n.*En)    sum2nan(n.*En .*n.*En)    sum2nan(En .*n.*En)];...
  [sum2nan(m.*n.*Em .*En)       sum2nan(m.*Em .*En)       sum2nan(n.*Em .*En)       sum2nan(Em .*En)...
   sum2nan(m.*n.*En .*En)       sum2nan(m.*En .*En)       sum2nan(n.*En .*En)       sum2nan(En .*En)]...
 ];

Derivatives = ...
 - [sum2nan(El .*m.*n.*Em); ...
    sum2nan(El .*m.*Em); ...
    sum2nan(El .*n.*Em); ...
    sum2nan(El .*Em); ...
    sum2nan(El .*m.*n.*En); ...
    sum2nan(El .*m.*En); ...
    sum2nan(El .*n.*En); ...
    sum2nan(El .*En) ...
   ];                         % vector of derivatives

parameters = DERIVATIVES\Derivatives;

disp('est_bilinear: adding identity and converting from pel to normalized [0,1) rep.')
parameters(:) = parameters(:) + [0;1;0;0; 0;0;1;0];  % convert relative change like u=func(x+deltax) to absolute like u=func(x)
parameters = parameters(:) .* [N;1;N/M;1/M; M;M/N;1;1/N];

if (nargout == 8) | (nargout == 0)
  % p1 = parameters(1);     % if called with no semicolon, do not want to see any ans=[], etc, so make no reference to p1
  p2 = parameters(2);
  p3 = parameters(3);
  p4 = parameters(4);
  p5 = parameters(5);
  p6 = parameters(6);
  p7 = parameters(7);
  p8 = parameters(8);
end%if
if nargout == 8
  p1 = parameters(1);
end%if

if nargout == 1
  p1 = parameters;
end%if

if nargout == 0
  disp('est_bilinear: 0 output arguments given so I am displaying result to screen:')
  disp(sprintf('%g %g %g %g %g %g %g %g',parameters(1),p2,p3,p4,p5,p6,p7,p8))
end%if

if (nargout ~=0) & (nargout ~= 1) & (nargout ~= 8)
  error('est_bilinear: number of output arguments must be 0, 1, or 8')
end%if