% est_transrot.m                                    Steve Mann, 1992
%
% 2-D image group parameter est; adapted for Peleg: Steve Mann, 1993
%
% transrot (not transrot2 because the 2 is obvious; no such thing as 1D rot)
%
% estimates parameters of the rigid body motion group
%
% Use: [b,a] = est_transrot(E1,E2);                 % complex trans; rot mag=1
% or : [trans_m, trans_n, rot] = est_transrot(E1,E2)% 3 real output arguments
% or : est_transrot(E1,E2);                         % nicely formatted screen
%                                                   % output in radians + deg
%
% sign convention: real down, imag to right
%
% properly handles situation when one or both images contain some NaN points
%
% Bugs???: Peleg Taylor series of Taylor series still needs to be double-checked

function [p1, p2, p3] = multi_parameter_function(E1,E2,K);

if nargin==1
  disp('est_transrotr: you must supply 2 images')
  return
end%if

if nargin ~=3
  disp('est_transrotr: number of itterations not specified; defaulting to 2')
  K=2;
end%if

a=1;  % initialize group parameters
b=0;
for k = 1:K
  [b,a] = est_transrot(E1,E2);
  resample(a,E2,b);
end%for

trans_m = real(b);
trans_n = imag(b);
rot     = angle(a);

if nargout == 3
  p1 = trans_m;
  p2 = trans_n;
  p3 = rot;
end%if

if nargout == 2
  p1 = trans_m + i*trans_n;    % the ``b'' in the ax+b group
  p2 = exp(i*rot);             % the ``a'' in ax+b; contains zoom=1 and rot
end%if

if nargout == 1
  disp('only 1 output argument was given; still need to decide what to do here')
  disp('i have not decided what to do in the case of 1 output argument')
  disp('please use either 3,2, or 0 output arguments')
  return
end%if

if nargout == 0
  % disp('0 output arguments were given so I am displaying result to screen:')
  o = pi/180;
  disp(sprintf('trans_m=%g pels;  trans_n=%g pels;  rot=%g =%go',...
  trans_m, trans_n, rot, rot/o))
  p1 = [trans_m, trans_n, 0, rot, 0,0,0];  % p1 will be returned if user calls
					   % this function without semicolon
end%if