function q = dummy(a,b,exponent)

% motion from fft2      2-D version           Steve Mann (steve@media.mit.edu)
% fast conv; see how much image is shifted over
% motion_estimation by fft methods: cross spectrum, CROSS SPECTRUM
%
% Example use: q=motion_cross_fft2(a,b); % should have a peak where motion is...
%              q=motion_cross_fft2(a,b,.5); % uses alternate exponent
%                                     default exponent is 1 (Girod method)
%
% experiments on using [trash,m,n]=max2(q) as a motion estimator show that:
% exponents from 0 to .3 give the same wrong answer
% exponents from .5 to 1 generally give the same right answer
%                .4 gave one wrong answer; .45 another wrong answer
%                .49 gave right answer
%
% Bugs: RUNS REALLY SLOW IF THERE IS NaN IN DATA (due to bug in Matlab's FFT)
%       workaround by using: motion_cross_fft2(A,chnan(B,0)), or the like
%
% used by est_trans_fft2
% (e.g. if you just want 2 numbers you want to use est_trans_fft2 and not this)

if nargin < 3
  disp('motion_cross_fft2: exponent defaulting to 1, so we have phase only')
  exponent = 1;
end%if

%disp('est_trans_fft2: about to do fft2 of each input')
%A = fft2(a);
%B = fft2(b);
disp('motion_cross_fft2.m: using add-hoc window (found far better than rect)')
[M,N]=size(a);
window=hanning(M)*hanning(N).';
A = fft2(a.*window);
B = fft2(b.*window);
%%%%B = fft2(rev(b));   % conj doesnt work quite right in 2D
                        % the phase shift seems to have effect???
                        % but this should not be a problem
% conj is like reversal in time domain
% Q = conj(B).*A./sqrt(A.*conj(A).*B.*conj(B));

if exponent == 1  % Girod method
  disp('motion_cross_fft2: about to mult FFTs and div by magnitudes (phase only)')
  Q = conj(B).*A./(abs(A).*abs(B));
end%if

if exponent == 0  % Autocorrelation method
  disp('motion_cross_fft2: about to mult FFTs (equiv to compute autocorrelation function)')
  Q = conj(B).*A;
end%if

if exponent == 2 % this is too much; what is the meaning???
                 % exponent should normally be 0 to 1 to be meaningful
  disp('motion_cross_fft: exponent normally be between 0 and 1 but will let you try 2')
  disp('motion_cross_fft2: about to mult conj and div by power spectra (too much div.)')
  Q = conj(B).*A./(A.*conj(A).*B.*conj(B));
end%if

if (exponent ~= 2) & (exponent ~= 1) & (exponent ~= 0)
  disp(sprintf('motion_cross_fft2: about to mult by conj and div by magnitudes^%g',exponent))
  Q = conj(B).*A./(abs(A).*abs(B)).^exponent;
end%if

if nargout == 0
  disp('motion_cross_fft2: no output arg. given so displaying images to screen')
  %dispmatb(log(real(q+max2(q)/1000000)))  % display as log image

  disp('motion_cross_fft2: about to take real part (imag part should be small)')
  q_noans = ifft2(Q);     % q should be real (e.g. imag part should be nearly 0)
  q_noans = real(q_noans);

  clg
  subplot(221)
  tvs(a)
  title('Reference frame')
  subplot(222)
  tvs(b)
  title('Comparison Frame')
  subplot(223)
  tvs(-q_noans)
  title('motion_cross_fft2 negated')
  subplot(224)
  disp('motion_cross_fft2: about to display fftshifted version')
  % log scale doesn't help         tvs(log(q+max2(q)/1000000))
  tvs(-fftshift(q_noans))
  title('motion_cross_fft2 fftshifted negated')
end%if

if nargout > 0
  q = ifft2(Q);     % q should be real (e.g. imag part should be nearly 0)
  q = real(q);
end%if

%dispmatb(log(real(q+max2(q)/1000000)))  % display as log image