function d=quadratic_form_distance(XI,XJ,A)
  % Implementation of the Quadratic form distance
  % (cf. "The Earth Movers' Distance as a Metric for Image Retrieval",
  %      Y. Rubner, C. Tomasi, L.J. Guibas, 2000)
  %
  % @author: B. Schauerte
  % @date:   2009
  % @url:    http://cvhci.anthropomatik.kit.edu/~bschauer/

  % Copyright 2009 B. Schauerte. All rights reserved.
  % 
  % Redistribution and use in source and binary forms, with or without 
  % modification, are permitted provided that the following conditions are 
  % met:
  % 
  %    1. Redistributions of source code must retain the above copyright 
  %       notice, this list of conditions and the following disclaimer.
  % 
  %    2. Redistributions in binary form must reproduce the above copyright 
  %       notice, this list of conditions and the following disclaimer in 
  %       the documentation and/or other materials provided with the 
  %       distribution.
  % 
  % THIS SOFTWARE IS PROVIDED BY B. SCHAUERTE ''AS IS'' AND ANY EXPRESS OR 
  % IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED 
  % WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE 
  % DISCLAIMED. IN NO EVENT SHALL B. SCHAUERTE OR CONTRIBUTORS BE LIABLE 
  % FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR 
  % CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF 
  % SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR 
  % BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, 
  % WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
  % OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
  % ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
  % 
  % The views and conclusions contained in the software and documentation
  % are those of the authors and should not be interpreted as representing 
  % official policies, either expressed or implied, of B. Schauerte.
  
	if nargin < 3
		error('Not enough arguments, i.e. similarity matrix is missing')
	end

  m=size(XJ,1); % number of samples of p
  p=size(XI,2); % dimension of samples
  
  assert(p == size(XJ,2)); % equal dimensions
  assert(size(XI,1) == 1); % pdist requires XI to be a single sample
  
  d=zeros(m,1); % initialize output array
  
	diff=zeros(1,p);
  for i=1:m
		diff=(XI - XJ(i,:));
		d(i) = sqrt( diff * A * diff' );
  end