imMlGauss

 Calculates max likelihood params of Gaussian that gave rise to image G.

 Suppose G contains an image of a gaussian distribution.  One way to
 recover the parameters of the gaussian is to threshold the image, and
 then estimate the mean/covariance based on the coordinates of the
 thresholded points.  A better method is to do no thresholding and instead
 use all the coordinates, weighted by their value. This function does the
 latter, except in a very efficient manner since all computations are done
 in parallel over the entire image.

 This function works over 2D or 3D images.  It makes most sense when G in
 fact contains an image of a single gaussian, but a result will be
 returned regardless.  All operations are performed on abs(G) in case it
 contains negative or complex values.

 symmFlag is an optional flag that if set to 1 then imMlGauss recovers
 the maximum likelihood symmetric gaussian.  That is the variance in each
 direction is equal, and all covariance terms are 0.  If symmFlag is set
 to 2 and G is 3D, imMlGauss recovers the ML guassian with equal
 variance in the 1st 2 dimensions (row and col) and all covariance terms
 equal to 0, but a possibly different variance in the 3rd (z or t)
 dimension.

 USAGE
  varargout = imMlGauss( G, [symmFlag], [show] )

 INPUTS
  G        - image of a gaussian (weighted pixels)
  symmFlag - [0] see above
  show     - [0] figure to use for optional display

 OUTPUTS
  mu       - 2 or 3 element vector specifying the mean [row,col,z]
  C        - 2x2 or 3x3 covariance matrix [row,col,z]
  GR       - image of the recovered gaussian (faster if omitted)
  logl     - log likelihood of G given recov. gaussian (faster if omitted)

 EXAMPLE - 2D
  R = rotationMatrix( pi/6 );  C=R'*[10^2 0; 0 20^2]*R;
  G = filterGauss( [200, 300], [150,100], C, 0 );
  [mu,C,GR,logl] = imMlGauss( G, 0, 1 );
  mask = maskEllipse( size(G,1), size(G,2), mu, C );
  figure(2); im(mask)

 EXAMPLE - 3D
  R = rotationMatrix( [1,1,0], pi/4 );
  C = R'*[5^2 0 0; 0 2^2 0; 0 0 4^2]*R;
  G = filterGauss( [50,50,50], [25,25,25], C, 0 );
  [mu,C,GR,logl] = imMlGauss( G, 0, 1 );

 See also GAUSS2ELLIPSE, PLOTGAUSSELLIPSES, MASKELLIPSE

 Piotr's Computer Vision Matlab Toolbox      Version 2.0
 Copyright 2014 Piotr Dollar.  [pdollar-at-gmail.com]
 Licensed under the Simplified BSD License [see external/bsd.txt]