# imMlGauss

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

## SYNOPSIS function varargout = imMlGauss( G, symmFlag, show )

## DESCRIPTION ``` 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 -  see above
show     -  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 );

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 );