function phi = invmoments(F)
%INVMOMENTS Compute invariant moments of image.
%   PHI = INVMOMENTS(F) computes the moment invariants of the image
%   F. PHI is a seven-element row vector containing the moment
%   invariants as defined in equations (11.3-17) through (11.3-23) of
%   Gonzalez and Woods, Digital Image Processing, 2nd Ed.
%
%   F must be a 2-D, real, nonsparse, numeric or logical matrix.

%   Copyright 2002-2004 R. C. Gonzalez, R. E. Woods, & S. L. Eddins
%   Digital Image Processing Using MATLAB, Prentice-Hall, 2004
%   $Revision: 1.5 $  $Date: 2003/11/21 14:39:19 $

if (ndims(F) ~= 2) | issparse(F) | ~isreal(F) | ~(isnumeric(F) | ...
                                                    islogical(F))
   error(['F must be a 2-D, real, nonsparse, numeric or logical ' ...
          'matrix.']); 
end

F = double(F);

phi = compute_phi(compute_eta(compute_m(F)));
  
%-------------------------------------------------------------------%
function m = compute_m(F)

[M, N] = size(F);
[x, y] = meshgrid(1:N, 1:M);
  
% Turn x, y, and F into column vectors to make the summations a bit
% easier to compute in the following.
x = x(:);
y = y(:);
F = F(:);
  
% DIP equation (11.3-12)
m.m00 = sum(F);
% Protect against divide-by-zero warnings.
if (m.m00 == 0)
   m.m00 = eps;
end
% The other central moments:  
m.m10 = sum(x .* F);
m.m01 = sum(y .* F);
m.m11 = sum(x .* y .* F);
m.m20 = sum(x.^2 .* F);
m.m02 = sum(y.^2 .* F);
m.m30 = sum(x.^3 .* F);
m.m03 = sum(y.^3 .* F);
m.m12 = sum(x .* y.^2 .* F);
m.m21 = sum(x.^2 .* y .* F);

%-------------------------------------------------------------------%
function e = compute_eta(m)

% DIP equations (11.3-14) through (11.3-16).

xbar = m.m10 / m.m00;
ybar = m.m01 / m.m00;

e.eta11 = (m.m11 - ybar*m.m10) / m.m00^2;
e.eta20 = (m.m20 - xbar*m.m10) / m.m00^2;
e.eta02 = (m.m02 - ybar*m.m01) / m.m00^2;
e.eta30 = (m.m30 - 3 * xbar * m.m20 + 2 * xbar^2 * m.m10) / m.m00^2.5;
e.eta03 = (m.m03 - 3 * ybar * m.m02 + 2 * ybar^2 * m.m01) / m.m00^2.5;
e.eta21 = (m.m21 - 2 * xbar * m.m11 - ybar * m.m20 + ...
           2 * xbar^2 * m.m01) / m.m00^2.5;
e.eta12 = (m.m12 - 2 * ybar * m.m11 - xbar * m.m02 + ...
           2 * ybar^2 * m.m10) / m.m00^2.5;

%-------------------------------------------------------------------% 
function phi = compute_phi(e)

% DIP equations (11.3-17) through (11.3-23).

phi(1) = e.eta20 + e.eta02;
phi(2) = (e.eta20 - e.eta02)^2 + 4*e.eta11^2;
phi(3) = (e.eta30 - 3*e.eta12)^2 + (3*e.eta21 - e.eta03)^2;
phi(4) = (e.eta30 + e.eta12)^2 + (e.eta21 + e.eta03)^2;
phi(5) = (e.eta30 - 3*e.eta12) * (e.eta30 + e.eta12) * ...
         ( (e.eta30 + e.eta12)^2 - 3*(e.eta21 + e.eta03)^2 ) + ...
         (3*e.eta21 - e.eta03) * (e.eta21 + e.eta03) * ...
         ( 3*(e.eta30 + e.eta12)^2 - (e.eta21 + e.eta03)^2 );
phi(6) = (e.eta20 - e.eta02) * ( (e.eta30 + e.eta12)^2 - ...
                                 (e.eta21 + e.eta03)^2 ) + ...
         4 * e.eta11 * (e.eta30 + e.eta12) * (e.eta21 + e.eta03);
phi(7) = (3*e.eta21 - e.eta03) * (e.eta30 + e.eta12) * ...
         ( (e.eta30 + e.eta12)^2 - 3*(e.eta21 + e.eta03)^2 ) + ...
         (3*e.eta12 - e.eta30) * (e.eta21 + e.eta03) * ...
         ( 3*(e.eta30 + e.eta12)^2 - (e.eta21 + e.eta03)^2 );