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）;

%-------------------------------------------------------------------%