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?）?+?...

?屬性????????????大小?????日期????時間???名稱
-----------?---------??----------?-----??----
?????目錄???????????0??2013-03-13?00:50??樹葉識別GUI+語音播報+文字識別\
?????文件???????20255??2017-02-14?15:19??樹葉識別GUI+語音播報+文字識別\1.png
?????文件???????11175??2017-02-14?15:55??樹葉識別GUI+語音播報+文字識別\2.png
?????文件???????11290??2017-02-14?16:00??樹葉識別GUI+語音播報+文字識別\3.png
?????文件???????26114??2017-02-15?11:48??樹葉識別GUI+語音播報+文字識別\4.png
?????文件???????62539??2017-02-15?11:49??樹葉識別GUI+語音播報+文字識別\5.png
?????文件???????44190??2017-02-15?11:50??樹葉識別GUI+語音播報+文字識別\6.png
?????文件???????23552??2019-03-13?00:09??樹葉識別GUI+語音播報+文字識別\Matlab課題說明推薦.doc
?????文件???????80044??2017-02-14?15:52??樹葉識別GUI+語音播報+文字識別\baiheye.wav
?????文件???????41526??2013-03-13?00:23??樹葉識別GUI+語音播報+文字識別\f.mat
?????文件???????80044??2017-02-14?15:49??樹葉識別GUI+語音播報+文字識別\fengye.wav
?????文件????????3319??2012-12-12?15:37??樹葉識別GUI+語音播報+文字識別\invmoments.m
?????文件???????80044??2017-02-14?15:51??樹葉識別GUI+語音播報+文字識別\lingye.wav
?????文件???????13485??2013-03-13?00:25??樹葉識別GUI+語音播報+文字識別\shuyeshibie.fig
?????文件????????7318??2013-03-13?00:25??樹葉識別GUI+語音播報+文字識別\shuyeshibie.m
?????文件??????456772??2006-12-29?18:54??樹葉識別GUI+語音播報+文字識別\train_1.tif
?????文件???????98456??2006-12-29?19:11??樹葉識別GUI+語音播報+文字識別\train_2.tif
?????文件?????1156394??2006-12-30?16:11??樹葉識別GUI+語音播報+文字識別\train_3.tif
?????文件??????162316??2013-03-13?00:20??樹葉識別GUI+語音播報+文字識別\運行截圖.png