一、简介
应用统计方法解决模式识别问题时，一再碰到的问题之一就是维数问题。在低维空间里解析上或计算上行得通的方法，在高维空间里往往行不通。因此，降低维数有时就会成为处理实际问题的关键。
1 问题描述：如何根据实际情况找到一条最好的、最易于分类的投影线，这就是Fisher判别方法所要解决的基本问题。
考虑把d维空间的样本投影到一条直线上，形成一维空间，即把维数压缩到一维。然而，即使样本在d维空间里形成若干紧凑的互相分得开的集群，当把它们投影到一条直线上时，也可能会是几类样本混在一起而变得无法识别。但是，在一般情况下，总可以找到某个方向，使在这个方向的直线上，样本的投影能分得开。下图可能会更加直观一点：
类效果。因此，上述寻找最佳投影方向的问题，在数学上就是寻找最好的变换向量w*的问题。
2 Fisher准则函数的定义
几个必要的基本参量：
2.1在d维X空间
（1）各类样本的均值向量mi
（2）样本类内离散度矩阵Si和总样本类内离散度矩阵Sw
其中Sw是对称半正定矩阵，而且当N>d时通常是非奇异的。（半正定矩阵：特征值都不小于零的实对称矩阵；非奇异矩阵：矩阵的行列式不为零）
（3）样本类间离散度矩阵Sb
Sb是对称半正定矩阵。
3.2 在一维Y空间
（1）各类样本的均值
（2）样本类内离散度 和总样本类内离散度
我们希望投影后，在一维Y空间中各类样本尽可能分得开些，即希望两类均值之差越大越好，同时希望各类样本内部尽量密集，即希望类内离散度越小越好。
Fisher准则函数定义
因此，
将上述各式代入JF(w)，可得：
其中Sb为样本类间离散度矩阵，Sw为总样本类内离散度矩阵。
4 最佳变换向量w*的求取
二、源代码
function varargout = faceCore(varargin)
% FACECORE M-file for faceCore.fig
% FACECORE, by itself, creates a new FACECORE or raises the existing
% singleton*.
%
% H = FACECORE returns the handle to a new FACECORE or the handle to
% the existing singleton*.
%
% FACECORE('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in FACECORE.M with the given input arguments.
%
% FACECORE('Property','Value',...) creates a new FACECORE or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before faceCore_OpeningFunction gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to faceCore_OpeningFcn via varargin.
%
% *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one
% instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES
% Copyright 2002-2003 The MathWorks, Inc.
% Edit the above text to modify the response to help faceCore
% Last Modified by GUIDE v2.5 28-May-2009 10:21:26
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @faceCore_OpeningFcn, ...
'gui_OutputFcn', @faceCore_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin && ischar(varargin{
1})
gui_State.gui_Callback = str2func(varargin{
1});
end
if nargout
[varargout{
1:nargout}] = gui_mainfcn(gui_State, varargin{
:});
else
gui_mainfcn(gui_State, varargin{
:});
end
% End initialization code - DO NOT EDIT
% --- Executes just before faceCore is made visible.
function faceCore_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% varargin command line arguments to faceCore (see VARARGIN)
% Choose default command line output for faceCore
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes faceCore wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = faceCore_OutputFcn(hObject, eventdata, handles)
% varargout cell array for returning output args (see VARARGOUT);
% hObject handle to figure
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Get default command line output from handles structure
varargout{
1} = handles.output;
% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
global TrainDatabasePath ;
TrainDatabasePath = uigetdir(strcat(matlabroot,'\work'), '训练库路径选择...' );
% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton2 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
global TestDatabasePath;
TestDatabasePath = uigetdir(strcat(matlabroot,'\work'), '测试库路径选择...');
% --- Executes on button press in pushbutton3.
%function pushbutton3_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton3 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
%[filename,pathname]=uigetfile({
'*.jpg';'*.bmp'},'');
%str=[pathname filename];
%im=imread(str);
%axes(handles.axes1);
%imshow(im);
% --- Executes on button press in pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton4 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
global TrainDatabasePath ;
global TestDatabasePath;
global T;
T = CreateDatabase(TrainDatabasePath);
%[m V_PCA V_Fisher ProjectedImages_Fisher] = FisherfaceCore(T);
% --- Executes on button press in pushbutton5.
function pushbutton9_Callback(hObject, eventdata, handles)
% hObject handle to pushbutton5 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
global im;
[filename,pathname]=uigetfile({
'*.jpg';'*.bmp'},'选择测试图片...');
str=[pathname filename];
im=imread(str);
axes(handles.axes1);
imshow(im);
function OutputName = Recognition(TestImage, m_database, V_PCA, V_Fisher, ProjectedImages_Fisher)
% Recognizing step....
%
% Description: This function compares two faces by projecting the images into facespace and
% measuring the Euclidean distance between them.
%
% Argument: TestImage - Path of the input test image
%
% m_database - (M*Nx1) Mean of the training database
% database, which is output of 'EigenfaceCore' function.
%
% V_PCA - (M*Nx(P-1)) Eigen vectors of the covariance matrix of
% the training database
% V_Fisher - ((P-1)x(C-1)) Largest (C-1) eigen vectors of matrix J = inv(Sw) * Sb
% ProjectedImages_Fisher - ((C-1)xP) Training images, which
% are projected onto Fisher linear space
%
% Returns: OutputName - Name of the recognized image in the training database.
%
% See also: RESHAPE, STRCAT
% Original version by Amir Hossein Omidvarnia, October 2007
% Email: aomidvar@ece.ut.ac.ir
Train_Number = size(ProjectedImages_Fisher,2);
%%%%%%%%%%%%%%%%%%%%%%%% Extracting the FLD features from test image
%InputImage = imread(TestImage);
temp=TestImage(:,:,1);
%temp = InputImage(:,:,1);
[irow icol] = size(temp);
InImage = reshape(temp',irow*icol,1);
Difference = double(InImage)-m_database; % Centered test image
ProjectedTestImage = V_Fisher' * V_PCA' * Difference; % Test image feature vector
三、运行结果
四、备注
完整代码或者代写添加QQ 912100926