【人脸识别】基于 Gabor+SV和PCA+SVM实现人脸识别matlab源码含 GUI

一、简介

Gabor+SVM：利用Gabor程序实现对人脸的特征提取，然后用SVM进行分类；\ 1 Gabor\ Gabor 特征提取算法可以在不同方向上描述局部人脸特征，对光照、遮挡以及表情变换等情况具有较强的鲁棒性，即Gabor算法在异常和危险情况下具有较强的系统生存的能力。

1.1 一维Gabor核：\ 其由一个高斯核与一个复数波的乘积定义为如下公式：\ \ 其中w(t)是高斯函数，s(t)是复数波，两者的一维数学表达式定义如下：\ \ 我们将s(t)代入一维Gabor公式可得下式：\ \ 我们将上述一维情况推广到二维\ 二维复数波定义如下，其中(x,y)表示空间域坐标，(u0,v0)表示频率域坐标。\ \ 二维高斯函数定义如下，其中σx,σy 分别为在x，y两个方向上的尺度参数，用来控制高斯函数在两个方向上的“展布”形状。(x0,y0)为高斯函数的中心点。K为高斯核的幅度的比例。\ \ 但是由于高斯函数还有旋转的操作，所以我们对坐标进行如下的变换：\ \ 由此，我们得到了坐标变换后的高斯函数公式，其中θ表示高斯核顺时针旋转的角度。\ \ 1.2 二维Gabor核\ 类似一维 Gabor 核，我们将二维高斯函数与二维复数波相乘，就得到了二维的Gabor核：\ \ 一个Gabor核能获取到图像某个频率邻域的响应情况，这个响应结果可以看做是图像的一个特征。如果我们用多个不同频率的Gabor核去获取图像在不同频率邻域的响应情况，最后就能形成图像在各个频率段的特征，这个特征就可以描述图像的频率信息了。

下图展示了一系列具有不同频率的 Gabor 核，用这些核与图像卷积，我们就能得到图像上每个点和其附近区域的频率分布情况。\ \ 经过 Gabor 滤波获到的人脸图像信息包含实部和虚部两部分，分别代表不同局部的人脸特征信息，为了提取更加全面的人脸特征信息，一般会采用两种特征值相结合的方法，比如幅值和相位信息。但 Gabor 的相位信息会因为人脸空间位置发生改变而不太稳定。Gabor 幅值信息变化相对稳定，并且充分反映了人脸图像的能量谱。因此采取 Gabor 幅值特征。经过Gabor幅值特征处理，得到了人脸 Gabor 特征信息。5 个尺度，8 个方向的 Gabor 特征提取图如下所示：\

2 PCA+SVM：\ 2.1 PCA\ 主成分分析(Principal Component Analysis, 简称PCA)是常用的一种降维方法.\ 算法步骤:\ \ 2.2 SVM介绍\ 支持向量机(Support Vector Machines, 简称SVM)是一种二类分类模型.\ 划分超平面为:\ \ \ 3 人脸识别步骤\ 将每张人脸图片(m,nm,n)读取并展开成(m×n,1m×n,1), 假设总有ll张图片, 所有排列到一起, 一列为一张图片, 最终形成一个(m×n,l)(m×n,l) 的矩阵作为原始数据;\ 数据中心化: 计算平均脸, 所有列都减去张平均脸;\ 计算矩阵的协方差矩阵/散布矩阵, 求出特征值及特征向量, 并将其从大到小排列取前K个特征; (到这步特征已将至K维)\ 计算中心化后的数据在K维特征的投影;\ 基于上一步的数据进行 One-VS-One Multiclass SVM模型训练;\ 读取用于测试的人脸图片, 同训练图片一样处理;\ 利用训练出的模型对测试图片进行分类;\ 计算准确率.

二、源代码

``` function varargout = pjimage(varargin) % PJIMAGE MATLAB code for pjimage.fig % PJIMAGE, by itself, creates a new PJIMAGE or raises the existing % singleton. % % H = PJIMAGE returns the handle to a new PJIMAGE or the handle to % the existing singleton. % % PJIMAGE('CALLBACK',hObject,eventData,handles,...) calls the local % function named CALLBACK in PJIMAGE.M with the given input arguments. % % PJIMAGE('Property','Value',...) creates a new PJIMAGE or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before pjimageOpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to pjimageOpeningFcn via varargin. % % *See GUI Options on GUIDE's Tools menu. Choose "GUI allows only one % instance to run (singleton)". % % See also: GUIDE, GUIDATA, GUIHANDLES

% Edit the above text to modify the response to help pjimage

% Last Modified by GUIDE v2.5 11-Jun-2018 08:06:08

% Begin initialization code - DO NOT EDIT guiSingleton = 1; guiState = struct('guiName', mfilename, ... 'guiSingleton', guiSingleton, ... 'guiOpeningFcn', @pjimageOpeningFcn, ... 'guiOutputFcn', @pjimageOutputFcn, ... 'guiLayoutFcn', [] , ... 'guiCallback', []); if nargin && ischar(varargin{1}) guiState.gui_Callback = str2func(varargin{1}); end

if nargout [varargout{1:nargout}] = guimainfcn(guiState, varargin{:}); else guimainfcn(guiState, varargin{:}); end % End initialization code - DO NOT EDIT

% --- Executes just before pjimage is made visible. function pjimage_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 pjimage (see VARARGIN)

% Choose default command line output for pjimage handles.output = hObject;

% Update handles structure guidata(hObject, handles);

% UIWAIT makes pjimage wait for user response (see UIRESUME) % uiwait(handles.figure_pjimage);

% --- Outputs from this function are returned to the command line. function varargout = pjimage_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;

% -------------------------------------------------------------------- function mfileCallback(hObject, eventdata, handles) % hObject handle to m_file (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% -------------------------------------------------------------------- function mfileopenCallback(hObject, eventdata, handles) % hObject handle to mfile_open (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% -------------------------------------------------------------------- function mfilesaveCallback(hObject, eventdata, handles) % hObject handle to mfile_save (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% -------------------------------------------------------------------- function mfileexitCallback(hObject, eventdata, handles) % hObject handle to mfile_exit (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% --- 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) figure(1); for i = 1:40 a = imread(strcat('C:\Users\lenovo\Desktop\人脸识别\人脸识别程序\ORL\s', num2str(i), '\1.pgm')); subplot(5,8,i); imshow(a); end

% --- 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) figure(2); r = round(112 / 2); c = round(92 / 2); gamma = 0.5; theta = pi / 8; a = sqrt(2); fmax = 0.22; for u = 0 : 4 f = a ^ (-u) * fmax; lambda = 1 / f; for v = 0 : 7 sigma = 0.56 * lambda; GK = getGaborKernel(r ,c ,v * theta ,sigma ,lambda ,gamma);%得到一个方向一个尺度的Gabor图像 subplot(5,8, u*8 + v + 1); imshow(GK); end end

% --- 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) p = imread('C:\Users\lenovo\Desktop\人脸识别\人脸识别程序\ORL\s1\1.pgm'); p = double(p); [m , n] = size(p); r = round(m / 2); c = round(n / 2); gamma = 0.5; theta = pi / 8; a = sqrt(2); fmax = 0.22; figure(3); for u = 0 : 4 f = a ^ (-u) * fmax; lambda = 1 / f; for v = 0 : 7 sigma = 0.56 * lambda; GK = getGaborKernel(r ,c ,v * theta ,sigma ,lambda ,gamma);%得到一个方向一个尺度的Gabor图像 x = conv2(p,GK,'same');%原图像与Gabor图像进行卷积 112 92 subplot(5, 8, u*8 + v +1); imshow(x); end end

% --- Executes during object deletion, before destroying properties. function axes1_DeleteFcn(hObject, eventdata, handles) % hObject handle to axes1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

function edit1_Callback(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of edit1 as text % str2double(get(hObject,'String')) returns contents of edit1 as a double

% --- Executes during object creation, after setting all properties. function edit1_CreateFcn(hObject, eventdata, handles) % hObject handle to edit1 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

function edit2_Callback(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA)

% Hints: get(hObject,'String') returns contents of edit2 as text % str2double(get(hObject,'String')) returns contents of edit2 as a double

% --- Executes during object creation, after setting all properties. function edit2_CreateFcn(hObject, eventdata, handles) % hObject handle to edit2 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles empty - handles not created until after all CreateFcns called

% Hint: edit controls usually have a white background on Windows. % See ISPC and COMPUTER. if ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor')) set(hObject,'BackgroundColor','white'); end

% --- Executes on button press in pushbutton6. function pushbutton6_Callback(hObject, eventdata, handles) % hObject handle to pushbutton6 (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) global ttlabel; global prelabel; % global ct; % global gam; trainLabel = []; k = 1; v = 1; %共280张图片 for i = 1 : 40 %40个人 for j = 1 : 7 %每个人7张照片 a = imread(strcat('C:\Users\lenovo\Desktop\人脸识别\人脸识别程序\ORL\s', num2str(i),'\', num2str(j), '.pgm')); a = double(a); [m,n] = size(a);

trainvector = GetOneImageVector(a);
    trainX(:, k) = trainvector;
    k = k + 1;
    %加标签    
    trainLabel = [trainLabel v];            %1X280
end
v = v + 1;

end %归一化 均值向量 方差向量
trainx = Normalize(trainX); %6440X280

% ct =str2double(get(handles.edit3,'String')); % gam = str2double(get(handles.edit4,'String')); %使用SVM得到模型

model = svmtrain(trainLabel', trainx','-s 0 -t 2 -c 1000 -g 0.0001'); % set(handles.edit1,'string',model); %处理测试集 u = 1; t = 1; testLabel = []; for i = 1:40 for j = 8:10 a = imread(strcat('C:\Users\lenovo\Desktop\人脸识别\人脸识别程序\ORL\s', num2str(i),'\', num2str(j), '.pgm')); a = double(a); [m,n] = size(a);

testvector = GetOneImageVector(a);
    testX(:, u) = testvector;
    u = u + 1;
    testLabel = [testLabel t];
end
 t = t + 1;

end ```

三、运行结果

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