一、簡(jiǎn)介

Gabor+SVM：利用Gabor程序?qū)崿F(xiàn)對(duì)人臉的特征提取，然后用SVM進(jìn)行分類；
1 Gabor
Gabor 特征提取算法可以在不同方向上描述局部人臉特征，對(duì)光照、遮擋以及表情變換等情況具有較強(qiáng)的魯棒性，即Gabor算法在異常和危險(xiǎn)情況下具有較強(qiáng)的系統(tǒng)生存的能力。

1.1 一維Gabor核：
其由一個(gè)高斯核與一個(gè)復(fù)數(shù)波的乘積定義為如下公式：

其中w(t)是高斯函數(shù)，s(t)是復(fù)數(shù)波，兩者的一維數(shù)學(xué)表達(dá)式定義如下：

我們將s(t)代入一維Gabor公式可得下式：

我們將上述一維情況推廣到二維
二維復(fù)數(shù)波定義如下，其中(x,y)表示空間域坐標(biāo)，(u0,v0)表示頻率域坐標(biāo)。

二維高斯函數(shù)定義如下，其中σx,σy 分別為在x，y兩個(gè)方向上的尺度參數(shù)，用來(lái)控制高斯函數(shù)在兩個(gè)方向上的“展布”形狀。(x0,y0)為高斯函數(shù)的中心點(diǎn)。K為高斯核的幅度的比例。

但是由于高斯函數(shù)還有旋轉(zhuǎn)的操作，所以我們對(duì)坐標(biāo)進(jìn)行如下的變換：

由此，我們得到了坐標(biāo)變換后的高斯函數(shù)公式，其中θ表示高斯核順時(shí)針旋轉(zhuǎn)的角度。

1.2 二維Gabor核
類似一維 Gabor 核，我們將二維高斯函數(shù)與二維復(fù)數(shù)波相乘，就得到了二維的Gabor核：

一個(gè)Gabor核能獲取到圖像某個(gè)頻率鄰域的響應(yīng)情況，這個(gè)響應(yīng)結(jié)果可以看做是圖像的一個(gè)特征。如果我們用多個(gè)不同頻率的Gabor核去獲取圖像在不同頻率鄰域的響應(yīng)情況，最后就能形成圖像在各個(gè)頻率段的特征，這個(gè)特征就可以描述圖像的頻率信息了。

下圖展示了一系列具有不同頻率的 Gabor 核，用這些核與圖像卷積，我們就能得到圖像上每個(gè)點(diǎn)和其附近區(qū)域的頻率分布情況。

經(jīng)過 Gabor 濾波獲到的人臉圖像信息包含實(shí)部和虛部?jī)刹糠?，分別代表不同局部的人臉特征信息，為了提取更加全面的人臉特征信息，一般會(huì)采用兩種特征值相結(jié)合的方法，比如幅值和相位信息。但 Gabor 的相位信息會(huì)因?yàn)槿四樋臻g位置發(fā)生改變而不太穩(wěn)定。Gabor 幅值信息變化相對(duì)穩(wěn)定，并且充分反映了人臉圖像的能量譜。因此采取 Gabor 幅值特征。經(jīng)過Gabor幅值特征處理，得到了人臉 Gabor 特征信息。5 個(gè)尺度，8 個(gè)方向的 Gabor 特征提取圖如下所示：

2 PCA+SVM：
2.1 PCA
主成分分析(Principal Component Analysis, 簡(jiǎn)稱PCA)是常用的一種降維方法.
算法步驟:

2.2 SVM介紹
支持向量機(jī)(Support Vector Machines, 簡(jiǎn)稱SVM)是一種二類分類模型.
劃分超平面為:

3 人臉識(shí)別步驟
將每張人臉圖片(m,nm,n)讀取并展開成(m×n,1m×n,1), 假設(shè)總有l(wèi)l張圖片, 所有排列到一起, 一列為一張圖片, 最終形成一個(gè)(m×n,l)(m×n,l) 的矩陣作為原始數(shù)據(jù);
數(shù)據(jù)中心化: 計(jì)算平均臉, 所有列都減去張平均臉;
計(jì)算矩陣的協(xié)方差矩陣/散布矩陣, 求出特征值及特征向量, 并將其從大到小排列取前K個(gè)特征; (到這步特征已將至K維)
計(jì)算中心化后的數(shù)據(jù)在K維特征的投影;
基于上一步的數(shù)據(jù)進(jìn)行 One-VS-One Multiclass SVM模型訓(xùn)練;
讀取用于測(cè)試的人臉圖片, 同訓(xùn)練圖片一樣處理;
利用訓(xùn)練出的模型對(duì)測(cè)試圖片進(jìn)行分類;
計(jì)算準(zhǔn)確率.

二、源代碼

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 pjimage_OpeningFcn gets called. ?An % ? ? ?unrecognized property name or invalid value makes property application % ? ? ?stop. ?All inputs are passed to pjimage_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 % 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 gui_Singleton = 1; gui_State = struct('gui_Name', ? ? ? mfilename, ... ? ? ? ? ? ? ? ? ? 'gui_Singleton', ?gui_Singleton, ... ? ? ? ? ? ? ? ? ? 'gui_OpeningFcn', @pjimage_OpeningFcn, ... ? ? ? ? ? ? ? ? ? 'gui_OutputFcn', ?@pjimage_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 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 m_file_Callback(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 m_file_open_Callback(hObject, eventdata, handles) % hObject ? ?handle to m_file_open (see GCBO) % eventdata ?reserved - to be defined in a future version of MATLAB % handles ? ?structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function m_file_save_Callback(hObject, eventdata, handles) % hObject ? ?handle to m_file_save (see GCBO) % eventdata ?reserved - to be defined in a future version of MATLAB % handles ? ?structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function m_file_exit_Callback(hObject, eventdata, handles) % hObject ? ?handle to m_file_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\人臉識(shí)別\人臉識(shí)別程序\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);%得到一個(gè)方向一個(gè)尺度的Gabor圖像 ? ? ? ? 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\人臉識(shí)別\人臉識(shí)別程序\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);%得到一個(gè)方向一個(gè)尺度的Gabor圖像 ? ? ? ? x = conv2(p,GK,'same');%原圖像與Gabor圖像進(jìn)行卷積 ? 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張圖片 for i = 1 : 40 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ?%40個(gè)人 ? ?for j = 1 : 7 ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? ? %每個(gè)人7張照片 ? ? ? ?a = imread(strcat('C:\Users\lenovo\Desktop\人臉識(shí)別\人臉識(shí)別程序\ORL\s', num2str(i),'\', num2str(j), '.pgm')); ? ? ? ?a = double(a); ? ? ? ?[m,n] = size(a); ? ? ? ? ? ? ? ?trainvector = GetOneImageVector(a); ? ? ? ?trainX(:, k) = trainvector; ? ? ? ?k = k + 1; ? ? ? ?%加標(biāo)簽 ? ? ? ? ? ?trainLabel = [trainLabel v]; ? ? ? ? ? ?%1X280 ? ?end ? ?v = v + 1; end %歸一化 ?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); %處理測(cè)試集 u = 1; t = 1; testLabel = []; for i = 1:40 ? ?for j = 8:10 ? ? ? ?a = imread(strcat('C:\Users\lenovo\Desktop\人臉識(shí)別\人臉識(shí)別程序\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、運(yùn)行結(jié)果

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