1 简介哈夫曼编码是一种数据编码方式,以哈夫曼树--即最优二叉树.用带杈路径长度最小的二叉树,对数据进行重编码,经常应用于数据压缩.在计算机信息处理中,哈夫曼编码是一种一致性编码法(又称熵编码法),用于数据的无损压缩.本文主要介绍了基于哈夫曼编码图像压缩技术的原理、算法、过程,并利用matlab作为编程开发工具,开发了一个对256色BMP图像进行压缩.解压缩的软件系统,验证了算法的合理性和可行性.为了节省空间,在对数据进行编码时,可以对那些经常出现的数据指定较少的位数表示, 而那些不常出现的数据指定较多的位数表示,从而降低冗余,这样从总的效果看就节省了存储空间。基于哈夫曼编码图像压缩的基本原理是频繁使用的数据用较短的代码代替,较少使用的数据用较长的代码代替,每个数据的代码各不相同,这是一种典型的无损编码方式。这些代码都是二进制码,且码字长度是不均匀的、平均码率可以接近信息源熵值的一种编码。编码过程是先对图像数据扫描一遍, 计算出各种像素出现的概率,按概率的大小建立最优二叉树(二叉树的叶子节点刚好表示的图像中的某种像素)并给二叉树的每个分支赋特定权值(0或1), 然后通过遍历二叉树读取从根节点到叶子节点的路径权值字符串,即给每种像素指定了不同长度的唯一编码, 由此得到一张该图像所有像素的哈夫曼编码表。编码后的图像数据记录的是每个像素的码字,而码字与实际像素值的对应关系记录在码表中,码表是附在图像文件中的。基于哈夫曼编码图像压缩技术借用了热力学中的名词“熵”(Entropy) 来表示一条信息中真正需要编码的信息量:如考虑用0 和1组成的二进制数码为含有n个符号的某条信息编码,假设符号En在整条信息中重复出现的概率为Pn,则该符号的熵也即表2 部分代码function varargout MainForm(varargin) % MAINFORM MATLAB code for MainForm.fig % MAINFORM, by itself, creates a new MAINFORM or raises the existing % singleton*. % % H MAINFORM returns the handle to a new MAINFORM or the handle to % the existing singleton*. % % MAINFORM(CALLBACK,hObject,eventData,handles,...) calls the local % function named CALLBACK in MAINFORM.M with the given input arguments. % % MAINFORM(Property,Value,...) creates a new MAINFORM or raises the % existing singleton*. Starting from the left, property value pairs are % applied to the GUI before MainForm_OpeningFcn gets called. An % unrecognized property name or invalid value makes property application % stop. All inputs are passed to MainForm_OpeningFcn via varargin. % % *See GUI Options on GUIDEs 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 MainForm % Last Modified by GUIDE v2.5 19-May-2012 11:20:45 % Begin initialization code - DO NOT EDIT gui_Singleton 1; gui_State struct(gui_Name, mfilename, ... gui_Singleton, gui_Singleton, ... gui_OpeningFcn, MainForm_OpeningFcn, ... gui_OutputFcn, MainForm_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 MainForm is made visible. function MainForm_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 MainForm (see VARARGIN) % Choose default command line output for MainForm handles.output hObject; clc; % axis(handles.axes1); cla reset; box on; % set(gca, XTickLabel, , YTickLabel, ); % % axis(handles.axes2); cla reset; box on; % set(gca, XTickLabel, , YTickLabel, ); handles.Img 0; handles.ImgH 0; handles.ImgL 0; handles.strH 0; handles.strL 0; InitFig(hObject,handles); % Update handles structure guidata(hObject, handles); % UIWAIT makes MainForm wait for user response (see UIRESUME) % uiwait(handles.figure1); % --- Outputs from this function are returned to the command line. function varargout MainForm_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 File_Callback(hObject, eventdata, handles) % hObject handle to File (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function OpenFile_Callback(hObject, eventdata, handles) % hObject handle to OpenFile (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % 打开 warning off all; % 载入图像 [FileName,PathName,FilterIndex] uigetfile({*.bmp;*.jpg;*.tif;*.png;*.gif, ... 所有图像文件;... *.*,所有文件 },载入图像,... .\images\\lena.bmp); if isequal(FileName, 0) || isequal(PathName, 0) return; end InitFig(hObject, handles); Img imread(fullfile(PathName, FileName)); axes(handles.axes1); imshow(Img, []); handles.Img Img; handles.ImgH 0; handles.ImgL 0; guidata(hObject, handles); function textInfo_Callback(hObject, eventdata, handles) % hObject handle to textInfo (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 textInfo as text % str2double(get(hObject,String)) returns contents of textInfo as a double % --- Executes during object creation, after setting all properties. function textInfo_CreateFcn(hObject, eventdata, handles) % hObject handle to textInfo (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 SnapImg_Callback(hObject, eventdata, handles) % hObject handle to SnapImg (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % 截图 SnapImage(); % -------------------------------------------------------------------- function SaveImg_Callback(hObject, eventdata, handles) % hObject handle to SaveImg (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % 保存 if isequal(handles.ImgH, 0) isequal(handles.ImgL, 0) msgbox(请进行压缩处理, 提示信息); return; end if ~isequal(handles.ImgH, 0) SaveImage(handles.ImgH); end if ~isequal(handles.ImgL, 0) SaveImage(handles.ImgL); end msgbox(处理结果保存成功, 提示信息); % -------------------------------------------------------------------- function Exit_Callback(hObject, eventdata, handles) % hObject handle to Exit (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) close(); % -------------------------------------------------------------------- function CompressAlgorithm_Callback(hObject, eventdata, handles) % hObject handle to CompressAlgorithm (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function Huffman_Callback(hObject, eventdata, handles) % hObject handle to Huffman (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) if isequal(handles.Img, 0) msgbox(请载入图像, 提示信息); return; end if isequal(handles.ImgH, 0) dataImg handles.Img; if ndims(dataImg) 3 dataImg rgb2gray(dataImg);%灰度化处理 axes(handles.axes2); imshow( dataImg , []);%显示 end sz size(dataImg); [zipped,info] Mat2Huff(dataImg);%霍夫编码 unzipped Huff2Mat(zipped, info);%霍夫解码 dataImg double(reshape(dataImg, sz)); unzipped double(reshape(unzipped, sz)); info_dataImg whos(dataImg); info_zipped whos(zipped); info_unzipped whos(unzipped); S PSNR(dataImg, unzipped); str0 sprintf(-----------------霍夫曼压缩-----------------\n); str1 sprintf(原始数据维数为%s占用空间大小为%d\n, num2str(info_dataImg.size), info_dataImg.bytes); str2 sprintf(解压数据维数为%s占用空间大小为%d\n, num2str(info_unzipped.size), info_unzipped.bytes); str3 sprintf(压缩数据维数为%s占用空间大小为%d\n, num2str(info_zipped.size), info_zipped.bytes); str4 sprintf(压缩比为%.3f%%\n, info_zipped.bytes/info_dataImg.bytes*100); str5 sprintf(PSNR%.3f\n, S); strH [str0 str1 str2 str3 str4 str5]; set(handles.textInfo, String, strH); tm im2uint8(mat2gray(unzipped)); axes(handles.axes3); imshow(tm, []); handles.strH strH; handles.ImgH tm; guidata(hObject, handles); else set(handles.textInfo, String, handles.strH); axes(handles.axes2); imshow(mat2gray(handles.ImgH), []); end % -------------------------------------------------------------------- function Help_Callback(hObject, eventdata, handles) % hObject handle to Help (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % -------------------------------------------------------------------- function HisteqContrast_Callback(hObject, eventdata, handles) % hObject handle to HisteqContrast (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) % 直方图对比 if isequal(handles.ImgH, 0) isequal(handles.ImgL, 0) msgbox(请进行压缩处理, 提示信息); return; end if ~isequal(handles.ImgH, 0) HisteqContrast(handles.Img, handles.ImgH); end if ~isequal(handles.ImgL, 0) HisteqContrast(handles.Img, handles.ImgL); end % -------------------------------------------------------------------- function AlgorithmFlow_Callback(hObject, eventdata, handles) % hObject handle to AlgorithmFlow (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) str 图像压缩系统首先载入图像然后选择压缩算法比较压缩效果最后可以观察直方图对比效果。; msgbox(str, 提示信息); % -------------------------------------------------------------------- function About_Callback(hObject, eventdata, handles) % hObject handle to About (see GCBO) % eventdata reserved - to be defined in a future version of MATLAB % handles structure with handles and user data (see GUIDATA) msgbox(图像压缩系统采用霍夫曼算法, 提示信息);3 仿真结果4 参考文献[1]田端财, 殷晓丽. 基于哈夫曼编码的图像压缩技术研究[J]. 科技资讯, 2009(8):2.部分理论引用网络文献若有侵权联系博主删除。