一、简介
1974年,法国工程师J.Morlet首先提出小波变换的概念,1986年著名数学家Y.Meyer偶然构造出一个真正的小波基,并与S.Mallat合作建立了构造小波基的多尺度分析之后,小波分析才开始蓬勃发展起来。小波分析的应用领域十分广泛,在数学方面,它已用于数值分析、构造快速数值方法、曲线曲面构造、微分方程求解、控制论等。在信号分析方面的滤波、去噪声、压缩、传递等。在图像处理方面的图像压缩、分类、识别与诊断,去噪声等。本章将着重阐述小波在图像中的应用分析。
1 小波变换原理
小波分析是一个比较难的分支,用户采用小波变换,可以实现图像压缩,振动信号的分解与重构等,因此在实际工程上应用较广泛。小波分析与Fourier变换相比,小波变换是空间域和频率域的局部变换,因而能有效地从信号中提取信息。小波变换通过伸缩和平移等基本运算,实现对信号的多尺度分解与重构,从而很大程度上解决了Fourier变换带来的很多难题。
小波分析作一个新的数学分支,它是泛函分析、Fourier分析、数值分析的完美结晶;小波分析也是一种“时间—尺度”分析和多分辨分析的新技术,它在信号分析、语音合成、图像压缩与识别、大气与海洋波分析等方面的研究,都有广泛的应用。
(1)小波分析用于信号与图像压缩。小波压缩的特点是压缩比高,压缩速度快,压缩后能保持信号与图像的特征不变,且在传递中能够抗干扰。基于小波分析的压缩方法很多,具体有小波压缩,小波包压缩,小波变换向量压缩等。
(2)小波也可以用于信号的滤波去噪、信号的时频分析、信噪分离与提取弱信号、求分形指数、信号的识别与诊断以及多尺度边缘检测等。
(3)小波分析在工程技术等方面的应用概括的包括计算机视觉、曲线设计、湍流、远程宇宙的研究与生物医学方面。
2 多尺度分析
3 图像的分解和量化
4 图像压缩编码
5 图像编码评价
二、源代码
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 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 MainForm
% Last Modified by GUIDE v2.5 01-May-2021 22:52:25
% 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;
axes(handles.axes1); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
axes(handles.axes2); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
axes(handles.axes3); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
% 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;
% --- 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)
clc;
axes(handles.axes1); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
axes(handles.axes2); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
axes(handles.axes3); cla reset; box on; set(gca, 'XTickLabel', '', 'YTickLabel', '');
handles.file1 = [];
handles.file2 = [];
handles.result = [];
[filename, pathname] = uigetfile({'*.jpg;*.bmp;*.tif;*.png;*.gif', 'All Image Files';...
'*.*', 'All Files' }, '选择图像1', ...
fullfile(pwd, 'images\\实验图像1\\a.tif'));
if isequal(filename, 0)
return;
end
handles.file1 = fullfile(pathname, filename);
Img1=imread(fullfile(pathname, filename));
% I=rgb2gray(Img);
% Img1 = imresize(I,[240,320]);
axes(handles.axes1);
imshow(Img1, []);
handles.Img1 =Img1 ;
guidata(hObject, handles);
% --- 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)
[filename, pathname] = uigetfile({'*.jpg;*.bmp;*.tif;*.png;*.gif', 'All Image Files';...
'*.*', 'All Files' }, '选择图像2', ...
fullfile(pwd, 'images\\实验图像1\\b.tif'));
if isequal(filename, 0)
return;
end
handles.file2 = fullfile(pathname, filename);
Img2 =imread(fullfile(pathname, filename));
axes(handles.axes2);
imshow(Img2, []);
handles.Img2 =Img2 ;
guidata(hObject, handles);
% --- 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)
%% 小波变换算法
imA = handles.Img1;
imB = handles.Img2;
M1 = double(imA) / 256;
M2 = double(imB) / 256;
zt = 2;
wtype = 'haar';
[c0, s0] = Wave_Decompose(M1, zt, wtype);
[c1, s1] = Wave_Decompose(M2, zt, wtype);
Coef_Fusion = Fuse_Process(c0, c1, s0, s1);
Y = Wave_Reconstruct(Coef_Fusion, s0, wtype);
handles.result = im2uint8(mat2gray(Y));
guidata(hObject, handles);
msgbox('小波融合处理完毕!', '提示信息', 'modal');
% if isempty(handles.result)
% msgbox('请进行填充处理!', '提示信息', 'modal');
% return;
% end
axes(handles.axes3);
imshow(handles.result, []);
title('小波变换融合处理结果')
% --- 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)
%% 拉普拉斯金字塔算法
addpath('./拉普拉斯金字塔算法图像融合')
imA = handles.Img1;
imB = handles.Img2;
% im1 = double(imA) / 256;
% im2= double(imB) / 256;
im1 = double(imA);
im2 = double(imB);
%%
%拉普拉斯滤波器
w = [1 4 6 4 1; 4 16 24 16 4; 6 24 36 24 6; 4 16 24 16 4; 1 4 6 4 1]/256;
G = cell(1,5);
H = cell(1,5);
I = cell(1,5);
G{1} = im1;%第一层为原图像
H{1} = im2;
function Y = Wave_Reconstruct(Coef_Fusion, s, wtype)
if nargin < 3
end
Y = waverec2(Coef_Fusion, s, wtype);
KK = size(c1);
Coef_Fusion = zeros(1, KK(2));
Coef_Fusion(1:s1(1,1)*s1(1,2)) = (c0(1:s1(1,1)*s1(1,2))+c1(1:s1(1,1)*s1(1,2)))/2;
MM1 = c0(s1(1,1)*s1(1,2)+1:KK(2));
MM2 = c1(s1(1,1)*s1(1,2)+1:KK(2));
mm = (abs(MM1)) > (abs(MM2));
Y = (mm.*MM1) + ((~mm).*MM2);
三、运行结果
四、matlab版本及参考文献
1 matlab版本
2014a
2 参考文献
[1] 蔡利梅.MATLAB图像处理——理论、算法与实例分析[M].清华大学出版社,2020.
[2]杨丹,赵海滨,龙哲.MATLAB图像处理实例详解[M].清华大学出版社,2013.
[3]周品.MATLAB图像处理与图形用户界面设计[M].清华大学出版社,2013.
[4]刘成龙.精通MATLAB图像处理[M].清华大学出版社,2015.