【图像几何】基于matlab GUI傅立叶+DCT图像变换【含Matlab源码 844期】

一、获取代码方式

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二、傅立叶+DCT简介

FFT(Fast Fourier transform)：快速傅里叶变换，是DFT的工程化实现方法。
DFT直接求解太过于复杂，FFT方法根据DFT求解过程中旋转因子的性质并引入分治算法思想，大大简化计算过程，被广泛应用在频谱分析的工程实践中，如matlab，C，C++，CUDA等底层实现

1 DFT简介
频谱分析是信号处理中的重要环节，从傅里叶变换FT，到拉普拉斯变换LT，离散时间傅里叶变换DTFT，Z变换ZT，到我们所讲的离散傅里叶变换DFT（他们之间的联系和区别见我的其他博客）。
相比于其他变换，DFT被广泛应用的原因是其输入的时域信号是离散的，输出的频域结果也是离散的。这就极大方便了我们进行基于计算机的频谱计算，存储和分析，没办法数字信号处理是大趋势。
DFT变换的公式为：

但为了分析方便，在FFT的计算过程中，我们依然使用k = 0 ∼ N − 1 k = 0 \sim N-1k=0∼N−1的选取策略。也即，如下：

2 旋转因子WWW的性质

3 FFT蝶形计算证明

4 FFT计算过程

三、部分源代码

function varargout = fushidctbianhuan(varargin)
% FUSHIDCTBIANHUAN M-file for fushidctbianhuan.fig
%      FUSHIDCTBIANHUAN, by itself, creates a new FUSHIDCTBIANHUAN or raises the existing
%      singleton*.
%
%      H = FUSHIDCTBIANHUAN returns the handle to a new FUSHIDCTBIANHUAN or the handle to
%      the existing singleton*.
%
%      FUSHIDCTBIANHUAN('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in FUSHIDCTBIANHUAN.M with the given input arguments.
%
%      FUSHIDCTBIANHUAN('Property','Value',...) creates a new FUSHIDCTBIANHUAN or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before fushidctbianhuan_OpeningFunction gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to fushidctbianhuan_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 fushidctbianhuan% Last Modified by GUIDE v2.5 06-Apr-2014 17:16:14% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @fushidctbianhuan_OpeningFcn, ...'gui_OutputFcn',  @fushidctbianhuan_OutputFcn, ...'gui_LayoutFcn',  [] , ...'gui_Callback',   []);
if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});
endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
elsegui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT% --- Executes just before fushidctbianhuan is made visible.
function fushidctbianhuan_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 fushidctbianhuan (see VARARGIN)
axes(handles.axes1);
img=imread('lena.bmp');
imshow(img);
axes(handles.axes2);
imgf=double(img);
imgs=fftshift(fft2(imgf));
imshow(log(1+abs(imgs)),[]);
set(handles.dct_radiobutton,'value',0);
set(handles.fft_radiobutton,'value',1);
% Choose default command line output for fushidctbianhuan
handles.output = hObject;% Update handles structure
guidata(hObject, handles);% UIWAIT makes fushidctbianhuan wait for user response (see UIRESUME)
% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.
function varargout = fushidctbianhuan_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 fft_radiobutton.
function fft_radiobutton_Callback(hObject, eventdata, handles)
% hObject    handle to fft_radiobutton (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
set(handles.dct_radiobutton,'value',0);
set(handles.fft_radiobutton,'value',1);
img = getimage(handles.axes1);
axes(handles.axes2);
imgf=double(img);
imgs=fftshift(fft2(imgf));
imshow(log(1+abs(imgs)),[]);set(handles.text2,'string','傅立叶变换谱');set(handles.text2,'fontsize',12);set(handles.text2,'fontname','宋体');set(handles.text2,'fontweight','bold');% Hint: get(hObject,'Value') returns toggle state of fft_radiobutton% --- Executes on button press in dct_radiobutton.
function dct_radiobutton_Callback(hObject, eventdata, handles)
% hObject    handle to dct_radiobutton (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
set(handles.dct_radiobutton,'value',1);
set(handles.fft_radiobutton,'value',0);
img = getimage(handles.axes1);
axes(handles.axes2);
imgd=img;
imgs=dct2(imgd);
imshow(log(abs(imgs)));
set(handles.text2,'string','DCT变换系数');
set(handles.text2,'fontsize',12);
set(handles.text2,'fontname','宋体');
set(handles.text2,'fontweight','bold');
% Hint: get(hObject,'Value') returns toggle state of dct_radiobutton% --- Executes on button press in close_button.
function close_button_Callback(hObject, eventdata, handles)
% hObject    handle to close_button (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
close(fushidctbianhuan);% --- Executes on selection change in fft_dct_pop.
function fft_dct_pop_Callback(hObject, eventdata, handles)
% hObject    handle to fft_dct_pop (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
val=get(hObject,'value');
str=get(hObject,'string');
switch str{val};case 'lena'lena = [];lena = imread('lena.bmp');img = lena;case 'Saturn',saturn = [];load imdemos saturnimg = saturn;case 'Tire',tire = [];load imdemos tireimg = tire;case 'Pout',pout = [];load imdemos poutimg = pout;case 'Trees',trees = [];load imdemos treesimg = trees;case 'Quarter',quarter = [];load imdemos quarterimg = quarter;case 'Circuit',circuit = [];load imdemos circuitimg = circuit;case 'Rice',rice = [];load imdemos riceimg = rice;case 'Fingerprint'fingerprint = [];fingerprint = imread('fingerprint.jpg');img = fingerprint;case 'Licenceplate'licenceplate = [];licenceplate = imread('licenceplate.jpg');img = licenceplate;case 'Haze'haze = [];haze = imread('haze.jpg');img = haze;case 'Cloudy'cloudy = [];cloudy = imread('cloudy.tif');img = cloudy;
end
axes(handles.axes1);
imshow(img);
control=get(handles.fft_radiobutton,'value');
switch control;

四、运行结果

五、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.
[5]陈浩,方勇,朱大洲,王成,陈子龙.基于蚁群算法的玉米植株热红外图像边缘检测[J].农机化研究. 2015,37(06)