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

一、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

二、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});
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 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 saturn
        img = saturn;
    case 'Tire',
        tire = [];
        load imdemos tire
        img = tire;
    case 'Pout',
        pout = [];
        load imdemos pout
        img = pout;
    case 'Trees',
        trees = [];
        load imdemos trees
        img = trees;
    case 'Quarter',
        quarter = [];
        load imdemos quarter
        img = quarter;
    case 'Circuit',
        circuit = [];
        load imdemos circuit
        img = circuit;
    case 'Rice',
        rice = [];
        load imdemos rice
        img = 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;

三、运行结果

四、备注

完整代码或者代写添加QQ 1564658423