一、简介
两维情况下radon变换大致可以这样理解：一个平面内沿不同的直线（直线与原点的距离为d，方向角为alfa）对f（x，y）做线积分，得到的像F(d,alfa)就是函数f的Radon变换。也就是说，平面（d，alfa）的每个点的像函数值对应了原始函数的某个线积分值。一个更直观的理解是，假设你的手指被一个很强的平行光源透射，你迎着光源看到的手指图像就是手指的光衰减系数的三维Radon变换（小小的推广）在给定方向（两个角坐标）的时候的值。
二、源代码
function varargout = Radon_trans(varargin)
% RADON_TRANS M-file for Radon_trans.fig
% RADON_TRANS, by itself, creates a new RADON_TRANS or raises the existing
% singleton*.
%
% H = RADON_TRANS returns the handle to a new RADON_TRANS or the handle to
% the existing singleton*.
%
% RADON_TRANS('CALLBACK',hObject,eventData,handles,...) calls the local
% function named CALLBACK in RADON_TRANS.M with the given input arguments.
%
% RADON_TRANS('Property','Value',...) creates a new RADON_TRANS or raises the
% existing singleton*. Starting from the left, property value pairs are
% applied to the GUI before Radon_trans_OpeningFunction gets called. An
% unrecognized property name or invalid value makes property application
% stop. All inputs are passed to Radon_trans_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 Radon_trans
% Last Modified by GUIDE v2.5 12-Jun-2009 20:15:52
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name', mfilename, ...
'gui_Singleton', gui_Singleton, ...
'gui_OpeningFcn', @Radon_trans_OpeningFcn, ...
'gui_OutputFcn', @Radon_trans_OutputFcn, ...
'gui_LayoutFcn', [] , ...
'gui_Callback', []);
if nargin & isstr(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 Radon_trans is made visible.
function Radon_trans_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 Radon_trans (see VARARGIN)
axes(handles.axes1);
img=imread('lena.bmp');
imshow(img);
axes(handles.axes2);
theta=0:180;
[R,xp]=radon(img,theta);
imagesc(theta,xp,R);
axes(handles.axes3);
[R,xp]=radon(img,[0 45]);
plot(xp,R(:,1));
axes(handles.axes4);
[R,xp]=radon(img,[0 45]);
plot(xp,R(:,2));
% Choose default command line output for Radon_trans
handles.output = hObject;
% Update handles structure
guidata(hObject, handles);
% UIWAIT makes Radon_trans wait for user response (see UIRESUME)
% uiwait(handles.figure1);
% --- Outputs from this function are returned to the command line.
function varargout = Radon_trans_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 during object creation, after setting all properties.
function popupmenu1_CreateFcn(hObject, eventdata, handles)
% hObject handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles empty - handles not created until after all CreateFcns called
% Hint: popupmenu controls usually have a white background on Windows.
% See ISPC and COMPUTER.
if ispc
set(hObject,'BackgroundColor','white');
else
set(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end
% --- Executes on selection change in popupmenu1.
function popupmenu1_Callback(hObject, eventdata, handles)
% hObject handle to popupmenu1 (see GCBO)
% eventdata reserved - to be defined in a future version of MATLAB
% handles structure with handles and user data (see GUIDATA)
% Hints: contents = get(hObject,'String') returns popupmenu1 contents as cell array
% contents{get(hObject,'Value')} returns selected item from popupmenu1
val=get(hObject,'value');
str=get(hObject,'string');
switch str{val};
case 'lena'
lena = [];
lena = imread('lena.bmp');
img = lena;
case 'cameraman'
cameraman=[];
cameraman=imread('cameraman.tif');
img=cameraman;
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);
axes(handles.axes2);
theta=0:180;
[R,xp]=radon(img,theta);
imagesc(theta,xp,R);
axes(handles.axes3);
[R,xp]=radon(img,[0 45]);
plot(xp,R(:,1));
axes(handles.axes4);
[R,xp]=radon(img,[0 45]);
plot(xp,R(:,2));
% --- 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(Radon_trans);
三、运行结果
