【图像几何】基于matlab GUI图像空间变换（仿射变换）【含Matlab源码 841期】

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二、空间变换（仿射变换）简介

1 概念
在图像处理中的空间变换（spatial transformation）分成两种情况，有仿射变换（Affine Transformation）及投影变换（Perspective Transformation）。
仿射变换是从一个二维坐标变换到另一个二维坐标，它是一种线性变换，保持了图像的平行性和平直性，即在变换之后，原先图像中的直线与平行线还是保持一致。只是位置存在变化。仿射变换包括平移(Translation)、缩放（Scale）、翻转（Flip）、旋转（Rotation）和剪切(Shear)。
而投影变换则是指利用投影光束映射图像到投影面上，原始图像与变换后的图像存在着投影变换的关系。
对于数学上的表示而言，这两者都是一样的，始终存在着一个变换矩阵使得原图像与变换后的图像能够互相转换。

2 举个例子

如上图所示，假设f为原图像，g为变换后图像。
通过一定的变换关系，使得f变换到g。如果我们知道对应角点的坐标，则可以通过以下的式子进行推算。

三、部分源代码

function varargout = affine_trans(varargin)
% AFFINE_TRANS M-file for affine_trans.fig
%      AFFINE_TRANS, by itself, creates a new AFFINE_TRANS or raises the existing
%      singleton*.
%
%      H = AFFINE_TRANS returns the handle to a new AFFINE_TRANS or the handle to
%      the existing singleton*.
%
%      AFFINE_TRANS('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in AFFINE_TRANS.M with the given input arguments.
%
%      AFFINE_TRANS('Property','Value',...) creates a new AFFINE_TRANS or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before affine_trans_OpeningFunction gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to affine_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 affine_trans% Last Modified by GUIDE v2.5 21-May-2009 16:53:05% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @affine_trans_OpeningFcn, ...'gui_OutputFcn',  @affine_trans_OutputFcn, ...'gui_LayoutFcn',  [] , ...'gui_Callback',   []);
if nargin & isstr(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 affine_trans is made visible.
function affine_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 affine_trans (see VARARGIN)
f = checkerboard(50);
axes(handles.axes1);
imshow(f);
s = 0.8;
theta = pi/6;
T = [s*cos(theta) s*sin(theta) 0-s*sin(theta) s*cos(theta) 00          0          1];
tform = maketform('affine',T);
g = imtransform(f,tform,'nearest');
axes(handles.axes2);
imshow(g);
set(handles.theta_edit,'string',30);% Choose default command line output for affine_trans
handles.output = hObject;% Update handles structure
guidata(hObject, handles);% UIWAIT makes affine_trans wait for user response (see UIRESUME)
% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.
function varargout = affine_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 theta_edit_CreateFcn(hObject, eventdata, handles)
% hObject    handle to θ_edit (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 ispcset(hObject,'BackgroundColor','white');
elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
endfunction theta_edit_Callback(hObject, eventdata, handles)
% hObject    handle to θ_edit (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 θ_edit as text
%        str2double(get(hObject,'String')) returns contents of θ_edit as a double% --- Executes during object creation, after setting all properties.
function interpolate_pop_menu_CreateFcn(hObject, eventdata, handles)
% hObject    handle to interpolate_pop_menu (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 ispcset(hObject,'BackgroundColor','white');
elseset(hObject,'BackgroundColor',get(0,'defaultUicontrolBackgroundColor'));
end% --- Executes on selection change in interpolate_pop_menu.
function interpolate_pop_menu_Callback(hObject, eventdata, handles)
% hObject    handle to interpolate_pop_menu (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 interpolate_pop_menu contents as cell array
%        contents{get(hObject,'Value')} returns selected item from interpolate_pop_menu

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)