一、简介

霍夫变换(Hough Transform)是图像处理中的一种特征提取技术，它通过一种投票算法检测具有特定形状的物体。该过程在一个参数空间中通过计算累计结果的局部最大值得到一个符合该特定形状的集合作为霍夫变换结果。霍夫变换于1962年由Paul Hough 首次提出[53]，后于1972年由Richard Duda和Peter Hart推广使用[54]，经典霍夫变换用来检测图像中的直线，后来霍夫变换扩展到任意形状物体的识别，多为圆和椭圆。

霍夫变换运用两个坐标空间之间的变换将在一个空间中具有相同形状的曲线或直线映射到另一个坐标空间的一个点上形成峰值，从而把检测任意形状的问题转化为统计峰值问题，上一节中已经介绍了车道的直线特征，本节中介绍hough变换检测直线的原理和检测结果。

我们知道，一条直线在直角坐标系下可以用y=kx+b表示, 霍夫变换的主要思想是将该方程的参数和变量交换，即用x,y作为已知量k,b作为变量坐标，所以直角坐标系下的直线y=kx+b在参数空间表示为点(k,b)，而一个点(x1,y1)在直角坐标系下表示为一条直线y1=x1·k+b，其中(k,b)是该直线上的任意点。为了计算方便，我们将参数空间的坐标表示为极坐标下的γ和θ。因为同一条直线上的点对应的(γ,θ)是相同的，因此可以先将图片进行边缘检测，然后对图像上每一个非零像素点，在参数坐标下变换为一条直线，那么在直角坐标下属于同一条直线的点便在参数空间形成多条直线并内交于一点。因此可用该原理进行直线检测。

如图 所示，对于原图内任一点(x,y)都可以在参数空间形成一条直线，以图中一条直线为例有参数(γ,θ)=(69.641,30°)，所有属于同一条直线上的点会在参数空间交于一点，该点即为对应直线的参数。由该图中所有直线所得到的(γ,θ)在参数空间中得到一系列对应曲线见图 霍夫统计变换结果。

二、源代码

function varargout = HoughObject(varargin)
% HOUGHOBJECT M-file for HoughObject.fig
%      HOUGHOBJECT, by itself, creates a new HOUGHOBJECT or raises the existing
%      singleton*.
%
%      H = HOUGHOBJECT returns the handle to a new HOUGHOBJECT or the handle to
%      the existing singleton*.
%
%      HOUGHOBJECT('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in HOUGHOBJECT.M with the given input arguments.
%
%      HOUGHOBJECT('Property','Value',...) creates a new HOUGHOBJECT or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before HoughObject_OpeningFunction gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to HoughObject_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 HoughObject

% Last Modified by GUIDE v2.5 07-Dec-2005 20:15:07

% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @HoughObject_OpeningFcn, ...
                   'gui_OutputFcn',  @HoughObject_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 HoughObject is made visible.
function HoughObject_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 HoughObject (see VARARGIN)

% Choose default command line output for HoughObject
handles.output = hObject;

% Update handles structure
guidata(hObject, handles);

% UIWAIT makes HoughObject wait for user response (see UIRESUME)
% uiwait(handles.figure1);


% --- Outputs from this function are returned to the command line.
function varargout = HoughObject_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 pbGenerate.
function pbGenerate_Callback(hObject, eventdata, handles)
% hObject    handle to pbGenerate (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
load ObjectTemplate
S1 = zeros(180,180);
Str = {'Sq','Sc','St'};

a = 1; b = 3;
x = round(a + (b-a) * rand(1));
S2 = eval(Str{x});

a = 1; b = 90;
x = round(a + (b-a) * rand(1));
S3 = imrotate(S2,x);

S = S1;
sz = size(S3);

a = 1; b = min(sz);
x = round(a + (b-a) * rand(1));


S(x:sz(1)+x-1,x:sz(2)+x-1)=S3;
S = im2bw(S);
axes(handles.axes1);

imshow(S);
title('Original Image');
handles.S = S;
guidata(hObject, handles);

三、运行结果

四、备注

版本：2014a
完整代码或代写加1564658423