数学形态学操作可以分为二值形态学和灰度形态学,灰度形态学由二值形态学扩展而来。数学形态学有2个基本的运算,即腐蚀和膨胀,而腐蚀和膨胀通过结合又形成了开运算和闭运算。
开运算就是先腐蚀再膨胀,闭运算就是先膨胀再腐蚀。

  • 二值形态学

粗略的说,腐蚀可以使目标区域范围“变小”,其实质造成图像的边界收缩,可以用来消除小且无意义的目标物。式子表达为:

【图像识别】路面裂缝识别含GUI源码_图像识别
该式子表示用结构B腐蚀A,需要注意的是B中需要定义一个原点,【而B的移动的过程与卷积核移动的过程一致,同卷积核与图像有重叠之后再计算一样】当B的原点平移到图像A的像元(x,y)时,如果B在(x,y)处,完全被包含在图像A重叠的区域,(也就是B中为1的元素位置上对应的A图像值全部也为1)则将输出图像对应的像元(x,y)赋值为1,否则赋值为0。
我们看一个演示图。

【图像识别】路面裂缝识别含GUI源码_图像识别_02
B依顺序在A上移动(和卷积核在图像上移动一样,然后在B的覆盖域上进行形态学运算),当其覆盖A的区域为[1,1;1,1]或者[1,0;1,1]时,(也就是B中‘1’是覆盖区域的子集)对应输出图像的位置才会为1。

  • 膨胀

粗略地说,膨胀会使目标区域范围“变大”,将于目标区域接触的背景点合并到该目标物中,使目标边界向外部扩张。作用就是可以用来填补目标区域中某些空洞以及消除包含在目标区域中的小颗粒噪声。【图像识别】路面裂缝识别含GUI源码_图像识别_03
该式子表示用结构B膨胀A,将结构元素B的原点平移到图像像元(x,y)位置。如果B在图像像元(x,y)处与A的交集不为空(也就是B中为1的元素位置上对应A的图像值至少有一个为1),则输出图像对应的像元(x,y)赋值为1,否则赋值为0。
演示图为:【图像识别】路面裂缝识别含GUI源码_图像识别_04

function varargout = Gui_Main(varargin)
% GUI_MAIN M-file for Gui_Main.fig
%      GUI_MAIN, by itself, creates a new GUI_MAIN or raises the existing
%      singleton*.
%
%      H = GUI_MAIN returns the handle to a new GUI_MAIN or the handle to
%      the existing singleton*.
%
%      GUI_MAIN('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in GUI_MAIN.M with the given input arguments.
%
%      GUI_MAIN('Property','Value',...) creates a new GUI_MAIN or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before Gui_Main_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to Gui_Main_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 Gui_Main
 
% Last Modified by GUIDE v2.5 29-Mar-2011 22:28:58
 
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
    'gui_Singleton',  gui_Singleton, ...
    'gui_OpeningFcn', @Gui_Main_OpeningFcn, ...
    'gui_OutputFcn',  @Gui_Main_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 Gui_Main is made visible.
function Gui_Main_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 Gui_Main (see VARARGIN)
 
% Choose default command line output for Gui_Main
handles.output = hObject;
handles.Result = [];
handles.File = [];
% Update handles structure
guidata(hObject, handles);
clc; warning off all;
InitAxes(handles);
 
% UIWAIT makes Gui_Main wait for user response (see UIRESUME)
% uiwait(handles.figure1);
 
 
% --- Outputs from this function are returned to the command line.
function varargout = Gui_Main_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 pushbuttonOpenFile.
function pushbuttonOpenFile_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonOpenFile (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
[filename, pathname] = uigetfile({'*.jpg;*.tif;*.png;*.gif;*.bmp','All Image Files';...
    '*.*','All Files' },'载入图像',...
    fullfile(pwd, 'images'));
if isequal(filename, 0) || isequal(pathname, 0)
    return;
end
I = imread(fullfile(pathname, filename));
Result = Process_Main(I);
handles.File = fullfile(pathname, filename);
handles.Result = Result;
guidata(hObject, handles);
InitAxes(handles)
axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
 
 
% --- Executes on button press in pushbuttonHisteq.
function pushbuttonHisteq_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonHisteq (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.hist); title('直方图均衡化图像');
end
 
 
 
% --- Executes on button press in pushbuttonMedfilt.
function pushbuttonMedfilt_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonMedfilt (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.Medfilt); title('中值滤波图像');
end
 
 
% --- Executes on button press in pushbuttonBw.
function pushbuttonBw_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonBw (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.Bw); title('二值图像');
end
 
% --- Executes on button press in pushbuttonEnance.
function pushbuttonEnance_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonEnance (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.Enance); title('增强图像');
end
 
% --- Executes on button press in pushbuttonBwfilter.
function pushbuttonBwfilter_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonBwfilter (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.Bw); title('二值图像');
    axes(handles.axes3); imshow(handles.Result.BwFilter); title('二值图像滤波');
end
 
% --- Executes on button press in pushbuttonCrackRec.
function pushbuttonCrackRec_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonCrackRec (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.Bw); title('二值图像');
    axes(handles.axes3); imshow(handles.Result.BwFilter); title('二值图像滤波');
    axes(handles.axes4); imshow(handles.Result.CrackRec); title('裂缝识别');
end
 
 
% --- Executes on button press in pushbuttonCrackJudge.
function pushbuttonCrackJudge_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonCrackJudge (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.BwFilter); title('二值图像滤波');
    axes(handles.axes3); imshow(handles.Result.CrackRec); title('裂缝识别');
    axes(handles.axes4); imshow(handles.Result.CrackJudge); title('裂缝判断');
end
 
% --- Executes on button press in pushbuttonCrackLoc.
function pushbuttonCrackLoc_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonCrackLoc (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.CrackJudge); title('裂缝图像');
    axes(handles.axes3); imshow(handles.Result.CrackJudge); title(handles.Result.str);
    axes(handles.axes4); imshow(handles.Result.CrackJudge); title('裂缝标记图像');
    hold on;
    rectangle('Position', handles.Result.rect, 'EdgeColor', 'g', 'LineWidth', 2);
    hold off;
end
 
% --- Executes on button press in pushbuttonProject.
function pushbuttonProject_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonProject (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.CrackJudge); title('裂缝图像');
    axes(handles.axes3); plot(1:size(handles.Result.Image, 1), handles.Result.Projectr);
    title('行投影');
    axes(handles.axes4); plot(1:size(handles.Result.Image, 2), handles.Result.Projectc);
    title('列投影');
end
 
 
% --- Executes on button press in pushbuttonClose.
function pushbuttonClose_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonClose (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
choice = questdlg('确定退出?', ...
    '退出', ...
    '是','否','否');
switch choice
    case '是'
        close;
    otherwise
        return;
end
 
 
 
% --- Executes on button press in pushbuttonSaveResult.
function pushbuttonSaveResult_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonSaveResult (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
try
    if ~isempty(handles.File)
        raw = [];
        xlsfile = fullfile(pwd, 'Result/result.xls');
        if exist(xlsfile, 'file')
            [num, txt, raw] = xlsread(xlsfile);
        end
        
        F = [];
        F{1, 1} = '文件名';
        F{1, 2} = '阈值信息';
        F{1, 3} = '面积信息';
        F{1, 4} = '长度信息';
        F{1, 5} = '最大宽度信息';
        F{1, 6} = '最小宽度信息';
        F{1, 7} = '形状信息';
        
        F{2, 1} = handles.File;
        F{2, 2} = handles.Result.BwTh;
        F{2, 3} = handles.Result.BwArea;
        F{2, 4} = handles.Result.BwLength;
        F{2, 5} = handles.Result.BwWidthMax;
        F{2, 6} = max(handles.Result.BwWidthMin,0.01);
        F{2, 7} = handles.Result.str;
        
        F = [raw; F];
        xlswrite(xlsfile, F);
        
        msgbox('保存结果成功!', '信息提示框');
    end
catch
    msgbox('保存结果失败,请检查程序!', '信息提示框');
end
 
 
% --- Executes on button press in pushbuttonBridge.
function pushbuttonBridge_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonBridge (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.Result)
    axes(handles.axes1); imshow(handles.Result.Image); title('原图像');
    axes(handles.axes2); imshow(handles.Result.BwFilter); title('二值图像滤波');
    axes(handles.axes3); imshow(handles.Result.CrackJudge); title('裂缝判断');
    axes(handles.axes4); imshow(handles.Result.CrackBridge); title('裂缝拼接');
end
 
 
% --- Executes on button press in pushbuttonSaveImage.
function pushbuttonSaveImage_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonSaveImage (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
[filename, pathname] = uiputfile({'*.jpg;*.tif;*.png;*.gif','All Image Files';...
    '*.*','All Files' },'Save Image',...
    fullfile(pwd, 'Result/result.png'));
if ~isequal(filename, 0)
    imwrite(handles.Result.BwEnd, fullfile(pathname, filename));
    msgbox('保存图像成功!', '信息提示框');
end
 
 
% --- Executes on button press in pushbuttonDiplay.
function pushbuttonDiplay_Callback(hObject, eventdata, handles)
% hObject    handle to pushbuttonDiplay (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
if ~isempty(handles.File)
    F = [];
    F{1} = sprintf('文件名:%s', handles.File);
    F{2} = sprintf('阈值信息%.2f', handles.Result.BwTh);
    F{3} = sprintf('面积信息%.2f', handles.Result.BwArea);
    F{4} = sprintf('长度信息%.2f', handles.Result.BwLength);
    F{5} = sprintf('最大宽度信息%.2f', handles.Result.BwWidthMax);
    F{6} = sprintf('最小宽度信息%.2f', max(handles.Result.BwWidthMin,0.01));
    F{7} = sprintf('形状信息%s', handles.Result.str);
    listdlg('PromptString', '参数显示:',...
        'Name', '参数信息', ...
        'ListSize', [300, 150], ...
        'SelectionMode','single',...
        'ListString', F);
end
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【图像识别】路面裂缝识别含GUI源码_图像识别_05