图像处理大作业（用霍夫变换检测硬币及统计硬币个数，并设计GUI界面）

实现所给硬币图像中的硬币检测及计数

要求完成功能：自行查找、阅读有关的采用Hough变换来检测图像中圆的资料，设计实现所给图像中圆形的检测，要求检测出图像中硬币个数以及各个硬币的直径。

本题难度系数：★★★★

GUI界面设计参考：MATLAB学习笔记（十一）——MATLAB图形用户界面设计

https://www.cnblogs.com/BlueMountain-HaggenDazs/p/4307777.html

我采用了霍夫变换对所给图形进行了检测和统计个数：

原图如下：

检测后的效果：

全部matlab代码如下：

Hough.m文件：

function varargout = Hough(varargin)
% HOUGH MATLAB code for Hough.fig
%      HOUGH, by itself, creates a new HOUGH or raises the existing
%      singleton*.
%
%      H = HOUGH returns the handle to a new HOUGH or the handle to
%      the existing singleton*.
%
%      HOUGH('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in HOUGH.M with the given input arguments.
%
%      HOUGH('Property','Value',...) creates a new HOUGH or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before Hough_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to Hough_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 Hough
% Last Modified by GUIDE v2.5 10-Jan-2019 20:43:12
% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...
                   'gui_Singleton',  gui_Singleton, ...
                   'gui_OpeningFcn', @Hough_OpeningFcn, ...
                   'gui_OutputFcn',  @Hough_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 Hough is made visible.
function Hough_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 Hough (see VARARGIN)

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

% Update handles structure
guidata(hObject, handles);

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


% --- Outputs from this function are returned to the command line.
function varargout = Hough_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 pushbutton4.
function pushbutton4_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton4 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%打开文件
global img
[filename, pathname]= ...
    uigetfile({'*.*';'*.bmp';'*.tif';'*.png';'*.jpg'},'select picture');
str= [pathname filename];
img= imread(str);
axes(handles.axes1);
imshow(img);

% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global img;
global Gray;
 img=imresize(img,0.5);
[m,n,l] = size(img);
if l == 3
    Gray = rgb2gray(img);    %如果为彩色图 则转化为灰度图
else
    Gray=img;
end
axes(handles.axes1);
imshow(Gray);

% --- Executes on button press in pushbutton3.
function pushbutton3_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton3 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --- Executes on button press in pushbutton5.
function pushbutton5_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton5 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global Gray;
global BW1;
BW1=im2bw(Gray,graythresh(Gray));   %转化为二值图像
axes(handles.axes2);
imshow(BW1)


% --- Executes on button press in pushbutton6.
function pushbutton6_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton6 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global BW1;
BW1=imopen(BW1,strel('disk',3));  %转化为二值图像
axes(handles.axes2);
imshow(BW1)


% --- Executes on button press in pushbutton7.
function pushbutton7_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton7 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global BW1;
BW1=imfill(~BW1,'holes');  %填充图像空洞   
axes(handles.axes2);
imshow(BW1)


% --- Executes on button press in pushbutton8.
function pushbutton8_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton8 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%sobel算子边缘检测
global BW1;
BW1 = edge(BW1,'sobel');  
axes(handles.axes2);
imshow(BW1)


% --- Executes on button press in pushbutton9.
function pushbutton9_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton9 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global BW1;
global para;
%hough检测
step_r = str2num(get(handles.edit1, 'String'));
step_angle = str2num(get(handles.edit2, 'String'));
minr =str2num(get(handles.edit3, 'String'));
maxr = str2num(get(handles.edit4, 'String')); 
thresh = str2num(get(handles.edit5, 'String'));

[Hough_Space,Hough_Circle,para] = hough_circle(BW1,step_r,step_angle,minr,maxr,thresh);  
axes(handles.axes2);
imshow(Hough_Circle);


% --- Executes on button press in pushbutton10.
function pushbutton10_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton10 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
global para;
global circleParaXYR;
circleParaXYR=para;  
%通过位置求圆心和半径
[r,c]=size(circleParaXYR);
for i=1:r
    a='handles.edit';
    b=5+i;
    c=[a num2str(b)];
    d=[a num2str(5+r+1)];
  set(eval(c),'string',['(' num2str(floor(circleParaXYR(i,1))) ',' num2str(floor(circleParaXYR(i,2))) ')', num2str(2*floor(circleParaXYR(i,3)))]);
  set(eval(d),'string',num2str(r));
end
 

% --- Executes on button press in pushbutton11.
function pushbutton11_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton11 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%标出圆  
global img;
global circleParaXYR;
axes(handles.axes2);
imshow(img);
hold on;  
 plot(circleParaXYR(:,2), circleParaXYR(:,1), 'r+');  
 for k = 1 : size(circleParaXYR, 1)  
  t=0:0.01*pi:2*pi;  
  x=cos(t).*circleParaXYR(k,3)+circleParaXYR(k,2);y=sin(t).*circleParaXYR(k,3)+circleParaXYR(k,1);  
  plot(x,y,'r-');  
 end  



function edit1_Callback(hObject, eventdata, handles)
% hObject    handle to edit1 (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 edit1 as text
%        str2double(get(hObject,'String')) returns contents of edit1 as a double


% --- Executes during object creation, after setting all properties.
function edit1_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit1 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit2_Callback(hObject, eventdata, handles)
% hObject    handle to edit2 (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 edit2 as text
%        str2double(get(hObject,'String')) returns contents of edit2 as a double


% --- Executes during object creation, after setting all properties.
function edit2_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit2 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit3_Callback(hObject, eventdata, handles)
% hObject    handle to edit3 (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 edit3 as text
%        str2double(get(hObject,'String')) returns contents of edit3 as a double


% --- Executes during object creation, after setting all properties.
function edit3_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit3 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit4_Callback(hObject, eventdata, handles)
% hObject    handle to edit4 (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 edit4 as text
%        str2double(get(hObject,'String')) returns contents of edit4 as a double


% --- Executes during object creation, after setting all properties.
function edit4_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit4 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit5_Callback(hObject, eventdata, handles)
% hObject    handle to edit5 (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 edit5 as text
%        str2double(get(hObject,'String')) returns contents of edit5 as a double


% --- Executes during object creation, after setting all properties.
function edit5_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit5 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit6_Callback(hObject, eventdata, handles)
% hObject    handle to edit6 (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 edit6 as text
%        str2double(get(hObject,'String')) returns contents of edit6 as a double


% --- Executes during object creation, after setting all properties.
function edit6_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit6 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit7_Callback(hObject, eventdata, handles)
% hObject    handle to edit7 (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 edit7 as text
%        str2double(get(hObject,'String')) returns contents of edit7 as a double


% --- Executes during object creation, after setting all properties.
function edit7_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit7 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit8_Callback(hObject, eventdata, handles)
% hObject    handle to edit8 (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 edit8 as text
%        str2double(get(hObject,'String')) returns contents of edit8 as a double


% --- Executes during object creation, after setting all properties.
function edit8_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit8 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit9_Callback(hObject, eventdata, handles)
% hObject    handle to edit9 (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 edit9 as text
%        str2double(get(hObject,'String')) returns contents of edit9 as a double


% --- Executes during object creation, after setting all properties.
function edit9_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit9 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit10_Callback(hObject, eventdata, handles)
% hObject    handle to edit10 (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 edit10 as text
%        str2double(get(hObject,'String')) returns contents of edit10 as a double


% --- Executes during object creation, after setting all properties.
function edit10_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit10 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit11_Callback(hObject, eventdata, handles)
% hObject    handle to edit11 (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 edit11 as text
%        str2double(get(hObject,'String')) returns contents of edit11 as a double


% --- Executes during object creation, after setting all properties.
function edit11_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit11 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end



function edit12_Callback(hObject, eventdata, handles)
% hObject    handle to edit12 (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 edit12 as text
%        str2double(get(hObject,'String')) returns contents of edit12 as a double


% --- Executes during object creation, after setting all properties.
function edit12_CreateFcn(hObject, eventdata, handles)
% hObject    handle to edit12 (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 ispc && isequal(get(hObject,'BackgroundColor'), get(0,'defaultUicontrolBackgroundColor'))
    set(hObject,'BackgroundColor','white');
end


% --------------------------------------------------------------------
function m_file_Callback(hObject, eventdata, handles)
% hObject    handle to m_file (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)


% --------------------------------------------------------------------
function m_file_save_Callback(hObject, eventdata, handles)
% hObject    handle to m_file_save (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
%保存文件
[FileName,PathName] = uiputfile({'*.jpg','JPEG(*.jpg)';
                                 '*.bmp','Bitmap(*.bmp)';
                                 '*.gif','GIF(*.gif)';
                                 '*.*',  'All Files (*.*)'},'Save Picture','Untitled');
if FileName==0
    return;
else
    h=getframe(handles.axes2);
    imwrite(h.cdata,[PathName,FileName]);
    warndlg('保存成功','保存成功');
end

hough_circle.m文件：

function [hough_space,hough_circle,para] = hough_circle(BW,step_r,step_angle,r_min,r_max,p)  
  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
% input  
% BW:二值图像；  
% step_r:检测的圆半径步长  
% step_angle:角度步长，单位为弧度  
% r_min:最小圆半径  
% r_max:最大圆半径  
% p:阈值，0，1之间的数 通过调此值可以得到图中圆的圆心和半径  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%  
% output  
% hough_space:参数空间，h(a,b,r)表示圆心在(a,b)半径为r的圆上的点数  
% hough_circl:二值图像，检测到的圆  
% para:检测到的圆的圆心、半径  
  
circleParaXYR=[];  
para=[];  
  
[m,n] = size(BW);  
size_r = round((r_max-r_min)/step_r)+1;%四舍五入  
size_angle = round(2*pi/step_angle);  
  
hough_space = zeros(m,n,size_r);  
  
[rows,cols] = find(BW);%查找非零元素的行列坐标  
ecount = size(rows);%非零坐标的个数  
  
% Hough变换  
% 将图像空间(x,y)对应到参数空间(a,b,r)  
  
% a = x-r*cos(angle)  
% b = y-r*sin(angle)  
  
for i=1:ecount  
    for r=1:size_r %半径步长数  
        for k=1:size_angle %按一定弧度把圆几等分  
            a = round(rows(i)-(r_min+(r-1)*step_r)*cos(k*step_angle));  
            b = round(cols(i)-(r_min+(r-1)*step_r)*sin(k*step_angle));  
            if(a>0&a<=m&b>0&b<=n)  
            hough_space(a,b,r) = hough_space(a,b,r)+1;%h(a,b,r)的坐标，圆心和半径  
            end  
        end  
    end  
end  
  
  
% 搜索超过阈值的聚集点。对于多个圆的检测，阈值要设的小一点！通过调此值，可以求出所有圆的圆心和半径  
max_para = max(max(max(hough_space)));%返回值就是这个矩阵的最大值  
index = find(hough_space>=max_para*p);%一个矩阵中，想找到其中大于max_para*p数的位置  
length = size(index);%符合阈值的个数  
hough_circle = false(m,n);  
%hough_circle = zeros(m,n);  
%通过位置求半径和圆心。  
for i=1:ecount  
    for k=1:length  
        par3 = floor(index(k)/(m*n))+1;  
        par2 = floor((index(k)-(par3-1)*(m*n))/m)+1;  
        par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m;  
        if((rows(i)-par1)^2+(cols(i)-par2)^2<(r_min+(par3-1)*step_r)^2+5&...  
                (rows(i)-par1)^2+(cols(i)-par2)^2>(r_min+(par3-1)*step_r)^2-5)  
              hough_circle(rows(i),cols(i)) = true;   %检测的圆  
        end  
    end  
end                 
  
% 从超过峰值阈值中得到  
for k=1:length  
    par3 = floor(index(k)/(m*n))+1;%取整  
    par2 = floor((index(k)-(par3-1)*(m*n))/m)+1;  
    par1 = index(k)-(par3-1)*(m*n)-(par2-1)*m;  
    circleParaXYR = [circleParaXYR;par1,par2,par3];  
    hough_circle(par1,par2)= true; %这时得到好多圆心和半径，不同的圆的圆心处聚集好多点，这是因为所给的圆不是标准的圆  
    %fprintf(1,'test1:Center %d %d \n',par1,par2);  
end  
  
%集中在各个圆的圆心处的点取平均，得到针对每个圆的精确圆心和半径！  
while size(circleParaXYR,1) >= 1  
    num=1;  
    XYR=[];  
    temp1=circleParaXYR(1,1);  
    temp2=circleParaXYR(1,2);  
    temp3=circleParaXYR(1,3);  
    c1=temp1;  
    c2=temp2;  
    c3=temp3;  
    temp3= r_min+(temp3-1)*step_r;  
   if size(circleParaXYR,1)>1       
     for k=2:size(circleParaXYR,1)  
      if (circleParaXYR(k,1)-temp1)^2+(circleParaXYR(k,2)-temp2)^2 > temp3^2  
         XYR=[XYR;circleParaXYR(k,1),circleParaXYR(k,2),circleParaXYR(k,3)];  %保存剩下圆的圆心和半径位置  
      else    
      c1=c1+circleParaXYR(k,1);  
      c2=c2+circleParaXYR(k,2);  
      c3=c3+circleParaXYR(k,3);  
      num=num+1;  
      end   
    end  
   end   
      %fprintf(1,'sum %d %d radius %d\n',c1,c2,r_min+(c3-1)*step_r);  
      c1=round(c1/num);  
      c2=round(c2/num);  
      c3=round(c3/num);  
      c3=r_min+(c3-1)*step_r;  
      %fprintf(1,'num=%d\n',num)  
      %fprintf(1,'Center %d %d radius %d\n',c1,c2,c3);     
      para=[para;c1,c2,c3]; %保存各个圆的圆心和半径的值  
      circleParaXYR=XYR;  
end 

以上完整源码仅供参考，此次任务小组合作完成，所以博主对以上代码一些部分不是很了解，谢谢合作。