How to find center and radius of an arc from binarized image

I have image of anulus, I need to find center and radius of inner and outer arc

Answer 1

[Mathieu NOE]

hello

this is what I can offer you today

you will need the attached function (CircleFitByTaubin.m) , and this Fex submission :

DBSCAN Clustering Algorithm - File Exchange - MATLAB Central (mathworks.com)

results

also you get the info's in the command window if you prefer

----------------------------

Circle # 1:

Re = 659.0384:

xc = 346.9044:

yc = 674.5627:

----------------------------

----------------------------

Circle # 2:

Re = 392.5529:

xc = 339.0362:

yc = 691.2823:

----------------------------

code :

filename = 'image.png';

%% read png file
% inpict = im2double(rgb2gray(imread(filename))); % for RGB pictures 
inpict = imread(filename); % for B&W pictures 

[m,n] = size(inpict);
% find values above threshold 
[y,x] = find(inpict>0.5);
% flip y direction (on the data, not the plot))
y = m-y;

%% some manual work first 
% remove left diagonal segment
ind = (x<300);
x(ind) = [];
y(ind) = [];

% remove top horizontal segment
ind = (y>600);
x(ind) = [];
y(ind) = [];

%% separate both curves 
% Run DBSCAN Clustering Algorithm
% see Fex : https://fr.mathworks.com/matlabcentral/fileexchange/52905-dbscan-clustering-algorithm
epsilon=100;
MinPts=5;
X = [x y];
IDX=DBSCAN(X,epsilon,MinPts);

%% Plot Results

    k=max(IDX);

    Colors=hsv(k);

    for i=0:k
        Xi=X(IDX==i,:);
        if i~=0
            Style = 'x';
            MarkerSize = 8;
            Color = Colors(i,:);
        else
            Style = 'o';
            MarkerSize = 6;
            Color = [0 0 0];
        end
        if ~isempty(Xi)
            %%
            % circle fit here then plot
            %%
            par = CircleFitByTaubin(Xi);

            %     Output: Par = [a b R] is the fitting circle:
            %     center (a,b) and radius R
            xc = par(1);
            yc = par(2);
            Re = par(3);
            
            % display results in command window 
            disp(['----------------------------']);
           disp([' Circle # ' num2str(i) ':']);
            disp([' Re =  ' num2str(Re) ':']);
            disp([' xc = ' num2str(xc) ':']);
            disp([' yc = ' num2str(yc) ':']);
            disp(['----------------------------']);
            

            % reconstruct circle from data
            n=100;
            th = (0:n)/n*2*pi;
            xe = Re*cos(th)+xc;
            ye = Re*sin(th)+yc;

            plot(Xi(:,1),Xi(:,2),Style,'MarkerSize',MarkerSize,'Color',Color)

            hold on
            plot(xe,ye,'--','Color',Color)
            title(' measured fitted circles')
            text(xc-Re*0.5,yc + 0.75*Re,sprintf('center (%g , %g );  R=%g',xc,yc,Re))
            axis equal
            
        end
    end
    hold off;
    axis equal;
    grid on;
    title(['DBSCAN Clustering (\epsilon = ' num2str(epsilon) ', MinPts = ' num2str(MinPts) ')']);

[sanyogita sanyogita]

Thanks

[Mathieu NOE]

my pleasure !

ifmy answer has fullfilled your expectations, do you mind accepting it ?

tx