Circle Fit at the Corner of the Step??

Hi,

I have a step curve (figure 1) and I want fit a circle to each corner of step (shown in figure 2). I wrote the following function for the circle fit:

function [xc,yc,R]=circfit(x,y)
  x=x(:); y=y(:);
  a=[x y ones(size(x))]\-(x.^2+y.^2);
  xc=-0.5*a(1);
  yc=-05*a(2);
  R=0.5*sqrt((a(1)^2+a(2)^2)-4*a(3));
  end

I read the corners coordinates manually and apply the following code to fit circle

y=C(1050:1100); % C is array of step
x=1050:1100;
[xc,yc,Re] = circfit(x,y);

I got the values of center and radius of circle, which are looking way to higher than I except and I don't understand how to plot this fitted circle. If I plot using

plot((x-xc).^2+(y-yc).^2-Re.^2)

It is same as the corner of the step. Could any one tell me that if approach is correct or not and how to plot fitted curve that I can show it in same way as shown in fig. 2? Is there any other way to find circle fit?

%

Answer 1

[Darshan Ramakant Bhat]

This is due to the different scaling of the axes. If you observe y axes varies from 0 to 1, while x axes varies from 0 to 2000. MATLAB automatically fits the aspect ration of the axes for the visualization purpose. You have to limit the x-axes range to view the circle.

Please refer to the below code:

clc;
clear all;
close all;
t = 1 : 2000;
sf = t>1000;
figure(1);
plot(t,sf);
xlim([1000 1002])
c = [1001.05,0.95];
r = 0.05;
hold on;
%Inbuilt function in image processing toolbox to plot the circle.
viscircles(c,r);

I hope this will help you.

[Swati Jain]

Thanks for your response. viscirles is working well. But my other problem is still not solved. My problem is that radius obtained from circfit function is way to higher than I expect and even if I limit the x-axis in my plot there is no change, since MATLAB is adjusting the axes according to the radius of the circle. I am not sure what is wrong with my function, however, I found similar function on google. If there is any other way to fit a circle please let me now. Attached is the image what I am getting as after circle fit.

[Darshan Ramakant Bhat]

I am not sure what you are trying to do in circfit() function. Can you elaborate on your logic ?

Answer 2

[Darshan Ramakant Bhat]

I guess there is something wrong going on in estimating the radius of curvature using the x,y points. Please refer below code to do the same:

http://matlab.wikia.com/wiki/FAQ#How_can_I_fit_a_circle_to_a_set_of_XY_data.3F

I hope this will help you.

Regards,

Darshan

[Swati Jain]

Hi,

This function is giving same result as I got from my function. Thanks!