How to detect & fitting curvature from the binary image?

I have a binary image, and I want to detect & draw curvature from the image.

This is my original image.

This is what I want.

Since the positions of arcs and straight lines in a binary image are not constant and thousands of images must be processed, I want to detect the pixel location without specifying it.

I did some searches, but not sure where should I start.

I would appreciate it if you could recommend some things to study.

Thank you.

Answer 1

[Mathieu NOE]

hello

this would be my suggestion, based on this Fex submission :

smoothn - File Exchange - MATLAB Central (mathworks.com)

result

code :

filename = 'image.png';

tmp = imread(filename);

inpict = im2double(rgb2gray(tmp));
[m,n] = size(inpict);

% find values above threshold 
[y,x] = find(inpict>0.5);
% flip y direction (on the data)
y = m-y;

% take unique values 
[y,ia,ic] = unique(y);
x = x(ia);

% smooth the data with smoothn
% FEX : https://fr.mathworks.com/matlabcentral/fileexchange/25634-smoothn?s_tid=srchtitle
  z = smoothn({x,y},1e3,'robust');
  xs = z{1};
  ys = z{2};

subplot(1,2,1)
imshow(inpict);
subplot(1,2,2)
plot(x,y,'*k',xs,ys,'r');

[DW]

Thank you so much.

That was helpful.

[Mathieu NOE]

as always , my pleasure !

Answer 2

[Image Analyst]

See my solution to your duplicate question:

https://www.mathworks.com/matlabcentral/answers/2050272-curvature-detection-from-outlines-of-the-binary-image#answer_1357322

If you want, you could split the curve up into right half and left half but I assumed that the "thing" is actually some single surface with a rod sticking into it so both sides would probably have the same curvature so I just fit both sides to one polynomial.

[DW]

I tried "Mathieu NOE" 's solution also, but your solution helped me more with my specific problem.

Since the curved surfaces on the left and right are subtly (sometimes very) different, now I'm trying to fit the curves separately for the left and right.

Thank you again!

[Image Analyst]

You could certainly split mine up into right and left sides. Note that @Mathieu NOE still had the spike in there, and it uses a File Exchange program, and smooths the data locally, while mine ignores the spike, uses only built-in functions, and fits the entire surface to a smooth polynomial rather than just smoothing locally. It just depends on how you prefer to do it.