get the inflection points of a contour

Hello,

I want to find the inflexion points of a contour made by adjacents pixels.

An example of contour can be find here : http://sylvain-ard.fr/temp/cnt.csv

It must delete noise (small inflexions).

Please help me

Thank you

The image of the example contour is here :

[Kanika Gupta]

I think you can find a solution here :

1. https://www.mathworks.com/matlabcentral/answers/131760-how-to-find-contour-inflection-points?s_tid=answers_rc1-2_p2_MLT
2. https://www.mathworks.com/matlabcentral/answers/385053-how-to-find-a-number-of-inflection-points-in-a-contour?s_tid=answers_rc1-1_p1_MLT

[Sylvain Ard]

I have already tested these solutions but they're don't work with my example, the result is too bad with every filtering method

Answer 1

[darova]

Here is a start:

• use boundary function to find (x,y) coordinates of your contour (and order)
• Smooth the curve: reduce points and interpolate the data using this 3d interpolation
• use cross product to find inflection points

simple example

x = 0:0.2:10;
y = sin(x).*x.^2;
dx = diff(x)';
dy = diff(y)';
v0 = dx(2:end)*0;
a1 = [dx(1:end-1) dy(1:end-1) v0];
b1 = [dx(2:end) dy(2:end) v0];
n = cross(a1,b1,2);
ix = find( diff(sign(n(:,3))) );
plot(x(ix),y(ix),'or')
line(x,y)

Answer 2

[Sylvain Ard]

finally I succeeded with the function approxPolyDP of OpenCV not Matlab function