Finding and plotting parabola in matlab

Question

I have been trying to find a parabola in an image. For the starting purposes I took an image with a black parabola on a white background. Then I found the black pixels on the image using the find command by ``` [yi xi] = find(im<10); % im is the image with black parabola and white background ``` After that I randomly took 3 points from the collection and solved the equation for the parabola using the symbolic toolbox using ``` syms x y; %solve them for the parabola equation A = [ x^2 x y 1 ;x0^2 x0 y0 1; x1^2 x1 y1 1; x2^2 x2 y2 1]; ``` where %(x0,y0) = (104,137) %(x1,y1) = (244,161) %(x2,y2) = (300,229) ``` S = solve(det(A),y); ``` Then I get the coeffcients a,b,c as a = 0.0100 b = -1.6800 c = 254.1900 where a, b and c are ``` a*x^2 + b*x + c = y; ``` Since now I have got the eqn I plot the parabola by putting the coefficient values and taking ``` xx = 1:300; yy = a*xx.^2 + b*xx +c ; ``` then I plot the parabola on the image as ``` plot(xx,yy,'-'); ``` For the confirmation that I hav…

Accepted Answer

I think you must be rounding somewhere in your calculation of a, b, and c.

I had a go with the three points you mentioned using the function fit (with fit type poly2) and my a,b,c were 0.0053, -1.6802 and 254.1895 (or add more decimal places when using format long).

Similarly, when using same the code you give, the output of solve is:

```
S = (73*x^2)/13720 - (5763*x)/3430 + 87187/343
S2 = double(coeffs(S))

S2 =

254.1895   -1.6802    0.0053
```

This gives me the same a, b, and c as with fit/poly2 (just from looking at it, the output of 73/13720 cannot be 0.01). Also, if I plot this curve over the original points using the same code you give, it works fine. So the only remaining source of error that I can see is some sort of rounding in whatever code you use to extract values of a, b, and c from the output of solve.

Finding and plotting parabola in matlab

Solution

Problem