Curve Fitting in a binary image, MATLAB

Question

I have this Binary image bw:

edges of an object to carry out some measurements. But firstly I have to do curve fitting for both edges. The result should be two smooth curves representing edges.

I have the indices for each edge but I can not use them in making x-y data to be input data to a fitting function. I mean they are not x and f(x), actually, they all have the same value (1) with different positions. It is not right to say [x y]=find(BW) ; y here is not the value at x, but for sure there should be a way to use them to some kind of scale the binary image. I seem confused and I'm stuck here.

Any recommendations?

Answer 1

Why not use polyfit?

[y x] = find( bw );  %// get x y coordinates of all curve points

There are two small "tricks" you need to use here:

1. You have two curves, thus you need to split your data points to the left and right curves

   right = x<300;
   xr = x(right);
   yr = y(right);
   xl = x(~right);
   yl = y(~right);
   

2. Since your curves are close to vertical, it would be better to fit x=f(y) rather than the "classic" y=f(x):

   pr = polyfit( yr, xr, 3 );  %// fit 3rd deg poly
   pl = polyfit( yl, xl, 3 ); 
   

Now you can plot them

yy = linspace( 1, size(bw,1), 50 );

figure; imshow(bw, 'border', 'tight' );
hold all
plot( polyval( pr, yy ), yy, '.-', 'LineWidth', 1 );
plot( polyval( pl, yy ), yy, '.-', 'LineWidth', 1 );

And you get:

If you want to create a new refined mask from the estimated curves, you can do the following:

yy = 1:size(bw,1);  %// single value per row
xxr=polyval(pr,yy); %// corresponding column values
xxl=polyval(pl,yy);

Set a new mask of the same size

nbw = false(size(bw)); 
nbw( sub2ind(size(bw),yy,round(xxr)) )=true;
nbw( sub2ind(size(bw), yy, round(xxl) )) = true; 

And the result

figure;imshow(nbw,'border','tight');