How to turn all parts of a binary image outside of an ellipse to zero.

I have the centeroid, major axis length, minor axis length, and orientation of an ellipse and I want to make everything outside of the ellipse on a binary image 0/black. How would I approach this?

Answer 1

[Matt J]

Express the elliptical region in equality form

(x-c).'*Q*(x-c)<=1

where c is the centroid, Q is the 2x2 matrix,

Q=R.'*diag(1./[a,b]).^2*R;

and R is a 2x2 rotation matrix.

Then test all pixels to see which satisfy the inequality. This can be vectorized as follows,

[x,y]=ndgrid((1:Nx)-cx,(1:Ny)-cy);
delta=[x(:),y(:)].';

mask= all( sum( (Q*delta).*delta )<=1 );
mask=reshape(mask, Nx,Ny);