Since I have no more than a picture of your data, a made up example must suffice.
t = linspace(0,2*pi,20);
x = sin(2*t + pi/4);
y = cos(3*t);
[xint,yint] = intersections(x,y);
There are clearly 7 points of intersection, all shown with the red stars. It looks like it also found the first point on the curve, since that also happens to be the last point as I created it. Intersections uses linear interpolation. But that should be entirely sufficient, since your data is quite closely spaced.