MATLAB: Fast interp1 with ‘spline’

interpolationmexspline

Now I am programming a matlab toolbox for computer vision. I use a lot the function 'interp1(, , ,'spline')', and this step actually accounts for 50% of the whole computation time. Just wondering if there is any faster approach to compute this, and something like mex file, etc. Thank you very much.

Best Answer

Well, the simple answer is to not use interp1. Just use spline and then ppval.
The problem is that for a spline interpolant, every time you call interp1, it must effectively call spline inside on your data. By calling spline once, this makes it more efficient.
For example...
x = linspace(-1,1,100);
y = exp(x);
xev = rand(1,1000)*2 - 1;
S = spline(x,y);
timeit(@() interp1(x,y,xev,'spline'))
ans =
    0.0003005
timeit(@() ppval(S,xev))
ans =
   0.00025177
Not as big of a difference as I thought it might be, but some.
You MIGHT also gain some time if you are willing to pre-interpolate the function to a finer interval, so that then you could do linear interpolation. Since linear interpolant will be faster to do, this should see some gain too.
x = linspace(-1,1,10);
y = exp(x);
xfine = linspace(-1,1,1000);
yfine = interp1(x,y,xfine,'spline');
xev = rand(1,1000)*2 - 1;
timeit(@() interp1(x,y,xev,'spline'))
ans =
   0.00028546
timeit(@() interp1(xfine,yfine,xev))
ans =
   0.00022313
You can also see some gain by using pchip instead of spline, as that is a faster way to build the spline, though sometimes not quite as smooth.
timeit(@() interp1(x,y,xev,'pship'))
ans =
   0.00026064
Finally I recall seeing some tools on the file exchange that tried to give a speedup for interp1, but they were mostly for linear interpolation.
Finally, while you could certainly use a mexfile to improve the time, that presumes that your skills are sufficient to write a spline interpolant, and to do so efficiently in C. I'm afraid that compiled MATLAB code would gain you nothing here.
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