# Algorithm of Bicubic Interpolation

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Tim on 5 Jun 2013
I am trying to recreate the matlab bicubic interpolation function in java. In matlab, I use interp2(...., 'cubic') and I am trying to write a program that does the exact same thing in java. I have basically tried to follow wikipedia's formula for it. The data that I am getting from my java program is close to matlab's, but slightly off. Does anyone know the actual formula for bicubic interpolation that is used by matlab's cubic interp2 function?

Alex Taylor on 5 Jun 2013
Edited: Alex Taylor on 5 Jun 2013
The algorithm is described in the following reference.
% "Cubic Convolution Interpolation for Digital Image % Processing", Robert G. Keys, IEEE Trans. on Acoustics, Speech, and % Signal Processing, Vol. 29, No. 6, Dec. 1981, pp. 1153-1160.
Its convolution based interpolation. The specific cubic convolution kernel is described in terms of a piecewise equation in MATLAB code before. This will make more sense if you have access to the paper.
y = zeros(1,length(x));
reshape(y,size(x));
x(x < 0.0) = -x(x < 0.0);
q = (x <= 1); % Coefficients: 1.5, -2.5, 0.0, 1.0
y(q) = ((1.5 * x(q) - 2.5) .* x(q)) .* x(q) + 1.0;
q = (1 < x & x <= 2); % Coefficients: -0.5, 2.5, -4.0, 2.0
y(q) = ((-0.5 * x(q) + 2.5) .* x(q) - 4.0) .* x(q) + 2.0;

Matt J on 5 Jun 2013
Edited: Matt J on 5 Jun 2013

Matt J on 5 Jun 2013
Edited: Matt J on 5 Jun 2013
You can also try corroborating your/MATLAB's spline interpolation against Example1.m and Example2.m from here
It uses an entirely different approach from INTERP2, so it should be useful as an independent comparison.
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Matt J on 5 Jun 2013
Ah, I see. Well, the FEX file lets you choose the kernel, so you could apply it the cubic convolution kernel as an additional test as well. It wouldn't be as distinct from INTERP2 as in the case of 'spline' interpolation, but it is somewhat distinct.