Algorithm of Bicubic Interpolation

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?

Answer 1

[Alex Taylor]

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;

Answer 2

[Matt J]

Are you sure you're not re-inventing the wheel? What about this:

http://commons.apache.org/proper/commons-math/apidocs/org/apache/commons/math3/analysis/interpolation/SplineInterpolator.html

Answer 3

[Matt J]

You can also try corroborating your/MATLAB's spline interpolation against Example1.m and Example2.m from here

http://www.mathworks.com/matlabcentral/fileexchange/26292-regular-control-point-interpolation-matrix-with-boundary-conditions

It uses an entirely different approach from INTERP2, so it should be useful as an independent comparison.

[Alex Taylor]

If the data being passed to interp2 is uniformly spaced, the algorithm is bicubic interpolation based on a cubic convolution kernel, not cubic spline interpolation.

[Matt J]

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.