Question

Can someone guide me along with the bicubic interpolation math as described on wikipedia with a numerical example?

http://en.wikipedia.org/wiki/Bicubic_interpolation

I need to understand the math to create the algorithm for image resize.

What i don’t understand from the wikipedia article is that how do i yield any of the 16 coefficients aij as mentioned in the article, how did they find the A^-1 matrix at the end? What’s the point of forming the matrix?

I do understand bilinear interpolation by the way.

Can someone please illustrate the math with a numerical example or a link to one with numerical example? Thanks in advance.

Answer 1

What’s the point of forming the matrix?

The point is to allow you to compute the 16 coefficients a_ij from the 16 values (actual values and derivatives describing the curvature of the surface you want to interpolate).

What you know is the vector x as defined in the article (you compute the derivates by “looking around” the four points of the square). You then get the unknown vector alpha by computing A^-1x. Knowing alpha you can now compute the bicubic interpolation function p(x, y) for any point inside the square.

how did they find the A^-1 matrix at the end?

They inverted A that was defined by the 16 equations of 16 unknown values. Inverting a matrix is pretty straightforward linear algebra.