Derivative of this bicubic interpolation kernel

[pamparana]

Hello everyone,

I am using the bicubic kernel described here ( http://en.wikipedia.org/wiki/Bicubic_interpolation#Bicubic_convolution_algorithm ) to interpolate my image after applying some transformations.

I an using the matrix kernel described here with a = -0.5.

Now, what I also need to do is estimate the kernel that is the derivative of this bicubic kernel. There is a bit of discussion in this page on the derivative but I am finding it impossible to be able to derive this kernel.

I would be really grateful if someone can help me derive this derivative kernel. My calculus skills are quite rusty but this is a roadblock for me for quite a few days now. I have also searched high and low on the internet for this derivative kernel but to no avail.

I look forward to any assistance you can give me.

Luc

 

[fresh_42]

I would write out $p(t)$, differentiate it, rewrite it as $p'(t)=(1,t,t^2) \cdot \text{ matrix } \cdot (f_1,f_0,f_1,f_2)$ and compute the kernel of that new matrix. There are programs which do it for you: see
https://www.physicsforums.com/threa...th-and-other-curiosities.970262/#post-6164027