Declaration

TCubicKernel = class(TCustomKernel)

Description

TCubicKernel implements Keys' cubic convolution interpolation polynomial with configurable sharpening parameter Coeff (default $a=-0.5$ for Catmull-Rom spline).

Cubic filtering is commonly used for high-quality resampling.

Mathematics

With parameter $a=\text{Coeff}$:

$$f(x)=\{\begin{array}{ll}(a+2)|x{|}^3-(a+3)|x{|}^2+1,& \text{if }|x|\le 1\\ a|x{|}^3-5a|x{|}^2+8a|x|-4a,& \text{if }1<|x|<2\\ 0,& \text{otherwise}\end{array}$$

References

• Robert G. Keys, "Cubic convolution interpolation for digital image processing", IEEE Transactions on Acoustics, Speech, and Signal Processing, 1981.
• Bicubic interpolation (Wikipedia)