Declaration

TSplineKernel = class(TCustomKernel)

Description

TSplineKernel implements a smooth cubic $B$-spline filter.

Mathematics

The cubic $B$-spline function is defined piecewise over $|x|<2$:

$$f(x)=\{\begin{array}{ll}\frac{1}{2}|x{|}^3-|x{|}^2+\frac{2}{3},& \text{if }|x|<1\\ \frac{1}{6}(2-|x|{)}^3,& \text{if }1\le |x|<2\\ 0,& \text{otherwise}\end{array}$$

The effective radius is $W=2.0$.

References

• B-spline (Wikipedia)