cupyx.scipy.signal.gauss_spline

cupyx.scipy.signal.gauss_spline(x, n)

Gaussian approximation to B-spline basis function of order n.

Parameters

• x (array_like) – a knot vector

• n (int) – The order of the spline. Must be nonnegative, i.e. n >= 0

Returns

res – B-spline basis function values approximated by a zero-mean Gaussian function.

Return type

ndarray

Notes

The B-spline basis function can be approximated well by a zero-mean Gaussian function with standard-deviation equal to \(\sigma=(n+1)/12\) for large n :

\[\frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma})\]

See 1, 2 for more information.

References

1

Bouma H., Vilanova A., Bescos J.O., ter Haar Romeny B.M., Gerritsen F.A. (2007) Fast and Accurate Gaussian Derivatives Based on B-Splines. In: Sgallari F., Murli A., Paragios N. (eds) Scale Space and Variational Methods in Computer Vision. SSVM 2007. Lecture Notes in Computer Science, vol 4485. Springer, Berlin, Heidelberg

2

http://folk.uio.no/inf3330/scripting/doc/python/SciPy/tutorial/old/node24.html