gauss_spline#
- scipy.signal.gauss_spline(x, n)[source]#
- Gaussian approximation to B-spline basis function of order n. - Parameters:
- xarray_like
- a knot vector 
- nint
- The order of the spline. Must be non-negative, i.e., n >= 0 
 
- Returns:
- resndarray
- B-spline basis function values approximated by a zero-mean Gaussian function. 
 
 - 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 : \[\frac{1}{\sqrt {2\pi\sigma^2}}exp(-\frac{x^2}{2\sigma})\]- 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 - Examples - We can calculate B-Spline basis functions approximated by a gaussian distribution: - >>> import numpy as np >>> from scipy.signal import gauss_spline >>> knots = np.array([-1.0, 0.0, -1.0]) >>> gauss_spline(knots, 3) array([0.15418033, 0.6909883, 0.15418033]) # may vary