n-dimensional B-Splines interpolation

Description

A pure python/numpy implementation of n-dimensional B-Splines.

This is currently not faster than scipy.interpolate.make_interp_spline or scipy.ndimage.map_coordinates. It might be more flexible in some situations, and less in others.

• (for now) assumes regularly spaced knots (e.g. image pixels)
• extensions:
  • 'constant': use constant value (default=0)
  • 'nearest': use nearest value
  • 'half-symmetric' ('mirror'): use center of boundary point as symmetry axis
  • 'whole-symmetric' ('reflect'): use extremity of boundary point as symmetry axis
  • 'anti-symmetric' ('natural'): use center of boundary point as anti-symmetry axis
  • 'true-periodic' ('grid-wrap'): use points from the opposite side
  • 'periodic' ('wrap'): use points from the opposite side (first and last must match)

Usage

# arguments: 
# `data`: (n1, n2, ...) ndim-ndarray
# `coords`: (ndim, npoint) 2d-ndarray, or ndim-list/tuple (nx, ny, ...) of 1d-ndarray
# `degree`: int or ndim-tuple of ints (for different degrees in different dimensions)
# `extension`: str (see above)
# `bounds`: None or ndim-sequence of 2-tuples, boundaries for the coordinates
#     if None, `coords[i]` is assumed to belong to [0, data.shape[i] - 1].

# basic usage: interpolate data at given coordinates
import bsplines
intp = bsplines.interpolate(data, coords, degree=3, extension='nearest')
# if `coords` is a 2d ndarray, nd-mode is assummed (see below)
# if `coords` is a list/tuple, grid mode is assumed (see below)

# only compute b-spline coefficients, returning a `BSpline` object
spl = bsplines.bspline(data, degree=3, extension='nearest')
# or equivalently
spl = bsplines.BSpline.prefilter(data, degree=3, ext='nearest')

# nd-mode: interpolate at coords: (ndim x npoint)
intp = spl(coords)
# grid-mode: interpolate at grid points (cx, cy, ...) (much faster, if applicable)
intp = spl(cx, cy)

# compute nth-order derivative BSpline in selected axis
spl_dn = spl.derivative(n, axis=0)
# compute jacobian matrix (1st derivatives at `coords` stacked on last axis)
jac = spl.jacobian(coords)

Examples

1D interpolation and derivatives (examples/bsplines_1d_derivatives.py):

2D interpolation (examples/bsplines_nd_interp.py.py)

Bibliography

Based on

Briand T, Monasse P, "Theory and Practice of Image B-Spline Interpolation". Image Processing On Line 2018; 8:99–141.

and other ressources for the derivatives, grid-mode, etc.