Question

I just want to interpolate, in the simplest possible terms, a 3D dataset. Linear interpolation, nearest neighbour, all that would suffice (this is to start off some algorithm, so no accurate estimate is required).

In new scipy versions, things like griddata would be useful, but currently I only have scipy 0.8. So I have a “cube” (data[:,:,:], (NixNjxNk)) array, and an array of flags (flags[:,:,:,], True or False) of the same size. I want to interpolate my data for the elements of data where the corresponding element of flag is False, using eg the nearest valid datapoint in data, or some linear combination of “close by” points.

There can be large gaps in the dataset in at least two dimensions. Other than coding a full-blown nearest neighbour algorithm using kdtrees or similar, I can’t really find a generic, N-dimensional nearest-neighbour interpolator.

Answer 1

You can set up a crystal-growth-style algorithm shifting a view alternately along each axis, replacing only data that is flagged with a False but has a True neighbor. This gives a “nearest-neighbor”-like result (but not in Euclidean or Manhattan distance — I think it might be nearest-neighbor if you are counting pixels, counting all connecting pixels with common corners) This should be fairly efficient with NumPy as it iterates over only axis and convergence iterations, not small slices of the data.

Crude, fast and stable. I think that’s what you were after:

import numpy as np
# -- setup --
shape = (10,10,10)
dim = len(shape)
data = np.random.random(shape)
flag = np.zeros(shape, dtype=bool)
t_ct = int(data.size/5)
flag.flat[np.random.randint(0, flag.size, t_ct)] = True
# True flags the data
# -- end setup --

slcs = [slice(None)]*dim

while np.any(~flag): # as long as there are any False's in flag
    for i in range(dim): # do each axis
        # make slices to shift view one element along the axis
        slcs1 = slcs[:]
        slcs2 = slcs[:]
        slcs1[i] = slice(0, -1)
        slcs2[i] = slice(1, None)

        # replace from the right
        repmask = np.logical_and(~flag[slcs1], flag[slcs2])
        data[slcs1][repmask] = data[slcs2][repmask]
        flag[slcs1][repmask] = True

        # replace from the left
        repmask = np.logical_and(~flag[slcs2], flag[slcs1])
        data[slcs2][repmask] = data[slcs1][repmask]
        flag[slcs2][repmask] = True

For good measure, here’s a visualization (2D) of the zones seeded by the data originally flagged True.