2D Nearest Neighbor Interpolation in Python

Question

Suppose that we have the following look up table

        | 1.23    2.63    4.74    6.43    5.64
 -------|--------------------------------------
 -------|--------------------------------------
 2.56   |  0       0      1        0       1
 4.79   |  0       1      1        1       0
 6.21   |  1       0      0        0       0

This table contains a labeling matrix (having only 0 and 1s), x values and y values. How one can have nearest-neighbor interpolation for this look up table?

Example:

Input: (5.1, 4.9)
Output: 1

Input: (3.54, 6.9)
Output: 0

Look up table

If you have the complete table you don't need interpolation, you just need to look up the index of the nearest (x, y) value and use it on the table

In [1]: import numpy
   ...: x = numpy.array([1.23, 2.63, 4.74, 6.43, 5.64])
   ...: y = numpy.array([2.56, 4.79, 6.21])
   ...: data = numpy.array([[0, 0, 1, 0, 1],
   ...:                     [0, 1, 1, 1, 0],
   ...:                     [1, 0, 0, 0, 0]])
   ...: 
   ...: def lookupNearest(x0, y0):
   ...:     xi = numpy.abs(x-x0).argmin()
   ...:     yi = numpy.abs(y-y0).argmin()
   ...:     return data[yi,xi]

In [2]: lookupNearest(5.1, 4.9)
Out[2]: 1

In [3]: lookupNearest(3.54, 6.9)
Out[3]: 0

Nearest-neighbor interpolation

scipy.interpolate.NearestNDInterpolator will be really useful if your data is composed by scattered points

For example, for data like:

with red = 1, blue =0

In [4]: points = numpy.array([[1.1, 2.5], 
   ...:                       [1.5, 5.2], 
   ...:                       [3.1, 3.0], 
   ...:                       [2.0, 6.0], 
   ...:                       [2.8, 4.7]])
   ...: values = numpy.array([0, 1, 1, 0, 0])

In [5]: from scipy.interpolate import NearestNDInterpolator
   ...: myInterpolator = NearestNDInterpolator(points, values)

In [6]: myInterpolator(1.7,4.5)
Out[6]: 1

In [7]: myInterpolator(2.5,4.0)
Out[7]: 0

Comments

[Filip Malczak]

First part of the answer is wrong. Consider points: A=(0, 0), B=(1, 100), C=(2, 2). Your code would state that nearest neighbour of A is B, even though it's not true. Try something like min(data, key=lambda point: (point.x-your_point.x)**2 + (point.y-your_point.y)**2) (it's a general idea, I know that you won't be able to get coordinates as properties). No downvote, because second, scipy/numpy related part seems to be more important.

[Vrekrer]

@FilipMalczak The first part of my answer will work if the data is arranged in a rectangular grid (a complete table)

[Filip Malczak]

Fair enough, I've generalized it to example from second part of the post.