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https://github.com/innolitics/natural-neighbor-interpolation

Fast, discrete natural neighbor interpolation in 3D on the CPU.
https://github.com/innolitics/natural-neighbor-interpolation

image-processing interpolation numpy python3

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Fast, discrete natural neighbor interpolation in 3D on the CPU.

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README 

        
.. image:: https://github.com/innolitics/natural-neighbor-interpolation/actions/workflows/test.yml/badge.svg

   :target: https://github.com/innolitics/natural-neighbor-interpolation/actions/workflows/test.yml



Discrete Sibson (Natural Neighbor) Interpolation

================================================



Natural neighbor interpolation is a method for interpolating scattered data

(i.e. you know the values of a function at scattered locations).  It is often superior to linear barycentric interpolation, which is a commonly used method of interpolation provided by Scipy's `griddata` function.



There are several implementations of 2D natural neighbor interpolation in Python.  We needed a fast 3D implementation that could run without a GPU, so we wrote an implementation of Discrete Sibson Interpolation (a version of natural neighbor interpolation that is fast but introduces slight errors as compared to "geometric" natural neighbor interpolation).



See https://doi.org/10.1109/TVCG.2006.27 for details.



Installation

------------



.. code-block:: bash



    pip install naturalneighbor



Dependencies

------------



- Python 3.5+

- Numpy (has been tested with 1.13+)



Demonstration

-------------



Natural neighbor interpolation can be more accurate than linear barycentric interpolation (Scipy's default) for smoothly varying functions.



Also, the final result looks better.



.. image:: https://raw.githubusercontent.com/innolitics/natural-neighbor-interpolation/master/demo/linear_comparison.png

   :target: https://raw.githubusercontent.com/innolitics/natural-neighbor-interpolation/master/demo/linear_comparison.png



.. image:: https://raw.githubusercontent.com/innolitics/natural-neighbor-interpolation/master/demo/sin_sin_comparison.png

   :target: https://raw.githubusercontent.com/innolitics/natural-neighbor-interpolation/master/demo/sin_sin_comparison.png



Note that the natural neighbor values usually are extrapolated; they were cut off in the demo to fairly compare with Scipy's linear barycentric method, which does not extrapolate.



Usage

-----



This module exposes a single function, :code:`griddata`.



The API for :code:`naturalneighbor.griddata` is similar to

:code:`scipy.interpolate.griddata`.  Unlike Scipy, the third argument is not a

dense mgrid, but instead is just the ranges that would have been passed to :code:`mgrid`.  This is because the discrete Sibson approach requires the interpolated points to lie on an evenly spaced grid.



.. code-block:: python



    import scipy.interpolate

    import numpy as np



    import naturalneighbor



    num_points = 10

    num_dimensions = 3

    points = np.random.rand(num_points, num_dimensions)

    values = np.random.rand(num_points)



    grids = tuple(np.mgrid[0:100:1, 0:50:100j, 0:100:2])

    scipy_interpolated_values = scipy.interpolate.griddata(points, values, grids)



    grid_ranges = [[0, 100, 1], [0, 50, 100j], [0, 100, 2]]

    nn_interpolated_values = naturalneighbor.griddata(points, values, grid_ranges)



Future Work

-----------



- Provide options for extrapolation handling

- Support floats and complex numbers (only support doubles at the moment)

- Support 2D (only support 3D)

- Add documentation with discussion on limitations of discrete sibson's method

- Uncomment cpplint from tox.ini and cleanup C++ code

- Generalize the threading model (currently it uses 8 threads---one for each quadrant)



Other Resources

---------------



- `Fast Discrete Approximation of Natural Neighbor Interpolation in 3D `_