Two-dimensional Savitzky-Golay filter

A Savitzky–Golay filter is a digital filter that can be applied to a set of digital data points for the purpose of smoothing the data, that is, to increase the precision of the data without distorting the signal tendency. (wikipedia)

This code implements two-dimensional Savitzky-Golay filter that can be used for smoothing surfaces or images [1, 2].

The example of usage

import numpy as np

import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

import sgolay2

np.random.seed(12345)

x, y = np.mgrid[-5:6:.5, -5:6:.5]
z = y * np.sin(x) + x * np.cos(y)
zn = z + np.random.randn(*x.shape) * 2.

zs = sgolay2.SGolayFilter2(window_size=9, poly_order=3)(zn)

fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')

ax.plot_wireframe(x, y, zn, linewidths=0.5, color='r')
ax.scatter(x, y, zn, s=5, c='r')

ax.plot_surface(x, y, zs, linewidth=0)
ax.plot_surface(x, y, z, color='y', linewidth=0, alpha=0.4)

plt.show()

<img width="592" alt="sgolay2_surface" src="https://user-images.githubusercontent.com/1299189/54092147-bc511b00-4399-11e9-9be2-c44ce697161e.png">

References

1. Ratzlaff, Kenneth L.; Johnson, Jean T. (1989). "Computation of two-dimensional polynomial least-squares convolution smoothing integers". Anal. Chem. 61 (11): 1303–5. doi:10.1021/ac00186a026.
2. Krumm, John. "Savitzky–Golay filters for 2D Images". Microsoft Research, Redmond.