"""
fire.py : Collection of Fuzzy Inference Ruled by ELSE-action (FIRE) filters.
"""
import numpy as np
from ..image import view_as_windows
from ..membership import trimf
[docs]def fire1d(x, l1=0, l2=1):
"""
1-D filtering using Fuzzy Inference Ruled by Else-action (FIRE) [1].
FIRE filtering is nonlinear, and is specifically designed to remove
impulse (salt and pepper) noise.
Parameters
----------
x : 1d array or iterable
Input sequence, filtered range limited by ``l1`` and ``l2``.
l1 : float
Lower input range limit for ``x``.
l2 : float
Upper input range limit for ``x``.
Returns
-------
y : 1d array
FIRE filtered sequence.
Notes
-----
Filtering occurs for ``l1 < |x| < l2``; for ``|x| < l1`` there is no
effect.
References
----------
.. [1] Fabrizio Russo, Fuzzy Filtering of Noisy Sensor Data, IEEE
Instrumentation and Measurement Technology Conference,
Brussels, Belgium, June 4 - 6, 1996, pp 1281 - 1285.
"""
from ..image import pad as padimg
# Enforce range limit
np.clip(x, -l2, l2, out=x)
# Fuzzy input sequence
dx = np.arange(-1000, 1001) * l2 / 1000.
# Fuzzy membership functions
po = np.atleast_2d(trimf(dx, [l1, l2, l2])).ravel()
ne = np.atleast_2d(trimf(dx, [-l2, -l2, -l1])).ravel()
# Fuzzy neighborhood rules (indices for comparison)
rules = np.r_[[[0, 1, 3],
[1, 3, 4],
[0, 3, 4],
[0, 1, 4]]]
# Padding the array
x = padimg(x, 2, mode='reflect')
# Generate rolling 5-point window view into the array
xx = view_as_windows(x, (5,))
# Zero each local window relative to center point
center = xx[:, 2]
dxx = xx - center[:, np.newaxis].repeat(5, axis=1)
# Conduct interpolation all at once, on every point, for po and ne
mpo = np.interp(dxx, dx, po)
mne = np.interp(dxx, dx, ne)
# Build output correction functions all at once
lam = np.zeros((0, len(mpo)))
lam2 = np.zeros((0, len(mne)))
for rule in rules:
lam = np.vstack((lam, np.atleast_2d(mpo[:, rule].min(axis=1))))
lam2 = np.vstack((lam2, np.atleast_2d(mne[:, rule].min(axis=1))))
lam = np.max(lam, axis=0)
lam2 = np.max(lam2, axis=0)
# Corrected result
y = xx[:, 2] + l2 * (lam - lam2)
return y
[docs]def fire2d(im, l1=0, l2=255, fuzzyresolution=1):
"""
2-D filtering using Fuzzy Inference Ruled by Else-action (FIRE) [1].
FIRE filtering is nonlinear, and is specifically designed to remove
impulse (salt and pepper) noise.
Parameters
----------
I : 2d array
Input image.
l1 : float
Lower limit of filtering range.
l2 : float
Upper limit of filtering range.
fuzzyresolution : float, default = 1
Resolution of fuzzy input sequence, or spacing between [-l2+1, l2-1].
The default assumes an integer input; for floating point images a
decimal value should be used approximately equal to the bit depth.
Returns
-------
J : 2d array
FIRE filtered image.
Notes
-----
Filtering occurs for ``l1 < |x| < l2``; outside this range the data is
unaffected.
References
----------
.. [1] Fabrizio Russo, Fuzzy Filtering of Noisy Sensor Data, IEEE
Instrumentation and Measurement Technology Conference,
Brussels, Belgium, June 4 - 6, 1996, pp 1281 - 1285.
"""
from ..image import pad as padimg
im = padimg(im.astype(float), 1, mode='reflect')
# Fuzzy input sequence
dx = np.arange(-l2 + fuzzyresolution,
l2 - fuzzyresolution,
fuzzyresolution)
# Fuzzy membership functions
po = np.atleast_2d(trimf(dx, [l1,
l2 - fuzzyresolution,
l2 - fuzzyresolution]))
ne = np.atleast_2d(trimf(dx, [fuzzyresolution - l2,
fuzzyresolution - l2,
- l1]))
# Combine into matrix
multi_stack_rules = np.hstack([po.T, ne.T])
rules1 = np.r_[[[2, 4, 8],
[4, 6, 8],
[2, 6, 8],
[2, 4, 6]]] - 1
rules2 = np.r_[[[1, 3, 7, 9],
[1, 4, 8, 9],
[3, 6, 7, 8],
[1, 2, 6, 9],
[2, 3, 4, 7]]] - 1
# Zero the local windows
local_win = view_as_windows(im, (3, 3))
im2 = im[1:-1, 1:-1].copy()
im2 = im2[..., np.newaxis, np.newaxis].repeat(3, axis=2).repeat(3, axis=3)
dx = local_win - im2
# Vectorization allows concise, fast calculation of lam and lam2
idx = l2 + dx
idx = idx.reshape((idx.shape[0], idx.shape[1], -1))
mu = multi_stack_rules[idx.astype(int), :]
lam = np.concatenate((np.min(mu[:, :, rules1[range(4), :], 0], axis=3),
np.min(mu[:, :, rules2[range(5), :], 0], axis=3)),
axis=2).max(axis=2)
lam2 = np.concatenate((np.min(mu[:, :, rules1[range(4), :], 1], axis=3),
np.min(mu[:, :, rules2[range(5), :], 1], axis=3)),
axis=2).max(axis=2)
return im[1:-1, 1:-1] + (l2 - 1) * (lam - lam2)
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