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validation.py
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validation.py
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"""A module for spurious vector detection."""
__licence__ = """
Copyright (C) 2011 www.openpiv.net
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
"""
import numpy as np
from scipy.ndimage import generic_filter
import matplotlib.pyplot as plt
def global_val(u, v, u_thresholds, v_thresholds):
"""Eliminate spurious vectors with a global threshold.
This validation method tests for the spatial consistency of the data
and outliers vector are replaced with Nan (Not a Number) if at
least one of the two velocity components is out of a specified global
range.
Parameters
----------
u : 2d np.ndarray
a two dimensional array containing the u velocity component.
v : 2d np.ndarray
a two dimensional array containing the v velocity component.
u_thresholds: two elements tuple
u_thresholds = (u_min, u_max). If ``u<u_min`` or ``u>u_max``
the vector is treated as an outlier.
v_thresholds: two elements tuple
``v_thresholds = (v_min, v_max)``. If ``v<v_min`` or ``v>v_max``
the vector is treated as an outlier.
Returns
-------
u : 2d np.ndarray
a two dimensional array containing the u velocity component,
where spurious vectors have been replaced by NaN.
v : 2d np.ndarray
a two dimensional array containing the v velocity component,
where spurious vectors have been replaced by NaN.
mask : boolean 2d np.ndarray
a boolean array. True elements corresponds to outliers.
"""
np.warnings.filterwarnings("ignore")
ind = np.logical_or(
np.logical_or(u < u_thresholds[0], u > u_thresholds[1]),
np.logical_or(v < v_thresholds[0], v > v_thresholds[1]),
)
u[ind] = np.nan
v[ind] = np.nan
mask = np.zeros_like(u, dtype=bool)
mask[ind] = True
return u, v, mask
def global_std(u, v, std_threshold=5):
"""Eliminate spurious vectors with a global threshold defined by the
standard deviation
This validation method tests for the spatial consistency of the data
and outliers vector are replaced with NaN (Not a Number) if at least
one of the two velocity components is out of a specified global range.
Parameters
----------
u : 2d masked np.ndarray
a two dimensional array containing the u velocity component.
v : 2d masked np.ndarray
a two dimensional array containing the v velocity component.
std_threshold: float
If the length of the vector (actually the sum of squared components) is
larger than std_threshold times standard deviation of the flow field,
then the vector is treated as an outlier. [default = 3]
Returns
-------
u : 2d np.ndarray
a two dimensional array containing the u velocity component,
where spurious vectors have been replaced by NaN.
v : 2d np.ndarray
a two dimensional array containing the v velocity component,
where spurious vectors have been replaced by NaN.
mask : boolean 2d np.ndarray
a boolean array. True elements corresponds to outliers.
"""
# both previous nans and masked regions are not
# participating in the magnitude comparison
# def reject_outliers(data, m=2):
# return data[abs(data - np.mean(data)) < m * np.std(data)]
# create nan filled arrays where masks
# if u,v, are non-masked, ma.copy() adds false masks
tmpu = np.ma.copy(u).filled(np.nan)
tmpv = np.ma.copy(v).filled(np.nan)
ind = np.logical_or(np.abs(tmpu - np.nanmean(tmpu)) > std_threshold * np.nanstd(tmpu),
np.abs(tmpv - np.nanmean(tmpv)) > std_threshold * np.nanstd(tmpv))
if np.all(ind): # if all is True, something is really wrong
print('Warning! probably a uniform shift data, do not use this filter')
ind = ~ind
u[ind] = np.nan
v[ind] = np.nan
mask = np.zeros_like(u, dtype=bool)
mask[ind] = True
return u, v, mask
def sig2noise_val(u, v, s2n, w=None, threshold=1.05):
"""Eliminate spurious vectors from cross-correlation signal to noise ratio.
Replace spurious vectors with zero if signal to noise ratio
is below a specified threshold.
Parameters
----------
u : 2d or 3d np.ndarray
a two or three dimensional array containing the u velocity component.
v : 2d or 3d np.ndarray
a two or three dimensional array containing the v velocity component.
s2n : 2d np.ndarray
a two or three dimensional array containing the value of the signal to
noise ratio from cross-correlation function.
w : 2d or 3d np.ndarray
a two or three dimensional array containing the w (in z-direction)
velocity component.
threshold: float
the signal to noise ratio threshold value.
Returns
-------
u : 2d or 3d np.ndarray
a two or three dimensional array containing the u velocity component,
where spurious vectors have been replaced by NaN.
v : 2d or 3d np.ndarray
a two or three dimensional array containing the v velocity component,
where spurious vectors have been replaced by NaN.
w : 2d or 3d np.ndarray
optional, a two or three dimensional array containing the w
(in z-direction) velocity component, where spurious vectors
have been replaced by NaN.
mask : boolean 2d np.ndarray
a boolean array. True elements corresponds to outliers.
References
----------
R. D. Keane and R. J. Adrian, Measurement Science & Technology, 1990,
1, 1202-1215.
"""
ind = s2n < threshold
u[ind] = np.nan
v[ind] = np.nan
mask = np.zeros_like(u, dtype=bool)
mask[ind] = True
if isinstance(w, np.ndarray):
w[ind] = np.nan
return u, v, w, mask
return u, v, mask
def local_median_val(u, v, u_threshold, v_threshold, size=1):
"""Eliminate spurious vectors with a local median threshold.
This validation method tests for the spatial consistency of the data.
Vectors are classified as outliers and replaced with Nan (Not a Number) if
the absolute difference with the local median is greater than a user
specified threshold. The median is computed for both velocity components.
The image masked areas (obstacles, reflections) are marked as masked array:
u = np.ma.masked(u, mask = image_mask)
and it should not be replaced by the local median, but remain masked.
Parameters
----------
u : 2d np.ndarray
a two dimensional array containing the u velocity component.
v : 2d np.ndarray
a two dimensional array containing the v velocity component.
u_threshold : float
the threshold value for component u
v_threshold : float
the threshold value for component v
Returns
-------
u : 2d np.ndarray
a two dimensional array containing the u velocity component,
where spurious vectors have been replaced by NaN.
v : 2d np.ndarray
a two dimensional array containing the v velocity component,
where spurious vectors have been replaced by NaN.
mask : boolean 2d np.ndarray
a boolean array. True elements corresponds to outliers.
"""
# make a copy of the data without the masked region, fill it also with
# NaN and then use generic filter with nanmean
#
u = np.ma.copy(u)
v = np.ma.copy(v)
# kernel footprint
f = np.ones((2*size+1, 2*size+1))
f[size,size] = 0
masked_u = np.where(~u.mask, u.data, np.nan)
masked_v = np.where(~v.mask, v.data, np.nan)
um = generic_filter(masked_u, np.nanmedian, mode='constant',
cval=np.nan, footprint=f)
vm = generic_filter(masked_v, np.nanmedian, mode='constant',
cval=np.nan, footprint=f)
ind = (np.abs((u - um)) > u_threshold) | (np.abs((v - vm)) > v_threshold)
u[ind] = np.nan
v[ind] = np.nan
mask = np.zeros(u.shape, dtype=bool)
mask[ind] = True
return u, v, mask
def typical_validation(u, v, s2n, settings):
"""
validation using gloabl limits and std and local median,
with a special option of 'no_std' for the case of completely
uniform shift, e.g. in tests.
see Settings() for the parameters:
MinMaxU : two elements tuple
sets the limits of the u displacment component
Used for validation.
MinMaxV : two elements tuple
sets the limits of the v displacment component
Used for validation.
std_threshold : float
sets the threshold for the std validation
median_threshold : float
sets the threshold for the median validation
"""
if settings.show_all_plots:
plt.figure()
plt.quiver(u,v,color='b')
mask = np.zeros(u.shape, dtype=bool)
u, v, mask_g = global_val(
u, v, settings.MinMax_U_disp, settings.MinMax_V_disp
)
# print(f"global filter invalidated {sum(mask_g.flatten())} vectors")
if settings.show_all_plots:
plt.quiver(u,v,color='m')
u, v, mask_s = global_std(
u, v, std_threshold=settings.std_threshold
)
# print(f"std filter invalidated {sum(mask_s.flatten())} vectors")
if settings.show_all_plots:
plt.quiver(u,v,color='k')
u, v, mask_m = local_median_val(
u,
v,
u_threshold=settings.median_threshold,
v_threshold=settings.median_threshold,
size=settings.median_size,
)
if settings.show_all_plots:
plt.quiver(u,v,color='r')
# print(f"median filter invalidated {sum(mask_m.flatten())} vectors")
mask = mask + mask_g + mask_m + mask_s
if settings.sig2noise_validate:
u, v, mask_s2n = sig2noise_val(
u, v, s2n,
threshold=settings.sig2noise_threshold
)
# print(f"s2n filter invalidated {sum(mask_s2n.flatten())} vectors")
if settings.show_all_plots:
plt.quiver(u,v,color='g')
plt.show()
if settings.show_all_plots and sum(mask_s2n.flatten()): # if not all NaN
plt.figure()
plt.hist(s2n[s2n>0].flatten(),31)
plt.show()
mask += mask_s2n
return u, v, mask