#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
metric: Colour metric functions. Part of the colourlab package.
Copyright (C) 2013-2017 Ivar Farup
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 . import data, space
# =============================================================================
# Auxiliary functions
# =============================================================================
[docs]def reshape_diff(diff, sh):
"""
Reshape the computed metric differences to fit with original data.
The purpose is for, e.g., the difference of two MxNx3 images to be
a MxN scalar image etc.
Parameters
----------
diff : ndarray
The computed differences
sh : tuple
The shape of the original data (not the diff)
"""
ell = len(sh)
if ell == 1: # one-dimensional colour data (one colour point)
return diff[0]
elif ell == 2: # two-dimensional colour data (list of colours)
return diff
else: # three or more dimensions (images++)
return np.reshape(diff, tuple(np.array(sh)[:-1]))
# =============================================================================
# Colour metric functions
# =============================================================================
[docs]def linear(sp, dat1, dat2, metric_tensor_function):
"""
Compute the linearised colour difference between the two data sets.
The function metric_tensor_function is used to compute the metric tensor
at the midpoint between the two data sets in the given colour space. Then
the colour metric is computed as dC^T * g * dC.
Parameters
----------
sp : Space
The colour space in which to compute the linearised metric.
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
metric_tensor_function : function
Function giving the metric tensors at given colour data points.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
d1 = dat1.get_flattened(sp)
d2 = dat2.get_flattened(sp)
midp = (d1 + d2) * .5
diff = d1 - d2
g = metric_tensor_function(data.Points(sp, midp))
g = g.get(sp)
m = np.zeros(np.shape(diff)[0])
for i in range(np.shape(m)[0]):
m[i] = np.sqrt(np.dot(diff[i].T, np.dot(g[i], diff[i])))
return reshape_diff(m, dat1.sh)
[docs]def euclidean(sp, dat1, dat2):
"""
Compute the Euclidean metric between the two data sets in the given space.
Parameters
----------
sp : Space
Colour space
dat1 : Points
Colour data set 1
dat2 : Points
Colour data set 2
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
d1 = dat1.get_flattened(sp)
d2 = dat2.get_flattened(sp)
diff = d1 - d2
m = np.sqrt(diff[:, 0]**2 + diff[:, 1]**2 + diff[:, 2]**2)
return reshape_diff(m, dat1.sh)
[docs]def poincare_disk(sp, dat1, dat2):
"""
Compute the Poincare Disk metric betwen the two data sets.
Compted in the given space. Assumes that the space is some form of
a Poincare Disk space, such that the radius of curvature is given
by sp.R. The first coordinate is treated as Euclidean.
Parameters
----------
sp : Space
Colour space (should be of Poincare Disk type)
dat1: Points
Colour data set 1
dat2: Points
Colour data set 2
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
d1 = dat1.get_flattened(sp)
d2 = dat2.get_flattened(sp)
diff = d1 - d2
delta = 2 * ((diff[:, 1]**2 + diff[:, 2]**2) /
((1 - d1[:, 1]**2 - d1[:, 2]**2) *
(1 - d2[:, 1]**2 - d2[:, 2]**2)))
duv = sp.R * np.arccosh(1 + delta)
d = np.sqrt(diff[:, 0]**2 + duv**2)
return reshape_diff(d, dat1.sh)
[docs]def dE_ab(dat1, dat2):
"""
Compute the DEab metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.cielab, dat1, dat2)
[docs]def dE_uv(dat1, dat2):
"""
Compute the DEuv metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.cieluv, dat1, dat2)
[docs]def dE_E(dat1, dat2):
"""
Compute the DEE metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.lgj_e, dat1, dat2)
[docs]def dE_DIN99(dat1, dat2):
"""
Compute the DIN99 metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.din99, dat1, dat2)
[docs]def dE_DIN99b(dat1, dat2):
"""
Compute the DIN99b metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.din99b, dat1, dat2)
[docs]def dE_DIN99c(dat1, dat2):
"""
Compute the DIN99c metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.din99c, dat1, dat2)
[docs]def dE_DIN99d(dat1, dat2):
"""
Compute the DIN99d metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
return euclidean(space.din99d, dat1, dat2)
[docs]def dE_00(dat1, dat2, k_L=1, k_C=1, k_h=1):
"""
Compute the CIEDE00 metric.
Parameters
----------
dat1 : Points
The colour data of the first data set.
dat2 : Points
The colour data of the second data set.
k_L : float
Parameter of the CIEDE00 metric
k_C : float
Parameter of the CIEDE00 metric
k_h : float
Parameter of the CIEDE00 metric
Returns
-------
distance : ndarray
Array of the difference or distances between the two data sets.
"""
lch1 = dat1.get_flattened(space.ciede00lch)
lch2 = dat2.get_flattened(space.ciede00lch)
avg_lch = .5 * (lch1 + lch2)
d_lch = lch1 - lch2
h_deg = np.rad2deg(avg_lch[:, 2])
h_deg[h_deg < 0] = h_deg[h_deg < 0] + 360
S_L = 1 + ((0.015 * (avg_lch[:, 0] - 50)**2) /
np.sqrt(20 + (avg_lch[:, 0] - 50)**2))
S_C = 1 + 0.045 * avg_lch[:, 1]
T = 1 - 0.17 * np.cos(np.deg2rad(h_deg - 30)) + \
.24 * np.cos(2*avg_lch[:, 2]) + \
.32 * np.cos(np.deg2rad(3 * h_deg + 6)) - \
.2 * np.cos(np.deg2rad(4 * h_deg - 63))
S_h = 1 + 0.015 * avg_lch[:, 1] * T
R_C = 2 * np.sqrt(avg_lch[:, 1]**7 / (avg_lch[:, 1]**7 + 25**7))
d_theta = 30 * np.exp(-((h_deg - 275) / 25)**2)
R_T = - R_C * np.sin(np.deg2rad(2 * d_theta))
dH = 2 * np.sqrt(lch1[:, 1] * lch2[:, 1]) * np.sin(d_lch[:, 2] / 2)
d = np.sqrt((d_lch[:, 0] / (k_L * S_L))**2 +
(d_lch[:, 1] / (k_C * S_C))**2 +
(dH / (k_h * S_h))**2 +
R_T * d_lch[:, 1] * dH / (k_C * S_C * k_h * S_h))
return reshape_diff(d, dat1.sh)