"""
Functions for calculating the "distance" between colors.
Implicit in these definitions of "distance" is the notion of "Just Noticeable
Distance" (JND). This represents the distance between colors where a human can
perceive different colors. Humans are more sensitive to certain colors than
others, which different deltaE metrics correct for with varying degrees of
sophistication.
The literature often mentions 1 as the minimum distance for visual
differentiation, but more recent studies (Mahy 1994) peg JND at 2.3
The delta-E notation comes from the German word for "Sensation" (Empfindung).
Reference
---------
https://en.wikipedia.org/wiki/Color_difference
"""
import numpy as np
from .._shared.utils import _supported_float_type
from .colorconv import lab2lch, _cart2polar_2pi
def _float_inputs(lab1, lab2, allow_float32=True):
lab1 = np.asarray(lab1)
lab2 = np.asarray(lab2)
if allow_float32:
float_dtype = _supported_float_type((lab1.dtype, lab2.dtype))
else:
float_dtype = np.float64
lab1 = lab1.astype(float_dtype, copy=False)
lab2 = lab2.astype(float_dtype, copy=False)
return lab1, lab2
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def deltaE_cie76(lab1, lab2, channel_axis=-1):
"""Euclidean distance between two points in Lab color space
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
channel_axis : int, optional
This parameter indicates which axis of the arrays corresponds to
channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
dE : array_like
distance between colors `lab1` and `lab2`
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] A. R. Robertson, "The CIE 1976 color-difference formulae,"
Color Res. Appl. 2, 7-11 (1977).
"""
lab1, lab2 = _float_inputs(lab1, lab2, allow_float32=True)
L1, a1, b1 = np.moveaxis(lab1, source=channel_axis, destination=0)[:3]
L2, a2, b2 = np.moveaxis(lab2, source=channel_axis, destination=0)[:3]
return np.sqrt((L2 - L1) ** 2 + (a2 - a1) ** 2 + (b2 - b1) ** 2)
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def deltaE_ciede94(
lab1, lab2, kH=1, kC=1, kL=1, k1=0.045, k2=0.015, *, channel_axis=-1
):
"""Color difference according to CIEDE 94 standard
Accommodates perceptual non-uniformities through the use of application
specific scale factors (`kH`, `kC`, `kL`, `k1`, and `k2`).
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
kH : float, optional
Hue scale
kC : float, optional
Chroma scale
kL : float, optional
Lightness scale
k1 : float, optional
first scale parameter
k2 : float, optional
second scale parameter
channel_axis : int, optional
This parameter indicates which axis of the arrays corresponds to
channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
dE : array_like
color difference between `lab1` and `lab2`
Notes
-----
deltaE_ciede94 is not symmetric with respect to lab1 and lab2. CIEDE94
defines the scales for the lightness, hue, and chroma in terms of the first
color. Consequently, the first color should be regarded as the "reference"
color.
`kL`, `k1`, `k2` depend on the application and default to the values
suggested for graphic arts
========== ============== ==========
Parameter Graphic Arts Textiles
========== ============== ==========
`kL` 1.000 2.000
`k1` 0.045 0.048
`k2` 0.015 0.014
========== ============== ==========
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE94.html
"""
lab1, lab2 = _float_inputs(lab1, lab2, allow_float32=True)
lab1 = np.moveaxis(lab1, source=channel_axis, destination=0)
lab2 = np.moveaxis(lab2, source=channel_axis, destination=0)
L1, C1 = lab2lch(lab1, channel_axis=0)[:2]
L2, C2 = lab2lch(lab2, channel_axis=0)[:2]
dL = L1 - L2
dC = C1 - C2
dH2 = get_dH2(lab1, lab2, channel_axis=0)
SL = 1
SC = 1 + k1 * C1
SH = 1 + k2 * C1
dE2 = (dL / (kL * SL)) ** 2
dE2 += (dC / (kC * SC)) ** 2
dE2 += dH2 / (kH * SH) ** 2
return np.sqrt(np.maximum(dE2, 0))
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def deltaE_ciede2000(lab1, lab2, kL=1, kC=1, kH=1, *, channel_axis=-1):
"""Color difference as given by the CIEDE 2000 standard.
CIEDE 2000 is a major revision of CIDE94. The perceptual calibration is
largely based on experience with automotive paint on smooth surfaces.
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
kL : float (range), optional
lightness scale factor, 1 for "acceptably close"; 2 for "imperceptible"
see deltaE_cmc
kC : float (range), optional
chroma scale factor, usually 1
kH : float (range), optional
hue scale factor, usually 1
channel_axis : int, optional
This parameter indicates which axis of the arrays corresponds to
channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
deltaE : array_like
The distance between `lab1` and `lab2`
Notes
-----
CIEDE 2000 assumes parametric weighting factors for the lightness, chroma,
and hue (`kL`, `kC`, `kH` respectively). These default to 1.
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.ece.rochester.edu/~gsharma/ciede2000/ciede2000noteCRNA.pdf
:DOI:`10.1364/AO.33.008069`
.. [3] M. Melgosa, J. Quesada, and E. Hita, "Uniformity of some recent
color metrics tested with an accurate color-difference tolerance
dataset," Appl. Opt. 33, 8069-8077 (1994).
"""
lab1, lab2 = _float_inputs(lab1, lab2, allow_float32=True)
channel_axis = channel_axis % lab1.ndim
unroll = False
if lab1.ndim == 1 and lab2.ndim == 1:
unroll = True
if lab1.ndim == 1:
lab1 = lab1[None, :]
if lab2.ndim == 1:
lab2 = lab2[None, :]
channel_axis += 1
L1, a1, b1 = np.moveaxis(lab1, source=channel_axis, destination=0)[:3]
L2, a2, b2 = np.moveaxis(lab2, source=channel_axis, destination=0)[:3]
# distort `a` based on average chroma
# then convert to lch coordinates from distorted `a`
# all subsequence calculations are in the new coordinates
# (often denoted "prime" in the literature)
Cbar = 0.5 * (np.hypot(a1, b1) + np.hypot(a2, b2))
c7 = Cbar**7
G = 0.5 * (1 - np.sqrt(c7 / (c7 + 25**7)))
scale = 1 + G
C1, h1 = _cart2polar_2pi(a1 * scale, b1)
C2, h2 = _cart2polar_2pi(a2 * scale, b2)
# recall that c, h are polar coordinates. c==r, h==theta
# cide2000 has four terms to delta_e:
# 1) Luminance term
# 2) Hue term
# 3) Chroma term
# 4) hue Rotation term
# lightness term
Lbar = 0.5 * (L1 + L2)
tmp = (Lbar - 50) ** 2
SL = 1 + 0.015 * tmp / np.sqrt(20 + tmp)
L_term = (L2 - L1) / (kL * SL)
# chroma term
Cbar = 0.5 * (C1 + C2) # new coordinates
SC = 1 + 0.045 * Cbar
C_term = (C2 - C1) / (kC * SC)
# hue term
h_diff = h2 - h1
h_sum = h1 + h2
CC = C1 * C2
dH = h_diff.copy()
dH[h_diff > np.pi] -= 2 * np.pi
dH[h_diff < -np.pi] += 2 * np.pi
dH[CC == 0.0] = 0.0 # if r == 0, dtheta == 0
dH_term = 2 * np.sqrt(CC) * np.sin(dH / 2)
Hbar = h_sum.copy()
mask = np.logical_and(CC != 0.0, np.abs(h_diff) > np.pi)
Hbar[mask * (h_sum < 2 * np.pi)] += 2 * np.pi
Hbar[mask * (h_sum >= 2 * np.pi)] -= 2 * np.pi
Hbar[CC == 0.0] *= 2
Hbar *= 0.5
T = (
1
- 0.17 * np.cos(Hbar - np.deg2rad(30))
+ 0.24 * np.cos(2 * Hbar)
+ 0.32 * np.cos(3 * Hbar + np.deg2rad(6))
- 0.20 * np.cos(4 * Hbar - np.deg2rad(63))
)
SH = 1 + 0.015 * Cbar * T
H_term = dH_term / (kH * SH)
# hue rotation
c7 = Cbar**7
Rc = 2 * np.sqrt(c7 / (c7 + 25**7))
dtheta = np.deg2rad(30) * np.exp(-(((np.rad2deg(Hbar) - 275) / 25) ** 2))
R_term = -np.sin(2 * dtheta) * Rc * C_term * H_term
# put it all together
dE2 = L_term**2
dE2 += C_term**2
dE2 += H_term**2
dE2 += R_term
ans = np.sqrt(np.maximum(dE2, 0))
if unroll:
ans = ans[0]
return ans
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def deltaE_cmc(lab1, lab2, kL=1, kC=1, *, channel_axis=-1):
"""Color difference from the CMC l:c standard.
This color difference was developed by the Colour Measurement Committee
(CMC) of the Society of Dyers and Colourists (United Kingdom). It is
intended for use in the textile industry.
The scale factors `kL`, `kC` set the weight given to differences in
lightness and chroma relative to differences in hue. The usual values are
``kL=2``, ``kC=1`` for "acceptability" and ``kL=1``, ``kC=1`` for
"imperceptibility". Colors with ``dE > 1`` are "different" for the given
scale factors.
Parameters
----------
lab1 : array_like
reference color (Lab colorspace)
lab2 : array_like
comparison color (Lab colorspace)
channel_axis : int, optional
This parameter indicates which axis of the arrays corresponds to
channels.
.. versionadded:: 0.19
``channel_axis`` was added in 0.19.
Returns
-------
dE : array_like
distance between colors `lab1` and `lab2`
Notes
-----
deltaE_cmc the defines the scales for the lightness, hue, and chroma
in terms of the first color. Consequently
``deltaE_cmc(lab1, lab2) != deltaE_cmc(lab2, lab1)``
References
----------
.. [1] https://en.wikipedia.org/wiki/Color_difference
.. [2] http://www.brucelindbloom.com/index.html?Eqn_DeltaE_CIE94.html
.. [3] F. J. J. Clarke, R. McDonald, and B. Rigg, "Modification to the
JPC79 colour-difference formula," J. Soc. Dyers Colour. 100, 128-132
(1984).
"""
lab1, lab2 = _float_inputs(lab1, lab2, allow_float32=True)
lab1 = np.moveaxis(lab1, source=channel_axis, destination=0)
lab2 = np.moveaxis(lab2, source=channel_axis, destination=0)
L1, C1, h1 = lab2lch(lab1, channel_axis=0)[:3]
L2, C2, h2 = lab2lch(lab2, channel_axis=0)[:3]
dC = C1 - C2
dL = L1 - L2
dH2 = get_dH2(lab1, lab2, channel_axis=0)
T = np.where(
np.logical_and(np.rad2deg(h1) >= 164, np.rad2deg(h1) <= 345),
0.56 + 0.2 * np.abs(np.cos(h1 + np.deg2rad(168))),
0.36 + 0.4 * np.abs(np.cos(h1 + np.deg2rad(35))),
)
c1_4 = C1**4
F = np.sqrt(c1_4 / (c1_4 + 1900))
SL = np.where(L1 < 16, 0.511, 0.040975 * L1 / (1.0 + 0.01765 * L1))
SC = 0.638 + 0.0638 * C1 / (1.0 + 0.0131 * C1)
SH = SC * (F * T + 1 - F)
dE2 = (dL / (kL * SL)) ** 2
dE2 += (dC / (kC * SC)) ** 2
dE2 += dH2 / (SH**2)
return np.sqrt(np.maximum(dE2, 0))
def get_dH2(lab1, lab2, *, channel_axis=-1):
"""squared hue difference term occurring in deltaE_cmc and deltaE_ciede94
Despite its name, "dH" is not a simple difference of hue values. We avoid
working directly with the hue value, since differencing angles is
troublesome. The hue term is usually written as:
c1 = sqrt(a1**2 + b1**2)
c2 = sqrt(a2**2 + b2**2)
term = (a1-a2)**2 + (b1-b2)**2 - (c1-c2)**2
dH = sqrt(term)
However, this has poor roundoff properties when a or b is dominant.
Instead, ab is a vector with elements a and b. The same dH term can be
re-written as:
|ab1-ab2|**2 - (|ab1| - |ab2|)**2
and then simplified to:
2*|ab1|*|ab2| - 2*dot(ab1, ab2)
"""
# This function needs double precision internally for accuracy
input_is_float_32 = _supported_float_type((lab1.dtype, lab2.dtype)) == np.float32
lab1, lab2 = _float_inputs(lab1, lab2, allow_float32=False)
a1, b1 = np.moveaxis(lab1, source=channel_axis, destination=0)[1:3]
a2, b2 = np.moveaxis(lab2, source=channel_axis, destination=0)[1:3]
# magnitude of (a, b) is the chroma
C1 = np.hypot(a1, b1)
C2 = np.hypot(a2, b2)
term = (C1 * C2) - (a1 * a2 + b1 * b2)
out = 2 * term
if input_is_float_32:
out = out.astype(np.float32)
return out
