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"""
This module contains the formulas for comparing Lab values with matrices
and vectors. The benefit of using NumPy's matrix capabilities is speed. These
calls can be used to efficiently compare large volumes of Lab colors.
"""
import numpy
def delta_e_cie1976(lab_color_vector, lab_color_matrix):
"""
Calculates the Delta E (CIE1976) between `lab_color_vector` and all
colors in `lab_color_matrix`.
"""
return numpy.sqrt(
numpy.sum(numpy.power(lab_color_vector - lab_color_matrix, 2), axis=1))
# noinspection PyPep8Naming
def delta_e_cie1994(lab_color_vector, lab_color_matrix,
K_L=1, K_C=1, K_H=1, K_1=0.045, K_2=0.015):
"""
Calculates the Delta E (CIE1994) of two colors.
K_l:
0.045 graphic arts
0.048 textiles
K_2:
0.015 graphic arts
0.014 textiles
K_L:
1 default
2 textiles
"""
C_1 = numpy.sqrt(numpy.sum(numpy.power(lab_color_vector[1:], 2)))
C_2 = numpy.sqrt(numpy.sum(numpy.power(lab_color_matrix[:, 1:], 2), axis=1))
delta_lab = lab_color_vector - lab_color_matrix
delta_L = delta_lab[:, 0].copy()
delta_C = C_1 - C_2
delta_lab[:, 0] = delta_C
delta_H_sq = numpy.sum(numpy.power(delta_lab, 2) * numpy.array([-1, 1, 1]), axis=1)
# noinspection PyArgumentList
delta_H = numpy.sqrt(delta_H_sq.clip(min=0))
S_L = 1
S_C = 1 + K_1 * C_1
S_H = 1 + K_2 * C_1
LCH = numpy.vstack([delta_L, delta_C, delta_H])
params = numpy.array([[K_L * S_L], [K_C * S_C], [K_H * S_H]])
return numpy.sqrt(numpy.sum(numpy.power(LCH / params, 2), axis=0))
# noinspection PyPep8Naming
def delta_e_cmc(lab_color_vector, lab_color_matrix, pl=2, pc=1):
"""
Calculates the Delta E (CIE1994) of two colors.
CMC values
Acceptability: pl=2, pc=1
Perceptability: pl=1, pc=1
"""
L, a, b = lab_color_vector
C_1 = numpy.sqrt(numpy.sum(numpy.power(lab_color_vector[1:], 2)))
C_2 = numpy.sqrt(numpy.sum(numpy.power(lab_color_matrix[:, 1:], 2), axis=1))
delta_lab = lab_color_vector - lab_color_matrix
delta_L = delta_lab[:, 0].copy()
delta_C = C_1 - C_2
delta_lab[:, 0] = delta_C
H_1 = numpy.degrees(numpy.arctan2(b, a))
if H_1 < 0:
H_1 += 360
F = numpy.sqrt(numpy.power(C_1, 4) / (numpy.power(C_1, 4) + 1900.0))
# noinspection PyChainedComparisons
if 164 <= H_1 and H_1 <= 345:
T = 0.56 + abs(0.2 * numpy.cos(numpy.radians(H_1 + 168)))
else:
T = 0.36 + abs(0.4 * numpy.cos(numpy.radians(H_1 + 35)))
if L < 16:
S_L = 0.511
else:
S_L = (0.040975 * L) / (1 + 0.01765 * L)
S_C = ((0.0638 * C_1) / (1 + 0.0131 * C_1)) + 0.638
S_H = S_C * (F * T + 1 - F)
delta_C = C_1 - C_2
delta_H_sq = numpy.sum(numpy.power(delta_lab, 2) * numpy.array([-1, 1, 1]), axis=1)
# noinspection PyArgumentList
delta_H = numpy.sqrt(delta_H_sq.clip(min=0))
LCH = numpy.vstack([delta_L, delta_C, delta_H])
params = numpy.array([[pl * S_L], [pc * S_C], [S_H]])
return numpy.sqrt(numpy.sum(numpy.power(LCH / params, 2), axis=0))
# noinspection PyPep8Naming
def delta_e_cie2000(lab_color_vector, lab_color_matrix, Kl=1, Kc=1, Kh=1):
"""
Calculates the Delta E (CIE2000) of two colors.
"""
L, a, b = lab_color_vector
avg_Lp = (L + lab_color_matrix[:, 0]) / 2.0
C1 = numpy.sqrt(numpy.sum(numpy.power(lab_color_vector[1:], 2)))
C2 = numpy.sqrt(numpy.sum(numpy.power(lab_color_matrix[:, 1:], 2), axis=1))
avg_C1_C2 = (C1 + C2) / 2.0
G = 0.5 * (1 - numpy.sqrt(numpy.power(avg_C1_C2, 7.0) / (numpy.power(avg_C1_C2, 7.0) + numpy.power(25.0, 7.0))))
a1p = (1.0 + G) * a
a2p = (1.0 + G) * lab_color_matrix[:, 1]
C1p = numpy.sqrt(numpy.power(a1p, 2) + numpy.power(b, 2))
C2p = numpy.sqrt(numpy.power(a2p, 2) + numpy.power(lab_color_matrix[:, 2], 2))
avg_C1p_C2p = (C1p + C2p) / 2.0
h1p = numpy.degrees(numpy.arctan2(b, a1p))
h1p += (h1p < 0) * 360
h2p = numpy.degrees(numpy.arctan2(lab_color_matrix[:, 2], a2p))
h2p += (h2p < 0) * 360
avg_Hp = (((numpy.fabs(h1p - h2p) > 180) * 360) + h1p + h2p) / 2.0
T = 1 - 0.17 * numpy.cos(numpy.radians(avg_Hp - 30)) + \
0.24 * numpy.cos(numpy.radians(2 * avg_Hp)) + \
0.32 * numpy.cos(numpy.radians(3 * avg_Hp + 6)) - \
0.2 * numpy.cos(numpy.radians(4 * avg_Hp - 63))
diff_h2p_h1p = h2p - h1p
delta_hp = diff_h2p_h1p + (numpy.fabs(diff_h2p_h1p) > 180) * 360
delta_hp -= (h2p > h1p) * 720
delta_Lp = lab_color_matrix[:, 0] - L
delta_Cp = C2p - C1p
delta_Hp = 2 * numpy.sqrt(C2p * C1p) * numpy.sin(numpy.radians(delta_hp) / 2.0)
S_L = 1 + ((0.015 * numpy.power(avg_Lp - 50, 2)) / numpy.sqrt(20 + numpy.power(avg_Lp - 50, 2.0)))
S_C = 1 + 0.045 * avg_C1p_C2p
S_H = 1 + 0.015 * avg_C1p_C2p * T
delta_ro = 30 * numpy.exp(-(numpy.power(((avg_Hp - 275) / 25), 2.0)))
R_C = numpy.sqrt((numpy.power(avg_C1p_C2p, 7.0)) / (numpy.power(avg_C1p_C2p, 7.0) + numpy.power(25.0, 7.0)))
R_T = -2 * R_C * numpy.sin(2 * numpy.radians(delta_ro))
return numpy.sqrt(
numpy.power(delta_Lp / (S_L * Kl), 2) +
numpy.power(delta_Cp / (S_C * Kc), 2) +
numpy.power(delta_Hp / (S_H * Kh), 2) +
R_T * (delta_Cp / (S_C * Kc)) * (delta_Hp / (S_H * Kh)))
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