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import numpy as np, scipy.optimize as optimize
from colour import *
from colour.difference import delta_E_CIE1976
from colour.colorimetry import *
# The same wavelength grid is used throughout
wvl = np.arange(360, 830, 5)
wvlp = (wvl - 360) / (830 - 360)
# This is the model of spectral reflectivity described in the article.
def model(wvlp, ccp):
yy = ccp[0] * wvlp**2 + ccp[1] * wvlp + ccp[2]
return 1 / 2 + yy / (2 * np.sqrt(1 + yy ** 2))
# Create a SpectralDistribution using given coefficients
def model_sd(ccp, primed=True):
# FIXME: don't hardcode the wavelength grid; there should be a way
# of creating a SpectralDistribution from the function alone
grid = wvlp if primed else wvl
return SpectralDistribution(model(grid, ccp), wvl, name="Model")
# The goal is to minimize the color difference between a given distrbution
# and the one computed from the model above.
def error_function(ccp, target, ill_sd, ill_xy):
# One thing they didn't mention in the text is that their polynomial
# is nondimensionalized (mapped from 360--800 nm to 0--1).
sd = model_sd(ccp)
Lab = XYZ_to_Lab(sd_to_XYZ(sd, illuminant=ill_sd) / 100, ill_xy)
return delta_E_CIE1976(target, Lab)
# Finds the parameters for Jakob and Hanika's model
def jakob_hanika(target_XYZ, ill_sd, ill_xy, ccp0=(0, 0, 0), verbose=True, try_hard=True):
def do_optimize(XYZ, ccp0):
Lab = XYZ_to_Lab(XYZ, ill_xy)
opt = optimize.minimize(
error_function, ccp0, (Lab, ill_sd, ill_xy),
method="Nelder-Mead", options={"disp": verbose}
)
if verbose:
print(opt)
return opt
# A special case that's hard to solve numerically
if np.allclose(target_XYZ, [0, 0, 0]):
return np.array([0, 0, -1e+9]), 0 # FIXME: dtype?
if verbose:
print("Trying the target directly, XYZ=%s" % target_XYZ)
opt = do_optimize(target_XYZ, ccp0)
if opt.fun < 0.1 or not try_hard:
return opt.x, opt.fun
good_XYZ = (1/3, 1/3, 1/3)
good_ccp = (2.1276356, -1.07293026, -0.29583292) # FIXME: valid only for D65
divisions = 3
while divisions < 10:
if verbose:
print("Trying with %d divisions" % divisions)
keep_divisions = False
ref_XYZ = good_XYZ
ref_ccp = good_ccp
ccp0 = ref_ccp
for i in range(1, divisions):
intermediate_XYZ = ref_XYZ + (target_XYZ - ref_XYZ) * i / (divisions - 1)
if verbose:
print("Intermediate step %d/%d, XYZ=%s with ccp0=%s" %
(i + 1, divisions, intermediate_XYZ, ccp0))
opt = do_optimize(intermediate_XYZ, ccp0)
if opt.fun > 0.1:
if verbose:
print("WARNING: intermediate optimization failed")
break
else:
good_XYZ = intermediate_XYZ
good_ccp = opt.x
keep_divisions = True
ccp0 = opt.x
else:
return opt.x, opt.fun
if not keep_divisions:
divisions += 2
raise Exception("optimization failed for target_XYZ=%s, ccp0=%s" \
% (target_XYZ, ccp0))
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