[BUG]: CIEDE2000 Color-Difference Calculation (deg/rad conversions)

[michel-leonard]

Description

Hello,

I've been using the CIEDE2000 color-difference calculation function (delta_E_CIE2000) in the library and noticed that the function performs an unnecessary conversion between radians and degrees. Specifically, it multiplies by 180 and then divides by 180 shortly afterward, which seems redundant. This conversion introduces a small epsilon error in certain cases.

• For example, with the inputs L1, a1, b1, L2, a2, b2 = 88, -124, 56, 97, 62, -28, the algorithm reaches a condition where it evaluates np.fabs(h1_prime - h2_prime) to "180.00000000000003" degrees, which is "π" (3.141592653589793) radians when you omit the conversion from radians to degrees.

• The specific branch taken right after when the value is greater than π (radians) or 180° is inconsistent due to this minor error, affecting the output of the algorithm.

Thank you for your attention to this detail, and I'm happy to provide further information or assist with testing if needed.

Best regards,
Michel Leonard

Environment Information

Linux version 4.19.0-27-cloud-amd64 ([e-mail]) (gcc version 8.3.0 (Debian 8.3.0-6)) #1 SMP Debian 4.19.316-1 (2024-06-25)

[michel-leonard]

My proposition (avoiding deg/rad conversion) based on your implementation would look like :

def delta_E_CIE2000(Lab1, Lab2):
	import numpy as np
	
	# Unpack Lab values
	L1, a1, b1 = np.ravel(Lab1)
	L2, a2, b2 = np.ravel(Lab2)

	# Constants
	kL = kC = kH = 1

	# Calculate the averages
	l_bar_prime = (L1 + L2) / 2

	# Calculate C1, C2, and their average
	c1 = np.hypot(a1, b1)
	c2 = np.hypot(a2, b2)
	c_bar = (c1 + c2) / 2

	# Calculate G factor
	c_bar7 = c_bar ** 7
	g = 0.5 * (1 - np.sqrt(c_bar7 / (c_bar7 + 25 ** 7)))

	# Calculate a_prime and c_prime values
	a1_prime = a1 * (1 + g)
	a2_prime = a2 * (1 + g)
	c1_prime = np.hypot(a1_prime, b1)
	c2_prime = np.hypot(a2_prime, b2)
	c_bar_prime = (c1_prime + c2_prime) / 2

	# Calculate h_prime values
	h1_prime = np.arctan2(b1, a1_prime)
	h2_prime = np.arctan2(b2, a2_prime)
	
	# Adjust h_prime values
	if h1_prime < 0:
		h1_prime += 2 * np.pi
	
	if h2_prime < 0:
		h2_prime += 2 * np.pi

	# Calculate the average hue
	if np.abs(h1_prime - h2_prime) > np.pi:
		h_bar_prime = (h1_prime + h2_prime + 2 * np.pi) / 2
	else:
		h_bar_prime = (h1_prime + h2_prime) / 2

	# Calculate T
	t = (1 
		 - 0.17 * np.cos(h_bar_prime - np.pi / 6)
		 + 0.24 * np.cos(2 * h_bar_prime)
		 + 0.32 * np.cos(3 * h_bar_prime + np.pi / 30)
		 - 0.20 * np.cos(4 * h_bar_prime - 7 * np.pi / 20))

	# Calculate delta_h_prime
	if np.abs(h2_prime - h1_prime) <= np.pi:
		delta_h_prime = h2_prime - h1_prime
	elif h2_prime <= h1_prime:
		delta_h_prime = h2_prime - h1_prime + 2 * np.pi
	else:
		delta_h_prime = h2_prime - h1_prime - 2 * np.pi

	# Calculate delta values
	delta_L_prime = L2 - L1
	delta_C_prime = c2_prime - c1_prime
	delta_H_prime = 2 * np.sqrt(c1_prime * c2_prime) * np.sin(delta_h_prime / 2)

	# Calculate S_L, S_C, S_H
	l50_sq = (l_bar_prime - 50) ** 2
	sL = 1 + 0.015 * l50_sq / np.sqrt(20 + l50_sq)
	sC = 1 + 0.045 * c_bar_prime
	sH = 1 + 0.015 * c_bar_prime * t

	# Calculate R_C and R_T
	c_bar_prime7 = c_bar_prime ** 7
	rC = np.sqrt(c_bar_prime7 / (c_bar_prime7 + 25 ** 7))
	rT = -2 * rC * np.sin(np.pi / 3 * np.exp(-((36 * h_bar_prime - 55 * np.pi) ** 2) / (25 * np.pi ** 2)))

	# Calculate delta_E
	delta_E = np.sqrt(
		(delta_L_prime / (kL * sL)) ** 2 +
		(delta_C_prime / (kC * sC)) ** 2 +
		(delta_H_prime / (kH * sH)) ** 2 +
		(delta_C_prime / (kC * sC)) * (delta_H_prime / (kH * sH)) * rT
	)

	return delta_E

[Thomas Mansencal]

Hi @michel-leonard,

Thanks for looking at that! I'm quite busy atm so I won't have time to look at that but I would be happy to take a PR if you have some cycles.

Cheers,

Thomas