How to compute Delta E CAM16 distance? #439
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Hi everyone, I'm trying to compute distance between two colors in the CAM16 SCD space. Here is my code: I got the following error: It is unclear to me if the formula to compute color distance changes or if it is always an Euclidean distance computed in different color space such as CAM16-UCS, CAM16-SCD, CAM16-LCD, ... I'm not even sure to perfectly understand what is exactly a color space. Thanks for your help! |
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Replies: 1 comment 52 replies
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@tvaillantdeguelis You need to also register Also, there are many delta E methods, so you have to specify what you are using (in this case from coloraide import Color as Base
from coloraide.distance.delta_e_cam16 import DECAM16
from coloraide.spaces.cam16_ucs import CAM16UCS, CAM16SCD, CAM16LCD, CAM16JMh
class Color(Base): ...
Color.register([CAM16UCS(), CAM16SCD(), CAM16LCD(), DECAM16(), CAM16JMh()])
Color('#a7aaa0').delta_e('#e9daae', method='cam16', space='cam16-scd')You can see it working live here.
The CAM16 model came about to try and give better ∆E calculations. The best ∆E calculation in CIELab is ∆E2000 and it puts most of the complexity in the calculation to get pretty good ∆E values. It's a pretty ugly algorithm, but the results are pretty good. CAM16 puts most of the complexity in calculating the model which then makes the ∆E calculations more simple and closer to Euclidean distance. CAM16 also allows specifying exact lighting conditions allowing you to better simulate the viewing environment. UCS, SCD, and LCD were kind of designed to give more specific environments for testing distancing. Distancing is normally applied directly to CAM16, but usually in one of these specific forms of CAM16. Each one is supposedly better suited for specific distances, SCD being better for colors that are a shorter distance apart and LCD for colors at a greater, longer distance apart. Basically, the shape of the model distorted in these forms to give better calculations in these scenarios.
You and probably a lot of people 🙂. There's really a difference between model and space, and we usually just call everything a "space" to make things more accessible to the user. A model is like a way to represent colors. I can represent colors in the RGB model, meaning the color is transformed to some Red, Green, Blue values, but sRGB (standard RGB) is a specific RGB representation with an actual gamut (range of colors) and specific conditions. HSL is a model that transforms an RGB space to a cylindrical form, but traditionally, it is still the sRGB space's gamut underneath, but it doesn't have to be. CAM16 doesn't really have a specific gamut, it is more a way of taking colors and arranging them so they are more perceptually uniform, it's more of a model. A lot of these perceptual color spaces came about specifically to calculate better color distances amount other things. Ideally to get closer to Euclidean distance. |
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Here is the complete code (see from coloraide import Color as Base
from coloraide.distance.delta_e_cam16 import DECAM16
from coloraide.spaces.cam16_ucs import CAM16UCS, CAM16SCD, CAM16LCD, CAM16JMh
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from matplotlib.colors import from_levels_and_colors
from matplotlib.ticker import MultipleLocator, FixedLocator, LogLocator
import matplotlib.cm as cm
class Color(Base): ...
Color.register([CAM16UCS(), CAM16SCD(), CAM16LCD(), DECAM16(), CAM16JMh()])
def interp_uniform_colormap(palette, space_interp, method_delta, space_delta, local_delta):
interp = Color.interpolate(palette, space=space_interp)
current = interp(0)
colors = [current]
last = 0
while last != 1:
low = last
high = 1
value = -1
while abs(low - high) > 1e-8:
value = (low + high) * 0.5
delta = current.delta_e(interp(value), method=method_delta, space=space_delta)
if delta < local_delta:
low = value
elif delta > local_delta:
high = value
else:
break
if value == -1:
break
last = value
current = interp(value)
colors.append(current)
return colors
def interp_colormap(palette, space_interp):
colors = []
for i in np.arange(len(palette)-1):
interp = Color.interpolate([palette[i], palette[i+1]], space=space_interp)
if i == 0:
nb_colors = 8 # nb intermediate colors including first color and excluding last color
colors += [interp(x/nb_colors) for x in range(nb_colors)]
elif i == len(palette)-2:
nb_colors = 8
colors += [interp(x/nb_colors) for x in range(nb_colors+1)] # +1 to add last color of palette
else:
nb_colors = 15
colors += [interp(x/nb_colors) for x in range(nb_colors)]
return colors
def colormap_distances(palette, method, space):
color_distance = np.ones(len(palette)-1)*-9999.
for i in np.arange(color_distance.size):
color_distance[i] = Color(palette[i]).delta_e(palette[i+1], method=method, space=space)
return color_distance
def plot_distances(distances, palette, ymax):
# fit = {'method': 'minde-chroma', 'jnd': 0, 'pspace': space}
for i in np.arange(len(palette)):
if i == 0:
y2 = np.array([distances[i], distances[i]])
elif i == len(palette) - 1:
y2 = np.array([distances[i-1], distances[i-1]])
else:
y2 = np.array([distances[i-1], distances[i]])
x = np.array([i-1, i]) + 0.5
y1 = np.array([0, 0])
if type(palette[0]) == str:
ax.fill_between(x, y1, y2, color=palette[i])
else:
ax.fill_between(x, y1, y2, color=palette[i].convert("srgb").to_string(hex=True))
plt.xlim(-0.5, distances.size + 0.5)
plt.ylim(0, ymax)
plt.plot(np.arange(distances.size)+0.5, distances, c='k')
plt.ylabel('$\Delta$E')
return
if __name__ == '__main__':
# ************************************
# *** Compute continuous colormaps ***
# Discrete colormap
palette = ['#000000', '#1e1f64', '#344376',
'#4f6687', '#788895', '#a7aaa0',
'#e9daae', '#fbff41', '#fea100',
'#ec2401', '#84110c', '#2b0000',
'#443b3b', '#606060', '#858585',
'#acacac', '#d5d5d5', '#ffffff']
# ************
# *** Plot ***
fig = plt.figure(figsize=(7, 9)) #, layout="constrained")
gs0 = fig.add_gridspec(4, 1, hspace=0.5)
# Plot discrete colormap
gs00 = gs0[0].subgridspec(2, 1, height_ratios=[7, 1])
ax = plt.subplot(gs00[0], facecolor='0.5')
method_delta = 'ok'
space_delta = 'lab-d65'
distances = colormap_distances(palette, method_delta, space_delta)
plot_distances(distances, palette, 0.35)
plt.xticks([])
plt.title(f"(a) Discrete colormap (18 colors)")
# Colorbar
ax = plt.subplot(gs00[1])
bounds = np.array([0.00001,
0.0001, 0.0003, 0.0006,
0.001, 0.0015, 0.002, 0.003, 0.004, 0.005, 0.006, 0.008,
0.01, 0.015, 0.02, 0.03, 0.05])
my_cmap, my_norm = from_levels_and_colors(bounds, palette, extend='both')
cbar = mpl.colorbar.ColorbarBase(ax, cmap=my_cmap, norm=my_norm, orientation='horizontal', drawedges=True)
plt.tick_params(axis='x', which='both', labelbottom=False)
plt.tick_params(axis='y', which='both', labelleft=False)
cbar.ax.xaxis.set_major_locator(LogLocator(numticks=15))
cbar.ax.get_yaxis().set_visible(False)
cbar_major_label = ['×$10^{-5}$', '×$10^{-4}$', '×$10^{-3}$', '×$10^{-2}$']
c_bar_major_values = np.array((1e-5, 1e-4, 1e-3, 1e-2))
for j, bound in enumerate(c_bar_major_values):
cbar.ax.text(bound, -2, cbar_major_label[j], ha='center', fontsize=8)
cbar.ax.xaxis.set_minor_locator(FixedLocator(bounds))
cbar_minor_label = ['1.0',
'1.0', '3.0', '6.0',
'1.0', '1.5', '2.0', '3.0', '4.0', '5.0', '6.0', '8.0',
'1.0', '1.5', '2.0', '3.0', '5.0']
for j, bound in enumerate(bounds):
cbar.ax.text(bound, -1.2, cbar_minor_label[j], ha='center', fontsize=8)
# Plot continuous colormap
gs01 = gs0[1].subgridspec(2, 1, height_ratios=[7, 1])
ax = plt.subplot(gs01[0], facecolor='0.5')
space_interp = 'oklab'
method_delta = 'ok'
space_delta = 'lab-d65'
# colormap = Color.steps(palette, steps=256, space=space_interp)
colormap = interp_colormap(palette, space_interp)
print(len(colormap))
distances = colormap_distances(colormap, method_delta, space_delta)
plot_distances(distances, colormap, 0.02)
plt.xticks([])
plt.title(f"(b) Continuous colormap (242 colors)")
# Colorbar
ax = plt.subplot(gs01[1])
discrete_bounds = np.array([0.00001,
0.0001, 0.0003, 0.0006,
0.001, 0.0015, 0.002, 0.003, 0.004, 0.005, 0.006, 0.008,
0.01, 0.015, 0.02, 0.03, 0.05])
nb_colors_between_mid_discrete_bin = 15 # 16*15+2 = 242
bounds = np.array(())
for i in range(discrete_bounds.size-1): # color of discrete bounds at the mid value of the range bin
bounds = np.append(bounds, np.linspace(discrete_bounds[i], discrete_bounds[i+1], nb_colors_between_mid_discrete_bin+1)[:-1])
bounds = np.append(bounds, discrete_bounds[-1])
colors = [colormap[i].convert("srgb").to_string(hex=True) for i in range(len(colormap))]
my_cmap, my_norm = from_levels_and_colors(bounds, colors, extend='both')
cbar = mpl.colorbar.ColorbarBase(ax, cmap=my_cmap, norm=my_norm, orientation='horizontal')
plt.tick_params(axis='x', which='both', labelbottom=False)
plt.tick_params(axis='y', which='both', labelleft=False)
cbar.ax.xaxis.set_major_locator(LogLocator(numticks=15))
cbar.ax.get_yaxis().set_visible(False)
cbar_major_label = ['×$10^{-5}$', '×$10^{-4}$', '×$10^{-3}$', '×$10^{-2}$']
c_bar_major_values = np.array((1e-5, 1e-4, 1e-3, 1e-2))
for j, bound in enumerate(c_bar_major_values):
cbar.ax.text(bound, -2, cbar_major_label[j], ha='center', fontsize=8)
minor_bounds = np.array([0.00001,
0.0001, 0.0003, 0.0006,
0.001, 0.0015, 0.002, 0.003, 0.004, 0.005, 0.006, 0.008,
0.01, 0.015, 0.02, 0.03, 0.05])
cbar.ax.xaxis.set_minor_locator(FixedLocator(minor_bounds))
cbar_minor_label = ['1.0',
'1.0', '3.0', '6.0',
'1.0', '1.5', '2.0', '3.0', '4.0', '5.0', '6.0', '8.0',
'1.0', '1.5', '2.0', '3.0', '5.0']
for j, bound in enumerate(minor_bounds):
cbar.ax.text(bound, -1.2, cbar_minor_label[j], ha='center', fontsize=8)
# Plot continuous perceptually uniform colormap
gs02 = gs0[2].subgridspec(2, 1, height_ratios=[7, 1])
ax = plt.subplot(gs02[0], facecolor='0.5')
space_interp = 'oklab'
method_delta = 'ok'
space_delta = 'lab-d65'
local_delta = 0.01099
colormap = interp_uniform_colormap(palette, space_interp, method_delta, space_delta, local_delta)
for i in range(len(colormap)):
print(colormap[i].convert('srgb').to_string(hex=True))
# print(len(colormap))
distances = colormap_distances(colormap, method_delta, space_delta)
plot_distances(distances, colormap, 0.02)
plt.xticks([])
plt.title(f"(c) Continuous perceptually uniform colormap (256 colors)")
# Colorbar
ax = plt.subplot(gs02[1])
bounds = np.arange(len(colormap)-1)+1
colors = [colormap[i].convert("srgb").to_string(hex=True) for i in range(len(colormap))]
my_cmap, my_norm = from_levels_and_colors(bounds, colors, extend='both')
cbar = mpl.colorbar.ColorbarBase(ax, cmap=my_cmap, norm=my_norm, orientation='horizontal')
ax.xaxis.set_major_locator(FixedLocator(np.array((1, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 255))))
ax.tick_params(axis='both', which='major', labelsize=8)
plt.minorticks_off()
# Plot jet colormap
gs03 = gs0[3].subgridspec(2, 1, height_ratios=[7, 1])
ax = plt.subplot(gs03[0], facecolor='0.5')
method_delta = 'ok'
space_delta = 'lab-d65'
my_cmap = cm.jet
palette_rgb = my_cmap(np.arange(256))*255
palette = []
for i in range(256):
palette.append('#%02x%02x%02x' % (int(palette_rgb[i,0]), int(palette_rgb[i,1]), int(palette_rgb[i,2])))
distances = colormap_distances(palette, method_delta, space_delta)
plot_distances(distances, palette, 0.02)
plt.xticks([])
plt.title(f"(d) Jet colormap (256 colors)")
# Colorbar
ax = plt.subplot(gs03[1])
bounds = np.arange(len(palette)-1)+1
my_cmap, my_norm = from_levels_and_colors(bounds, palette, extend='both')
cbar = mpl.colorbar.ColorbarBase(ax, cmap=my_cmap, norm=my_norm, orientation='horizontal')
ax.xaxis.set_major_locator(FixedLocator(np.array((1, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 255))))
ax.tick_params(axis='both', which='major', labelsize=8)
plt.minorticks_off()
plt.subplots_adjust(left=0.11, bottom=0.04, right=0.98, top=0.96)
plt.savefig('colormap_distances.png', dpi=500) |
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@tvaillantdeguelis I don't know exactly what you are trying to do, and I don't know what you are trying to show. I get the feeling you expect a smooth transition between colors, but I don't know why as you haven't really specified why you think there should be a smooth transition. It seems you are just taking the Jet colormap, calculating the distance between the colors, but are unhappy with the fact that it is not more uniform or smooth? Your other graphs are taking the colors and interpolating the palette, but these palettes are currently still in full precision. This Jet colormap is in 8bit precision. Whatever these colors were before being clamped to 8bit precision is impossible to tell, so you are going to introduce noise due to the 8bit precision. I'm not quite sure exactly what the question is here. You can certainly smooth your data points in matplotlib, but taking the raw points will have the noise. |
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Thank you @facelessuser . I got similar sawtooth patterns when I was making the interpolation in one color space and the computation in another color space. Then, I wondered if the sawtooth pattern I got with Jet was due to something similar or a kind of artifact. From what you say, my understanding is that it is due to the rounded color values when set to 8-bit precision.
Actually, I think I am clamping the colormap to 8-bit precision when I convert the RGB values to hex. Indeed, the values stored in the Jet array of the Matplotlib package are in float64. cm.jet(range(10))array([[0. , 0. , 0.5 , 1. ],
[0. , 0. , 0.51782531, 1. ],
[0. , 0. , 0.53565062, 1. ],
[0. , 0. , 0.55347594, 1. ],
[0. , 0. , 0.57130125, 1. ],
[0. , 0. , 0.58912656, 1. ],
[0. , 0. , 0.60695187, 1. ],
[0. , 0. , 0.62477718, 1. ],
[0. , 0. , 0.6426025 , 1. ],
[0. , 0. , 0.66042781, 1. ]])In the following function def colormap_distances(palette, method, space):
color_distance = np.ones(len(palette)-1)*-9999.
for i in np.arange(color_distance.size):
color_distance[i] = Color(palette[i]).delta_e(palette[i+1], method=method, space=space)
return color_distanceWould it be possible to compute distances directly with the RGB values? Below I've tried to make a distance computation from two random RGB colors but I get very different results depending on the space I specify. I'm not sure if that's what is expected. Color("srgb", [0.19, 0.56, 0.58]).delta_e(Color("srgb", [0.14, 0.57, 0.49]), method="2000")10.356706485878705Color("srgb", [0.19, 0.56, 0.58]).delta_e(Color("srgb", [0.14, 0.57, 0.49]), method="ok", space="lab-d65")0.04024149200929929Using the Jet RGB values in |
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I don't understand this question. What do you mean by "directly"? If you are using the "ok" ∆E method, colors are always converted to Oklab for the distancing. You can provide the color with whatever input you desire as long as it is supported. Also, passing >>> Color('red').delta_e('blue', method='ok')
0.5370898164568613
>>> Color('red').delta_e('blue', method='ok', space='lab-d65')
0.5370898164568613
I don't know exactly what you are doing, but this is the code I used: # Plot jet colormap
gs03 = gs0[3].subgridspec(2, 1, height_ratios=[7, 1])
ax = plt.subplot(gs03[0], facecolor='0.5')
method_delta = 'ok'
space_delta = 'lab-d65'
colormap = [Color('srgb', c[:-1]) for c in cm.jet(np.arange(256))]
for i in range(len(colormap)):
print(colormap[i].convert('srgb').to_string(hex=True))
distances = colormap_distances(colormap, method_delta, space_delta)
plot_distances(distances, colormap, 0.02)
plt.xticks([])
plt.title(f"(d) Jet colormap (256 colors)")
# Colorbar
ax = plt.subplot(gs03[1])
bounds = np.arange(len(colormap)-1)+1
colors = [colormap[i].convert("srgb").to_string(hex=True) for i in range(len(colormap))]
my_cmap, my_norm = from_levels_and_colors(bounds, colors, extend='both')
cbar = mpl.colorbar.ColorbarBase(ax, cmap=my_cmap, norm=my_norm, orientation='horizontal')
ax.xaxis.set_major_locator(FixedLocator(np.array((1, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 240, 255))))
ax.tick_params(axis='both', which='major', labelsize=8)
plt.minorticks_off()This is the result I get. 
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That was a very basic question about the syntax of an RGB color. I think it is:
Thank you very much! I found my error: I used a list of 0-255 instead of 0-1 values in Color(). I know get the same result than yours. |
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@tvaillantdeguelis You need to also register
CAM16JMhas that is the model we got through to get to CAM16 UCS, SCD, and LCD. This map shows what spaces everything passes through to get to what: https://facelessuser.github.io/coloraide/colors/#color-space-map. Granted, I do see the Delta E docs do not specifically mentionCAM16JMhwhich is a mistake on my part. I'll have to correct that.Also, there are many delta E methods, so you have to specify what you are using (in this case
method='cam16') or it assumes ∆E76 IIRC, which uses CIELab. It probably wouldn't hurt if I showed that part in the example as well and not just the registering of the plugins.