没有视觉扭曲的循环色图用于相角图？

Question

我正在寻找一个好的圆形/循环色图来表示相角信息（其中值被限制在[0,2π]范围内，其中0和2π表示相同的相位角）。

背景：我想通过绘制系统中振荡的功率谱密度和相对相位信息来可视化正常模式。

我承认以前我使用'彩虹'色图作为功率图，'hsv'色图用于相图（见[1]）。然而，由于缺乏感知线性和排序[2] [3]，因此极不鼓励使用彩虹色图。所以我切换到了'coolwarm'色彩图，以获得我非常喜欢的功率图。不幸的是，'hsv'色彩图似乎引入了与'彩虹'地图相同的视觉扭曲（并且它与'coolwarm'地图也不太相配，因为它看起来有点丑陋和华而不实）

有没有人对替代圆形色图有很好的推荐，我可以用它来制作相图？

要求：

• 它必须是圆形的，以便0和2π的值用相同的颜色表示。

• 不应引入任何视觉扭曲;特别是，它应该是感知线性的（'hsv'色图似乎不是）。我不认为感性排序对于阶段信息来说是如此重要，但它当然不会造成任何伤害。

• 与'coolwarm'色彩图组合使用时，它应具有视觉吸引力。但是，如果有另一对漂亮的色彩图可以显示振幅和相位信息，我很高兴考虑其他选项。

如果色图可用（或可以轻松创建）以在matplotlib中使用，则获得奖励。

非常感谢任何建议！

[1] http://matplotlib.org/examples/color/colormaps_reference.html

[2] http://www.renci.org/~borland/pdfs/RainbowColorMap_VisViewpoints.pdf

[3] http://medvis.org/2012/08/21/rainbow-colormaps-what-are-they-good-for-absolutely-nothing/

Answer 1

您可以尝试"husl" system，它类似于hls / hsv但具有更好的视觉属性。它位于seaborn和standalone package。

这是一个简单的例子：

import numpy as np
from numpy import sin, cos, pi
import matplotlib.pyplot as plt
import seaborn as sns

n = 314
theta = np.linspace(0, 2 * pi, n)

x = cos(theta)
y = sin(theta)

f = plt.figure(figsize=(10, 5))
with sns.color_palette("husl", n):
    ax = f.add_subplot(121)
    ax.plot([np.zeros_like(x), x], [np.zeros_like(y), y], lw=3)
    ax.set_axis_off()
    ax.set_title("HUSL space")

with sns.color_palette("hls", n):
    ax = f.add_subplot(122)
    ax.plot([np.zeros_like(x), x], [np.zeros_like(y), y], lw=3)
    ax.set_axis_off()
    ax.set_title("HLS space")

f.tight_layout()

Answer 2

hue-HUSL 色彩映射的问题在于从它读取角度并不直观。我不知道任何预定义的色彩映射，这是可能的。

因此，我建议制作自己的色彩映射表。这里有几种可能性：

• 对于线性分段色彩图，我们定义了一些颜色。然后，色彩图是颜色之间的线性插值。这有视觉扭曲。
• 对于 luminosity-HSLUV map ，我们使用HUSL（“HSLUV”）空间，但不仅仅是色调通道，我们使用两种颜色和光度通道。这有distortions in the chroma，但颜色鲜艳。
• luminosity-HPLUV map ，我们使用HPLUV色彩空间（关注@ mwaskom的评论）。这是真正没有视觉扭曲的唯一方法，但颜色并未饱和 这就是他们的样子：

我们在自定义色彩映射中看到，白色代表0，蓝色代表1i等。 在右上角，我们看到hue-HUSL地图进行比较。在那里，颜色角度分配是随机的。

同样在绘制更复杂的函数时，使用我们的彩色图片时，可以直接读出结果的相位。

以下是图表的代码：

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as col
import seaborn as sns
import hsluv # install via pip
import scipy.special # just for the example function

##### generate custom colormaps
def make_segmented_cmap(): 
    white = '#ffffff'
    black = '#000000'
    red = '#ff0000'
    blue = '#0000ff'
    anglemap = col.LinearSegmentedColormap.from_list(
        'anglemap', [black, red, white, blue, black], N=256, gamma=1)
    return anglemap

def make_anglemap( N = 256, use_hpl = True ):
    h = np.ones(N) # hue
    h[:N//2] = 11.6 # red 
    h[N//2:] = 258.6 # blue
    s = 100 # saturation
    l = np.linspace(0, 100, N//2) # luminosity
    l = np.hstack( (l,l[::-1] ) )

    colorlist = np.zeros((N,3))
    for ii in range(N):
        if use_hpl:
            colorlist[ii,:] = hsluv.hpluv_to_rgb( (h[ii], s, l[ii]) )
        else:
            colorlist[ii,:] = hsluv.hsluv_to_rgb( (h[ii], s, l[ii]) )
    colorlist[colorlist > 1] = 1 # correct numeric errors
    colorlist[colorlist < 0] = 0 
    return col.ListedColormap( colorlist )

N = 256
segmented_cmap = make_segmented_cmap()
flat_huslmap = col.ListedColormap(sns.color_palette('husl',N))
hsluv_anglemap = make_anglemap( use_hpl = False )
hpluv_anglemap = make_anglemap( use_hpl = True )

##### generate data grid
x = np.linspace(-2,2,N)
y = np.linspace(-2,2,N)
z = np.zeros((len(y),len(x))) # make cartesian grid
for ii in range(len(y)): 
    z[ii] = np.arctan2(y[ii],x) # simple angular function
    z[ii] = np.angle(scipy.special.gamma(x+1j*y[ii])) # some complex function

##### plot with different colormaps
fig = plt.figure(1)
fig.clf()
colormapnames = ['segmented map', 'hue-HUSL', 'lum-HSLUV', 'lum-HPLUV']
colormaps = [segmented_cmap, flat_huslmap, hsluv_anglemap, hpluv_anglemap]
for ii, cm in enumerate(colormaps):
    ax = fig.add_subplot(2, 2, ii+1)
    pmesh = ax.pcolormesh(x, y, z/np.pi, 
        cmap = cm, vmin=-1, vmax=1)
    plt.axis([x.min(), x.max(), y.min(), y.max()])
    cbar = fig.colorbar(pmesh)
    cbar.ax.set_ylabel('Phase [pi]')
    ax.set_title( colormapnames[ii] )
plt.show()

编辑：我最近想出了如何在没有视觉扭曲的情况下制作这样的色彩图，所以我扩展了原来的答案

Answer 3

从matplotlib version 3.0开始，内置了循环perceptually uniform colormaps。好的，暂时只有一个颜色图，但是在循环中有两个开始和结束选择，即twilight and twilight_shifted。

一个简短的例子来演示它们的外观：

width: calc(100vw / [crop_width]px));

上面产生了下图：

这些全新的色彩图是对现有感知统一（顺序）色彩图集合的惊人补充，它们分别是 viridis ， plasma ， inferno ，岩浆和 cividis （最后一个是a new addition in 2.2，它不仅在感知上是统一的，因此对色盲友好，但看起来应该尽可能接近色盲和非色盲人士。

Answer 4

我刚刚意识到cmocean有一个用于此目的的色彩映射。

import cmocean
import matplotlib.pyplot as plt
import numpy as np

azimuths = np.arange(0, 361, 1)
zeniths = np.arange(40, 70, 1)
values = azimuths * np.ones((30, 361))
fig, ax = plt.subplots(subplot_kw=dict(projection='polar'))
ax.pcolormesh(azimuths*np.pi/180.0, zeniths, values, cmap=cmocean.cm.phase)
ax.set_yticks([])
plt.show()

结果是

Answer 5

我喜欢上面的彩色地图，但想要将一些现代色彩理论引入其中。通过使用CIECAM02色彩空间，您可以获得更具感知的统一色彩空间。

colorspacious包很适合转换成这个很棒的色彩空间。使用这个包，我将上述答案引导到我自己的自定义cmap中。

from colorspacious import cspace_convert
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.colors as col
import seaborn as sns

# first draw a circle in the cylindrical JCh color space. 
# the third channel is hue in degrees. First is lightness and the second chroma
color_circle = np.ones((256,3))*60
color_circle[:,1] = np.ones((256))*45
color_circle[:,2] = np.arange(0,360,360/256)
color_circle_rgb = cspace_convert(color_circle, "JCh","sRGB1")

cm = col.ListedColormap(color_circle_rgb)

##### generate data grid like in above
N=256
x = np.linspace(-2,2,N)
y = np.linspace(-2,2,N)
z = np.zeros((len(y),len(x))) # make cartesian grid
for ii in range(len(y)): 
    z[ii] = np.arctan2(y[ii],x) # simple angular function

fig = plt.figure()
ax = plt.gca()
pmesh = ax.pcolormesh(x, y, z/np.pi, 
    cmap = cm, vmin=-1, vmax=1)
plt.axis([x.min(), x.max(), y.min(), y.max()])
cbar = fig.colorbar(pmesh)
cbar.ax.set_ylabel('Phase [pi]')

如果您不想安装colorspacious包，只需复制并粘贴此颜色列表，然后直接创建颜色图：

colors = array([[0.91510904, 0.55114749, 0.67037311],
   [0.91696411, 0.55081563, 0.66264366],
   [0.91870995, 0.55055664, 0.65485881],
   [0.92034498, 0.55037149, 0.64702356],
   [0.92186763, 0.55026107, 0.63914306],
   [0.92327636, 0.55022625, 0.63122259],
   [0.9245696 , 0.55026781, 0.62326754],
   [0.92574582, 0.5503865 , 0.6152834 ],
   [0.92680349, 0.55058299, 0.6072758 ],
   [0.92774112, 0.55085789, 0.59925045],
   [0.9285572 , 0.55121174, 0.59121319],
   [0.92925027, 0.551645  , 0.58316992],
   [0.92981889, 0.55215808, 0.57512667],
   [0.93026165, 0.55275127, 0.56708953],
   [0.93057716, 0.5534248 , 0.55906469],
   [0.93076407, 0.55417883, 0.55105838],
   [0.93082107, 0.55501339, 0.54307696],
   [0.93074689, 0.55592845, 0.53512681],
   [0.9305403 , 0.55692387, 0.52721438],
   [0.93020012, 0.55799943, 0.51934621],
   [0.92972523, 0.55915477, 0.51152885],
   [0.92911454, 0.56038948, 0.50376893],
   [0.92836703, 0.56170301, 0.49607312],
   [0.92748175, 0.56309471, 0.48844813],
   [0.9264578 , 0.56456383, 0.48090073],
   [0.92529434, 0.56610951, 0.47343769],
   [0.92399062, 0.56773078, 0.46606586],
   [0.92254595, 0.56942656, 0.45879209],
   [0.92095971, 0.57119566, 0.4516233 ],
   [0.91923137, 0.5730368 , 0.44456642],
   [0.91736048, 0.57494856, 0.4376284 ],
   [0.91534665, 0.57692945, 0.43081625],
   [0.91318962, 0.57897785, 0.42413698],
   [0.91088917, 0.58109205, 0.41759765],
   [0.90844521, 0.58327024, 0.41120533],
   [0.90585771, 0.58551053, 0.40496711],
   [0.90312676, 0.5878109 , 0.3988901 ],
   [0.90025252, 0.59016928, 0.39298143],
   [0.89723527, 0.5925835 , 0.38724821],
   [0.89407538, 0.59505131, 0.38169756],
   [0.89077331, 0.59757038, 0.37633658],
   [0.88732963, 0.60013832, 0.37117234],
   [0.88374501, 0.60275266, 0.36621186],
   [0.88002022, 0.6054109 , 0.36146209],
   [0.87615612, 0.60811044, 0.35692989],
   [0.87215369, 0.61084868, 0.352622  ],
   [0.86801401, 0.61362295, 0.34854502],
   [0.86373824, 0.61643054, 0.34470535],
   [0.85932766, 0.61926872, 0.3411092 ],
   [0.85478365, 0.62213474, 0.3377625 ],
   [0.85010767, 0.6250258 , 0.33467091],
   [0.84530131, 0.62793914, 0.3318397 ],
   [0.84036623, 0.63087193, 0.32927381],
   [0.8353042 , 0.63382139, 0.32697771],
   [0.83011708, 0.63678472, 0.32495541],
   [0.82480682, 0.63975913, 0.32321038],
   [0.81937548, 0.64274185, 0.32174556],
   [0.81382519, 0.64573011, 0.32056327],
   [0.80815818, 0.6487212 , 0.31966522],
   [0.80237677, 0.65171241, 0.31905244],
   [0.79648336, 0.65470106, 0.31872531],
   [0.79048044, 0.65768455, 0.31868352],
   [0.78437059, 0.66066026, 0.31892606],
   [0.77815645, 0.66362567, 0.31945124],
   [0.77184076, 0.66657827, 0.32025669],
   [0.76542634, 0.66951562, 0.3213394 ],
   [0.75891609, 0.67243534, 0.32269572],
   [0.75231298, 0.67533509, 0.32432138],
   [0.74562004, 0.6782126 , 0.32621159],
   [0.73884042, 0.68106567, 0.32836102],
   [0.73197731, 0.68389214, 0.33076388],
   [0.72503398, 0.68668995, 0.33341395],
   [0.7180138 , 0.68945708, 0.33630465],
   [0.71092018, 0.69219158, 0.33942908],
   [0.70375663, 0.69489159, 0.34278007],
   [0.69652673, 0.69755529, 0.34635023],
   [0.68923414, 0.70018097, 0.35013201],
   [0.6818826 , 0.70276695, 0.35411772],
   [0.67447591, 0.70531165, 0.3582996 ],
   [0.667018  , 0.70781354, 0.36266984],
   [0.65951284, 0.71027119, 0.36722061],
   [0.65196451, 0.71268322, 0.37194411],
   [0.64437719, 0.71504832, 0.37683259],
   [0.63675512, 0.71736525, 0.38187838],
   [0.62910269, 0.71963286, 0.38707389],
   [0.62142435, 0.72185004, 0.39241165],
   [0.61372469, 0.72401576, 0.39788432],
   [0.60600841, 0.72612907, 0.40348469],
   [0.59828032, 0.72818906, 0.40920573],
   [0.59054536, 0.73019489, 0.41504052],
   [0.58280863, 0.73214581, 0.42098233],
   [0.57507535, 0.7340411 , 0.42702461],
   [0.5673509 , 0.7358801 , 0.43316094],
   [0.55964082, 0.73766224, 0.43938511],
   [0.55195081, 0.73938697, 0.44569104],
   [0.54428677, 0.74105381, 0.45207286],
   [0.53665478, 0.74266235, 0.45852483],
   [0.52906111, 0.74421221, 0.4650414 ],
   [0.52151225, 0.74570306, 0.47161718],
   [0.5140149 , 0.74713464, 0.47824691],
   [0.506576  , 0.74850672, 0.48492552],
   [0.49920271, 0.74981912, 0.49164808],
   [0.49190247, 0.75107171, 0.4984098 ],
   [0.48468293, 0.75226438, 0.50520604],
   [0.47755205, 0.7533971 , 0.51203229],
   [0.47051802, 0.75446984, 0.5188842 ],
   [0.46358932, 0.75548263, 0.52575752],
   [0.45677469, 0.75643553, 0.53264815],
   [0.45008317, 0.75732863, 0.5395521 ],
   [0.44352403, 0.75816207, 0.54646551],
   [0.43710682, 0.758936  , 0.55338462],
   [0.43084133, 0.7596506 , 0.56030581],
   [0.42473758, 0.76030611, 0.56722555],
   [0.41880579, 0.76090275, 0.5741404 ],
   [0.41305637, 0.76144081, 0.58104704],
   [0.40749984, 0.76192057, 0.58794226],
   [0.40214685, 0.76234235, 0.59482292],
   [0.39700806, 0.7627065 , 0.60168598],
   [0.39209414, 0.76301337, 0.6085285 ],
   [0.38741566, 0.76326334, 0.6153476 ],
   [0.38298304, 0.76345681, 0.62214052],
   [0.37880647, 0.7635942 , 0.62890454],
   [0.37489579, 0.76367593, 0.63563704],
   [0.37126045, 0.76370246, 0.64233547],
   [0.36790936, 0.76367425, 0.64899736],
   [0.36485083, 0.76359176, 0.6556203 ],
   [0.36209245, 0.76345549, 0.66220193],
   [0.359641  , 0.76326594, 0.66873999],
   [0.35750235, 0.76302361, 0.67523226],
   [0.35568141, 0.76272903, 0.68167659],
   [0.35418202, 0.76238272, 0.68807086],
   [0.3530069 , 0.76198523, 0.69441305],
   [0.35215761, 0.7615371 , 0.70070115],
   [0.35163454, 0.76103888, 0.70693324],
   [0.35143685, 0.76049114, 0.71310742],
   [0.35156253, 0.75989444, 0.71922184],
   [0.35200839, 0.75924936, 0.72527472],
   [0.3527701 , 0.75855647, 0.73126429],
   [0.3538423 , 0.75781637, 0.73718884],
   [0.3552186 , 0.75702964, 0.7430467 ],
   [0.35689171, 0.75619688, 0.74883624],
   [0.35885353, 0.75531868, 0.75455584],
   [0.36109522, 0.75439565, 0.76020396],
   [0.36360734, 0.75342839, 0.76577905],
   [0.36637995, 0.75241752, 0.77127961],
   [0.3694027 , 0.75136364, 0.77670417],
   [0.37266493, 0.75026738, 0.7820513 ],
   [0.37615579, 0.74912934, 0.78731957],
   [0.37986429, 0.74795017, 0.79250759],
   [0.38377944, 0.74673047, 0.797614  ],
   [0.38789026, 0.74547088, 0.80263746],
   [0.3921859 , 0.74417203, 0.80757663],
   [0.39665568, 0.74283455, 0.81243022],
   [0.40128912, 0.74145908, 0.81719695],
   [0.406076  , 0.74004626, 0.82187554],
   [0.41100641, 0.73859673, 0.82646476],
   [0.41607073, 0.73711114, 0.83096336],
   [0.4212597 , 0.73559013, 0.83537014],
   [0.42656439, 0.73403435, 0.83968388],
   [0.43197625, 0.73244447, 0.8439034 ],
   [0.43748708, 0.73082114, 0.84802751],
   [0.44308905, 0.72916502, 0.85205505],
   [0.44877471, 0.72747678, 0.85598486],
   [0.45453694, 0.72575709, 0.85981579],
   [0.46036897, 0.72400662, 0.8635467 ],
   [0.4662644 , 0.72222606, 0.86717646],
   [0.47221713, 0.72041608, 0.87070395],
   [0.47822138, 0.71857738, 0.87412804],
   [0.4842717 , 0.71671065, 0.87744763],
   [0.4903629 , 0.71481659, 0.88066162],
   [0.49649009, 0.71289591, 0.8837689 ],
   [0.50264864, 0.71094931, 0.88676838],
   [0.50883417, 0.70897752, 0.88965898],
   [0.51504253, 0.70698127, 0.89243961],
   [0.52126981, 0.70496128, 0.8951092 ],
   [0.52751231, 0.70291829, 0.89766666],
   [0.53376652, 0.70085306, 0.90011093],
   [0.54002912, 0.69876633, 0.90244095],
   [0.54629699, 0.69665888, 0.90465565],
   [0.55256715, 0.69453147, 0.90675397],
   [0.55883679, 0.69238489, 0.90873487],
   [0.56510323, 0.69021993, 0.9105973 ],
   [0.57136396, 0.68803739, 0.91234022],
   [0.57761655, 0.68583808, 0.91396258],
   [0.58385872, 0.68362282, 0.91546336],
   [0.59008831, 0.68139246, 0.91684154],
   [0.59630323, 0.67914782, 0.9180961 ],
   [0.60250152, 0.67688977, 0.91922603],
   [0.60868128, 0.67461918, 0.92023033],
   [0.61484071, 0.67233692, 0.921108  ],
   [0.62097809, 0.67004388, 0.92185807],
   [0.62709176, 0.66774097, 0.92247957],
   [0.63318012, 0.66542911, 0.92297153],
   [0.63924166, 0.66310923, 0.92333301],
   [0.64527488, 0.66078227, 0.92356308],
   [0.65127837, 0.65844919, 0.92366082],
   [0.65725076, 0.65611096, 0.92362532],
   [0.66319071, 0.65376857, 0.92345572],
   [0.66909691, 0.65142302, 0.92315115],
   [0.67496813, 0.64907533, 0.92271076],
   [0.68080311, 0.64672651, 0.92213374],
   [0.68660068, 0.64437763, 0.92141929],
   [0.69235965, 0.64202973, 0.92056665],
   [0.69807888, 0.6396839 , 0.91957507],
   [0.70375724, 0.63734122, 0.91844386],
   [0.70939361, 0.63500279, 0.91717232],
   [0.7149869 , 0.63266974, 0.91575983],
   [0.72053602, 0.63034321, 0.91420578],
   [0.72603991, 0.62802433, 0.9125096 ],
   [0.7314975 , 0.62571429, 0.91067077],
   [0.73690773, 0.62341425, 0.9086888 ],
   [0.74226956, 0.62112542, 0.90656328],
   [0.74758193, 0.61884899, 0.90429382],
   [0.75284381, 0.6165862 , 0.90188009],
   [0.75805413, 0.61433829, 0.89932181],
   [0.76321187, 0.6121065 , 0.89661877],
   [0.76831596, 0.6098921 , 0.89377082],
   [0.77336536, 0.60769637, 0.89077786],
   [0.77835901, 0.6055206 , 0.88763988],
   [0.78329583, 0.6033661 , 0.88435693],
   [0.78817477, 0.60123418, 0.88092913],
   [0.79299473, 0.59912616, 0.87735668],
   [0.79775462, 0.59704339, 0.87363986],
   [0.80245335, 0.59498722, 0.86977904],
   [0.8070898 , 0.592959  , 0.86577468],
   [0.81166284, 0.5909601 , 0.86162732],
   [0.81617134, 0.5889919 , 0.8573376 ],
   [0.82061414, 0.58705579, 0.85290625],
   [0.82499007, 0.58515315, 0.84833413],
   [0.82929796, 0.58328538, 0.84362217],
   [0.83353661, 0.58145389, 0.83877142],
   [0.8377048 , 0.57966009, 0.83378306],
   [0.8418013 , 0.57790538, 0.82865836],
   [0.84582486, 0.57619119, 0.82339871],
   [0.84977422, 0.57451892, 0.81800565],
   [0.85364809, 0.57289   , 0.8124808 ],
   [0.85744519, 0.57130585, 0.80682595],
   [0.86116418, 0.56976788, 0.80104298],
   [0.86480373, 0.56827749, 0.79513394],
   [0.86836249, 0.56683612, 0.789101  ],
   [0.87183909, 0.56544515, 0.78294645],
   [0.87523214, 0.56410599, 0.77667274],
   [0.87854024, 0.56282002, 0.77028247],
   [0.88176195, 0.56158863, 0.76377835],
   [0.88489584, 0.56041319, 0.75716326],
   [0.88794045, 0.55929505, 0.75044023],
   [0.89089432, 0.55823556, 0.74361241],
   [0.89375596, 0.55723605, 0.73668312],
   [0.89652387, 0.55629781, 0.72965583],
   [0.89919653, 0.55542215, 0.72253414],
   [0.90177242, 0.55461033, 0.71532181],
   [0.90425   , 0.55386358, 0.70802274],
   [0.90662774, 0.55318313, 0.70064098],
   [0.90890408, 0.55257016, 0.69318073],
   [0.91107745, 0.55202582, 0.68564633],
   [0.91314629, 0.55155124, 0.67804225]])

cmap = col.ListedColormap(colors)

Answer 6

我的 CMasher package 包含大量科学色图，包括循环色图。 与接近感知统一的 twilight 不同，CMasher 的所有颜色图都是感知统一的顺序。 您可以在其 online documentation 中查看其所有颜色图。

CMasher 的政策还规定，如果您对其提供的任何颜色图不满意，您可以要求我为您创建一个您喜欢的颜色图。