第6章 Python 数字图像处理(DIP) - 彩色图像处理1 - RGB彩色模型，RGB to Gray，CMK和CMYK彩色模型，HSI彩色模型
第6章主要讲的是彩色图像处理，一些彩色模型如RGB，CMK，CMYK，HSI等色彩模型；彩色模型的变换关系；还包含由灰度图像怎样处理成假彩色图像；使用彩色分割图像等。本章比较少理论还有变换的描述，主要以代码为主，如有需要，请自行查看书本。
这里写目录标题
- 色彩基础
-
- 彩色模型
-
- RGB彩色模型
- RGB to Gray
- CMK和CMYK 彩色模型
- HSI
import numpy as np
import cv2
import matplotlib
import matplotlib.pyplot as plt
import PIL
print(f"Numpy version: {np.__version__}")
print(f"Opencv version: {cv2.__version__}")
print(f"Matplotlib version: {matplotlib.__version__}")
print(f"Pillow version: {PIL.__version__}")
Numpy version: 1.18.1
Opencv version: 4.2.0
Matplotlib version: 3.1.3
Pillow version: 7.0.0
def normalize(mask):
return (mask - mask.min()) / (mask.max() - mask.min())
色彩基础
区别不同颜色的特性通常是亮度、色调和饱和度。亮度体现的发光强度的消色概念；色调是混合光波中与主波长书的人属性，表示被观察者感知的主导色；饱和度是指相对的纯度，或与一种色调混合的白光量。
色调与饱和度一起称为色度，因此一种颜色可由其亮度和色度来表征。形成任何一种特殊颜色的红色量、绿色量和蓝色量称为三色值，并分别表示为X，Y和Z。因此一种彩色就可由其三色系数来规定。
x = X X + Y + Z (6.1) x = \frac{X}{X + Y + Z} \tag{6.1} x=X+Y+ZX(6.1)
y = Y X + Y + Z (6.2) y = \frac{Y}{X + Y + Z} \tag{6.2} y=X+Y+ZY(6.2)
z = Z X + Y + Z (6.3) z = \frac{Z}{X + Y + Z} \tag{6.3} z=X+Y+ZZ(6.3)
x + y + z = 1 (6.4) x + y + z = 1 \tag{6.4} x+y+z=1(6.4)
彩色模型
彩色模型（也称彩色空间或彩色系统）的目的是以某种师傅微软方式来方便地规定颜色。彩色模型本质上规定：坐标系；坐标系内的子空间，模型内的每种颜色都可由子空间内包含的一个点来表示。
针对彩色显示器和彩色摄像机开发的RGB(Red, Green, Blue)模型；针对彩色打印开发的CMY(Cyan, Magenta, Yellow)模型和CMYK(K is Black)；针对人们描述和解释颜色的方式开发的HSI(Hue, Saturation, Intensity)模型。
HSI能名解除图像中颜色和灰度级信息的联系，使其更适合灰度级处理技术。
RGB彩色模型
根根笛卡儿坐标系建立的。R，G和B的值都已经归一化在区间[0, 1]内。RGB原色可解释为发源于立方体原点的一个向量。
表示每个像素所用的比特数称为像素深度。
RGB三个通道，每个通道像素深度为8比特图像，RGB彩色像素的深度为24比特。值域为[0, 255]
# RGB 彩色模型
img_bgr = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0608(RGB-full-color-cube).tif')
img_rgb = img_bgr[:, :, ::-1]
plt.figure(figsize=(5, 5))
plt.imshow(img_rgb), plt.xticks([]), plt.yticks([])
plt.show()
# RGB 三个隐藏面，合成显示RGB，R = 127
temp = np.zeros([512, 512], np.uint8)
x = np.linspace(0, 1, temp.shape[0])
X = np.uint8(normalize(x) * 255)
X = np.tile(X, [512, 1])
y = np.linspace(0, 1, temp.shape[0])
Y = np.uint8(normalize(y) * 255)
Y = np.tile(Y, [512, 1])
R = temp + 127
G = X
B = np.rot90(Y)
plt.figure(figsize=(20, 5))
plt.gray()
plt.subplot(143), plt.imshow(R, vmin=0, vmax=255), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(142), plt.imshow(G, ), plt.title('Green Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(141), plt.imshow(B, ), plt.title('Blue Channel'), plt.xticks([]), plt.yticks([])
img = np.dstack([R, G, B])
plt.subplot(144),plt.imshow(img), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
# RGB 三个隐藏面，R = 0
temp = np.zeros([512, 512], np.uint8)
x = np.linspace(0, 1, temp.shape[0])
X = np.uint8(normalize(x) * 255)
X = np.tile(X, [512, 1])
y = np.linspace(0, 1, temp.shape[0])
Y = np.uint8(normalize(y) * 255)
Y = np.tile(Y, [512, 1])
R = temp
G = X
B = np.rot90(Y)
plt.figure(figsize=(20, 5))
plt.gray()
plt.subplot(141), plt.imshow(R, vmin=0, vmax=255), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(142), plt.imshow(G, ), plt.title('Green Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(B, ), plt.title('Blue Channel'), plt.xticks([]), plt.yticks([])
img = np.dstack([R, G, B])
plt.subplot(144),plt.imshow(img), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
# RGB 三个隐藏面，G = 0
temp = np.zeros([512, 512], np.uint8)
x = np.linspace(0, 1, temp.shape[0])
X = np.uint8(normalize(x) * 255)
X = np.tile(X, [512, 1])
y = np.linspace(0, 1, temp.shape[0])
Y = np.uint8(normalize(y) * 255)
Y = np.tile(Y, [512, 1])
G = temp
R = np.flip(X)
B = np.rot90(Y)
plt.figure(figsize=(20, 5))
plt.gray()
plt.subplot(141), plt.imshow(R, vmin=0, vmax=255), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(142), plt.imshow(G, ), plt.title('Green Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(B, ), plt.title('Blue Channel'), plt.xticks([]), plt.yticks([])
img = np.dstack([R, G, B])
plt.subplot(144),plt.imshow(img), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
# RGB 三个隐藏面，B = 0
temp = np.zeros([512, 512], np.uint8)
x = np.linspace(0, 1, temp.shape[0])
X = np.uint8(normalize(x) * 255)
X = np.tile(X, [512, 1])
y = np.linspace(0, 1, temp.shape[0])
Y = np.uint8(normalize(y) * 255)
Y = np.tile(Y, [512, 1])
B = temp
G = X
R = np.rot90(np.fliplr(Y))
plt.figure(figsize=(20, 5))
plt.gray()
plt.subplot(141), plt.imshow(R, vmin=0, vmax=255), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(142), plt.imshow(G, ), plt.title('Green Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(B, ), plt.title('Blue Channel'), plt.xticks([]), plt.yticks([])
img = np.dstack([R, G, B])
plt.subplot(144),plt.imshow(img), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
RGB to Gray
模式“L”:
模式“L”为灰色图像，它的每个像素用8个bit表示，0表示黑，255表示白，其他数字表示不同的灰度。在PIL中，从模式“RGB”转换为“L”模式是按照下面的公式转换的：
L = R * 299/1000 + G * 587/1000+ B * 114/1000
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
img_rgb = img_ori[:, :, ::-1] # 这个下面实现是一样的效果[0, 1, 2]， 反转为[2, 1, 0]
# img_rgb = img_ori[..., ::-1]
plt.figure(figsize=(20, 5))
img_b = img_ori[:, :, 0]
img_g = img_ori[:, :, 1]
img_r = img_ori[:, :, 2]
plt.subplot(141), plt.imshow(img_rgb), plt.title('Original'), plt.xticks([]), plt.yticks([])
plt.gray()
plt.subplot(142), plt.imshow(img_b, ), plt.title('Blue Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(img_g, ), plt.title('Green Channel'), plt.xticks([]), plt.yticks([])
plt.subplot(144), plt.imshow(img_r, ), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
def rgb2gray(img):
"""
convert RGB image to gray image
param: img: input RGB 3 channels image
return: grayscale image
"""
img_gray = np.zeros((img.shape[:2]))
img_r = img[:, :, 0].astype(np.float32)
img_g = img[:, :, 1].astype(np.float32)
img_b = img[:, :, 2].astype(np.float32)
img_gray = (img_r * 299 + img_g * 587 + img_b * 114) / 1000
img_gray = (normalize(img_gray) * 255).astype(np.uint8)
return img_gray
def bgr2gray(img):
"""
convert RGB image to gray image
param: img: input RGB 3 channels image
return: grayscale image
"""
img_gray = np.zeros((img.shape[:2]))
img_r = img[:, :, 2].astype(np.float32)
img_g = img[:, :, 1].astype(np.float32)
img_b = img[:, :, 0].astype(np.float32)
img_gray = (img_r * 299 + img_g * 587 + img_b * 114) / 1000
img_gray = (normalize(img_gray) * 255).astype(np.uint8)
return img_gray
# RGB2GRAY
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif') # BGR
img_rgb = img_ori[:, :, ::-1] # 这个下面实现是一样的效果[0, 1, 2]， 反转为[2, 1, 0]
img_gray = rgb2gray(img_rgb)
bgr_gray = bgr2gray(img_ori)
plt.figure(figsize=(20, 5))
plt.subplot(141), plt.imshow(img_rgb), plt.title('Original'), plt.xticks([]), plt.yticks([])
plt.gray()
plt.subplot(142), plt.imshow(img_gray, ), plt.title('RGB to Gray'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(bgr_gray, ), plt.title('BGR to Gray'), plt.xticks([]), plt.yticks([])
# plt.subplot(144), plt.imshow(img_r, ), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
CMK和CMYK 彩色模型
RGB 归一化到【0， 1】
[ C M Y ] = [ 1 1 1 ] − [ R G B ] \begin{bmatrix} C \\ M \\ Y\end{bmatrix} = \begin{bmatrix} 1 \\ 1 \\ 1\end{bmatrix} - \begin{bmatrix} R \\ G \\ B\end{bmatrix} ⎣⎡CMY⎦⎤=⎣⎡111⎦⎤−⎣⎡RGB⎦⎤
从CMY到CMYK的转换如下：
K = m i n ( C , M , Y ) K= min(C,M,Y) K=min(C,M,Y)
若 K = 1 K=1 K=1，则产生无颜色贡献的纯黑色，由此得出 C = 0 , M = 0 , Y = 0 C = 0, M=0, Y=0 C=0,M=0,Y=0，否则：
C = ( C − K ) / ( 1 − K ) C = (C - K)/(1 - K) C=(C−K)/(1−K)
M = ( M − K ) / ( 1 − K ) M = (M - K)/(1 - K) M=(M−K)/(1−K)
Y = ( Y − k ) / ( 1 − K ) Y = (Y - k)/(1 - K) Y=(Y−k)/(1−K)
从CMYK到CMY的转换是：
C = C ( 1 − K ) + K C = C(1 - K) + K C=C(1−K)+K
M = M ( 1 − K ) + K M = M(1 - K)+ K M=M(1−K)+K
Y = Y ( 1 − K ) + K Y = Y(1 - K) + K Y=Y(1−K)+K
def rgb_2_cmy(img):
"""
RGB image convert to CMY
param: img: input RGB image
return CMY image
"""
img_norm = normalize(img).astype(np.float32)
img_cmy = 1 - img_norm
# img_cmy = np.uint8(img_cmy * 255)
return img_cmy
def rgb_2_cmyk(img):
"""
RGB image convert to CMYK
param: img: input RGB image
return CMYK image
"""
height, width, channel = img.shape
img_cmy = 1 - normalize(img).astype(np.float32)
img_c = np.zeros((height, width), dtype=np.float32)
img_m = np.zeros((height, width), dtype=np.float32)
img_y = np.zeros((height, width), dtype=np.float32)
img_k = np.zeros((height, width), dtype=np.float32)
for h in range(height):
for w in range(width):
temp = img[h, w]
k = min(temp[0], temp[1], temp[2])
c, m, y = img_cmy[h, w]
if k == 1:
img_c[h, w] = 0
img_m[h, w] = 0
img_y[h, w] = 0
img_k[h, w] = 1
else:
img_c[h, w] = (c - k) / (1 - k)
img_m[h, w] = (m - k) / (1 - k)
img_y[h, w] = (y - k) / (1 - k)
img_k[h, w] = k
img_cmyk = np.dstack((img_c, img_m, img_y, img_k))
img_dst = normalize(img_cmyk)
# img_dst = np.uint8(normalize(img_cmyk) * 255)
return img_dst
def rgb_2_cmyk_2(img):
"""There still have some problem"""
height, width, channel = img.shape
img_cmy = 1 - normalize(img)
k = np.min(img_cmy, axis=2)
img_c = img_cmy[:, :, 0]
img_m = img_cmy[:, :, 1]
img_y = img_cmy[:, :, 2]
# 当 K != 1 时
img_c = np.where(k == 1, img_c, (img_c - k) / (1 - k + 1e-5))
img_m = np.where(k == 1, img_m, (img_m - k) / (1 - k + 1e-5))
img_y = np.where(k == 1, img_y, (img_y - k) / (1 - k + 1e-5))
# 当 K = 1 时
img_c = np.where(k != 1, img_c, 0)
img_m = np.where(k != 1, img_m, 0)
img_y = np.where(k != 1, img_y, 0)
img_cmyk = np.dstack((img_c, img_m, img_y))
img_cmyk = normalize(img_cmyk)
return img_cmyk
# RGB 2 CMYK
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
# 这里需要先转为float，不然会出现意想不到的结果
img_ori_norm = normalize(img_ori).astype(np.float32)
img_rgb = img_ori_norm[:, :, ::-1] # 这个下面实现是一样的效果[0, 1, 2]， 反转为[2, 1, 0]
# img_rgb = img_ori[..., ::-1]
print(img_rgb[0, 0])
plt.figure(figsize=(20, 5))
img_b = img_ori_norm[:, :, 0]
img_g = img_ori_norm[:, :, 1]
img_r = img_ori_norm[:, :, 2]
img_cmy = rgb_2_cmy(img_rgb)
print(img_cmy[0, 0])
img_cmyk = rgb_2_cmyk(img_rgb)
print(img_cmyk[0, 0])
plt.subplot(141), plt.imshow(img_rgb, ), plt.title('Original'), plt.xticks([]), plt.yticks([])
plt.subplot(142), plt.imshow(img_cmy, ), plt.title('CMY'), plt.xticks([]), plt.yticks([])
plt.subplot(143), plt.imshow(img_cmyk, ), plt.title('CMYK'), plt.xticks([]), plt.yticks([])
plt.subplot(144), plt.imshow(img_r, ), plt.title('Red Channel'), plt.xticks([]), plt.yticks([])
plt.tight_layout()
plt.show()
[0.7882353 0.29411766 0.00392157]
[0.2117647 0.7058823 0.99607843]
[0.78587306 0.9201019 0.9989347 0.7304729 ]
# Pillow CMYK
img_ori = PIL.Image.open('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
img_cmyk = img_ori.convert("CMYK")
print(f"Mode: {img_cmyk.mode}, shape: {np.array(img_cmyk).shape}")
print(f'Pixel value: RGB: {img_ori.getpixel((0, 0))}, CMYK: {img_cmyk.getpixel((0, 0))}')
plt.figure(figsize=(20, 5))
plt.subplot(141), plt.imshow(img_ori, ), plt.title('Original')
plt.subplot(142), plt.imshow(img_cmyk, ), plt.title('CMYK')
plt.tight_layout()
plt.show()
Mode: CMYK, shape: (512, 512, 4)
Pixel value: RGB: (201, 75, 1), CMYK: (54, 180, 254, 0)
HSI
H = { θ , B ≤ G 360 − θ , B > G H = \begin{cases} \theta, & B \leq G \\ 360 - \theta, & B > G \end{cases} H={ θ,360−θ,B≤GB>G
θ = a r c c o s [ 1 2 [ ( R − G ) + ( R − B ) ] [ ( R − G ) 2 + ( R − B ) ( G − B ) ] 1 / 2 ] \theta = arccos\bigg[\frac{\frac{1}{2}[(R-G) + (R-B)]}{[(R-G)^2 + (R-B)(G-B)]^{1/2}} \bigg] θ=arccos[[(R−G)2+(R−B)(G−B)]1/221[(R−G)+(R−B)]]
S = 1 − 3 ( R + G + B ) [ m i n ( R , G , B ) ] S = 1 - \frac{3}{(R + G + B)}[min(R, G, B)] S=1−(R+G+B)3[min(R,G,B)]
I = 1 3 ( R + G + B ) I = \frac{1}{3}(R + G + B) I=31(R+G+B)
RGB 值已被归一化到区间【0，1】，并且角度 θ \theta θ是相对于HSI空间的红色轴来测量的，将得到的所有值除以360，可将色调归一化到区间【0， 1】。
def rgb2hsi(img):
"""
RGB image convert to CMYK
param: img: input RGB image
return CMYK image
"""
img_rgb = img.copy()
H = np.zeros(img_rgb.shape[:2])
S = np.zeros(img_rgb.shape[:2])
I = np.zeros(img_rgb.shape[:2])
height, width = img_rgb.shape[:2]
for h in range(height):
for w in range(width):
temp = img_rgb[h, w]
R = temp[0]
G = temp[1]
B = temp[2]
numerator = ((R - G) + (R - B)) / 2
denominator = np.power((R - G)**2 + (R - B) * (G - B), 1/2)
theta = np.arccos(numerator / (denominator + 1e-5))
print(theta)
if B <= G:
H[h, w] = theta / 360
else:
H[h, w] = (360 - theta) / 360
S[h, w] = 1 - ((3 * min(R, G, B))/ (R + G + B + 1e-5))
I[h, w] = (R + G + B + 1e-5) / 3
img_HSI = np.dstack((H, S, I))
img_HSI = np.uint8(normalize(img_HSI) * 255)
return img_HSI
# RGB 2 HSI
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
img_ori_norm = normalize(img_ori)
img_rgb = img_ori_norm[:, :, ::-1] # 这个下面实现是一样的效果[0, 1, 2]， 反转为[2, 1, 0]
# img_rgb = img_ori[..., ::-1]
print(img_rgb[0, 0])
plt.figure(figsize=(20, 5))
# 这里需要先转为float，不然会出现意想不到的结果
img_b = img_ori_norm[:, :, 0].astype(np.float32)
img_g = img_ori_norm[:, :, 1].astype(np.float32)
img_r = img_ori_norm[:, :, 2].astype(np.float32)
H = np.zeros(img_rgb.shape[:2])
S = np.zeros(img_rgb.shape[:2])
I = np.zeros(img_rgb.shape[:2])
height, width = img_rgb.shape[:2]
for h in range(height):
for w in range(width):
R = img_r[h, w]
G = img_g[h, w]
B = img_b[h, w]
numerator = ((R - G) + (R - B))
denominator = 2 * np.sqrt((R - G)**2 + (R - B) * (G - B))
theta = np.arccos(numerator / (denominator + 1e-5))
degree = np.rad2deg(theta)
# print(degree)
if B <= G:
H[h, w] = degree
else:
H[h, w] = (360 - degree)
S[h, w] = 1 - ((3 * min(R, G, B))/ (R + G + B + 1e-5))
I[h, w] = (R + G + B) / 3
H = normalize(H)
H = H.reshape(H.shape[0], H.shape[1], 1)
S = S.reshape(S.shape[0], S.shape[1], 1)
I = I.reshape(H.shape[0], H.shape[1], 1)
S = normalize(S)
I = normalize(I)
img_HSI = np.concatenate((H, S, I), axis=2)
# img_HSI = img_HSI.reshape(img_ori.shape[0], img_ori.shape[1], 3)
# img_HSI = img_HSI.transpose((1, 2, 0))
print(img_HSI.shape)
# img_HSI = np.uint8(normalize(img_HSI) * 255)
plt.subplot(141), plt.imshow(img_rgb, ), plt.title('Original')
plt.subplot(142), plt.imshow(img_HSI, ), plt.title('HSI')
# plt.subplot(143), plt.imshow(img_cmyk, ), plt.title('CMYK')
# plt.subplot(144), plt.imshow(img_r, ), plt.title('Red Channel')
plt.tight_layout()
plt.show()
[0.78823529 0.29411765 0.00392157]
(512, 512, 3)
# RGB 2 HSI
img_ori = cv2.imread('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
img_hsi = cv2.cvtColor(img_ori, cv2.COLOR_BGR2HSV_FULL)
plt.figure(figsize=(20, 5))
plt.subplot(141), plt.imshow(img_rgb, ), plt.title('Original')
plt.subplot(142), plt.imshow(img_hsi, ), plt.title('HSI')
# plt.subplot(143), plt.imshow(img_cmyk, ), plt.title('CMYK')
# plt.subplot(144), plt.imshow(img_r, ), plt.title('Red Channel')
plt.tight_layout()
plt.show()
img_ori = PIL.Image.open('DIP_Figures/DIP3E_Original_Images_CH06/Fig0646(a)(lenna_original_RGB).tif')
img_HSI = img_ori.convert("HSV")
print(f"Mode: {img_HSI.mode}, shape: {np.array(img_HSI).shape}")
print(f'Pixel value: RGB: {img_ori.getpixel((0, 0))}, HSI: {img_HSI.getpixel((0, 0))}')
plt.figure(figsize=(20, 5))
plt.subplot(141), plt.imshow(img_ori, ), plt.title('Original')
plt.subplot(142), plt.imshow(img_HSI, ), plt.title('HSI')
plt.tight_layout()
plt.show()
Mode: HSV, shape: (512, 512, 3)
Pixel value: RGB: (201, 75, 1), HSI: (15, 253, 201)
