第2章图像变换

**写得比较粗错，详解后续跟上。**
第2章图像变换
- 2.1 反色变换
- - 2.1.1 基本原理
  - 2.1.2 源码
  - 2.1.3 样例
- 2.2 线性变换
- - 2.2.1 基本原理
  - 2.2.2 源码
  - 2.2.3 样例
  - 加入滚动条
- 2.3 对数变换
- - 2.3.1 基本原理
  - 2.3.2 源码
  - 2.3.3 样例
  - - 加入滚动条
- 2.4 gamma变换
- - 2.4.1 基本原理
  - 2.4.2 源码
  - 2.4.3 样例
  - 使用滑动条操作
- 2.5 分段线性变换
- - 2.5.1 基本原理
  - 2.5.2 源码
  - 2.5.3 样例

写得比较粗错，详解后续跟上。

第2章图像变换

图像变换主要通过调节像素数值，调节色彩明暗度，显示图像细节，方便人眼观察。图像变换的本质是调节像素分布。本节主要讲述常用的线性变换和非线性变换。
在这里插入图片描述

本节要点：

反色变换
线性变换
对数变换
gamma变换
分段线性变换

2.1 反色变换

反色变换是一种非常简单实用的线性变换，适用于过暗或者过亮的图片，通过反色，使得暗色区域变得明亮，凸显图像中关注的部分。

2.1.1 基本原理

反色变换的基本原理将灰度图像素值翻转，即用图像最大值减去所有的像素值，使黑白色发生翻转。

2.1.2 源码

反色变换的步骤：

求取图像的最大值
最大值减去原像素值

# 2.1 反色变换，可以让暗色区域变亮，

def col_invert(img):
    max_p = np.max(img)
    table = [max_p-i for i in range(255)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img,table)

2.1.3 样例

在图像变换过程中先计算每个像素值变换后的数值，并存放在table变量中，然后用cv2.LUT()函数在table中查找像素变换后对应的数值，这样减少重复计算，加快运算速度。

import cv2
import numpy as np
import matplotlib.pyplot as plt

def col_invert(img):
    max_p = np.max(img)
    table = [max_p-i for i in range(255)]  # 把像素变换后的值放入table中，方便cv2.LUT()查找。
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img,table)   # cv2.LUT()是批量对像素进行查找和扫描，节省重复计算。

img = cv2.imread('f1.png',0)
img1 = col_invert(img)

plt.subplot(121)
plt.title('img')
plt.imshow(img,'gray')
plt.subplot(122)
plt.title('img1')
plt.imshow(img1,'gray')
plt.show()

在这里插入图片描述

2.2 线性变换

图像通过线性变换可以增加图片的对比度，调节图像的亮度。
在这里插入图片描述

2.2.1 基本原理

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0,1,100)
y_05 = 0.5*x
y_1 = x
y_2 = 2*x
plt.plot(x,y_05,'-',label = '0.5')
plt.plot(x,y_1,'--',label = '1')
plt.plot(x,y_2,'-.',label = '2')
plt.ylim(0,1)
plt.xlim(0,1)
plt.legend()
plt.title('line_convert')
plt.scatter(0.2,0.4)
plt.scatter(0.4,0.8)
plt.scatter(0.2,0.1)
plt.scatter(0.4,0.2)

plt.text(0.2,0.45,'A1(0.2,0.4)')
plt.text(0.4,0.85,'A2(0.4,0.8)')
plt.text(0.2,0.15,'B1(0.2,0.1)')
plt.text(0.4,0.25,'B2(0.4,0.2)')

img1 = c*img+b

c:调节像素映射后的区间，c大于1，变换后的区间就越大，数据越离散；反之，c小于1，像素变换后就越聚集，颜色对比度就越小。
b:决定像素直方图的中心位置，b值越大，图像就越亮，反之，越暗。

2.2.2 源码

def line_convert(img,c,b):
    table = [c * i+b for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

2.2.3 样例

import cv2
import numpy as np
import matplotlib.pyplot as plt

def line_convert(img,c,b):
    table = [c * i+b for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

img = cv2.imread('f4.png',1)
img1 = line_convert(img,3,1)
plt.subplot(121)
plt.title('img')
plt.imshow(img[...,::-1])
plt.subplot(122)
plt.title('img1')
plt.imshow(img1[...,::-1])
plt.show()

在这里插入图片描述

加入滚动条


import cv2
import numpy as np
from matplotlib.widgets import Slider,Button,RadioButtons
import matplotlib.pyplot as plt
from PIL import Image   # pip install pillow


def set_chinese():
    import matplotlib as mp
    mp.rcParams['font.sans-serif']=['SimHei']
    mp.rcParams['axes.unicode_minus'] = False

def line_convert(img,c,b):
    table = [c * i+b for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

def update_para(val):
    c = slider_1.val
    b = slider_2.val   # 得到滑动条数值
    img1 = line_convert(img,c,b)
    ax2.set_title('c=%f,c=%f'%(c,b))
    ax2.imshow(img1[..., ::-1], vmin=0, vmax=255)


if __name__ == '__main__':
    set_chinese()
    img = cv2.imread('f4.png',1)   # base = 86

    fig = plt.figure()
    ax0 = fig.add_subplot(121)
    ax0.set_title('原图')
    ax0.imshow(img[...,::-1],vmin=0,vmax=255)

    ax2 = fig.add_subplot(122)  # 设置第二幅图

    # 添加滑动条
    plt.subplots_adjust(bottom=0.3)   # [0.25,0.1,0.45,0.03]
    s1 = plt.axes([0.25,0.1,0.55,0.03],facecolor='lightgoldenrodyellow')
    slider_1 = Slider(s1,'c',0.,10.,valfmt='%.f',valinit=5.0,valstep=0.5) # 0.0,2.0 是参数取值范围
    # 把监控到的gamma变换传入update_gamma函数中去
    slider_1.on_changed(update_para)

    s2 = plt.axes([0.25, 0.16, 0.55, 0.03], facecolor='lightgoldenrodyellow')
    slider_2 = Slider(s2, 'b', 0., 255., valfmt='%.f', valinit=0, valstep=1)
    slider_2.on_changed(update_para)

    slider_1.reset()
    slider_1.set_val(1)

    slider_2.reset()
    slider_2.set_val(1)

2.3 对数变换

对图像进行对数变换，可以压缩图像像素的取值范围，使得图像以肉眼可分辨的灰度值显示出来，即图像经过对数变换可以显示更多的细节。
在这里插入图片描述

def log(base,x):
    return np.log(1+base*x)/np.log(base+1)


x = np.linspace(0,1,100)
y = 1*x
y_1 = log(1,x)
y_10 = log(10,x)
y_30 = log(30,x)
y_100 = log(100,x)
y_300 = log(300,x)
plt.plot(x,y,label = 'origin')
plt.plot(x,y_1,label = 'b=1')
plt.plot(x,y_10,label = 'b=10')
plt.plot(x,y_30,label = 'b=30')
plt.plot(x,y_100,label = 'b=100')
plt.plot(x,y_300,label = 'b=300')

plt.ylim(0,1)
plt.xlim(0,1)
plt.legend()
plt.title('log_line')
plt.xlabel('input intensity level')
plt.ylabel('output intensity level')
plt.text(0.35,0.350,'origin')
plt.text(0.32,0.43,'b=1')
plt.text(0.23,0.52,'b=10')
plt.text(0.2,0.6,'b=30')
plt.text(0.18,0.66,'b=100')
plt.text(0.16,0.75,'b=300')
plt.show()

2.3.1 基本原理


img1 = c*log_{base+1}(1+base*img/255)*255

2.3.2 源码


import cv2
import numpy as np
import matplotlib.pyplot as plt

def log(base,x):
    return np.log(x)/np.log(base+1)

def log_convert(img,base,c):
    table = [c*log(base,(1+i)/255)*255 for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img,table)

2.3.3 样例

import cv2
import numpy as np
import matplotlib.pyplot as plt

def log(base,x):
    return np.log(x)/np.log(base+1)
    
def log_convert(img,base,c):
    table = [c*log(base,1+(base)*i/255)*255 for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img,table)


img = cv2.imread('yejing.png',1)
img1 = log_convert(img,80,0.9)
plt.subplot(121)
plt.title('img')
plt.imshow(img[...,::-1])
plt.subplot(122)
plt.title('img1')
plt.imshow(img1[...,::-1])
plt.show()

在这里插入图片描述

加入滚动条

import cv2
import numpy as np
from matplotlib.widgets import Slider,Button,RadioButtons
import matplotlib.pyplot as plt
from PIL import Image   # pip install pillow


def set_chinese():
    import matplotlib as mp
    mp.rcParams['font.sans-serif']=['SimHei']
    mp.rcParams['axes.unicode_minus'] = False


def log(base, x):
    return np.log(x) / np.log(base + 1)

def log_convert(img, base, c=1):
    table = [c * log(base, 1 + (base) * i / 255) * 255 for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

def update_gamma(val):
    base = slider1.val # 得到滑动条数值
    img1 = log_convert(img, base, c=1)
    ax2.set_title('base=%f'%(base))
    ax2.imshow(img1[..., ::-1], vmin=0, vmax=255)


if __name__ == '__main__':
    set_chinese()
    img = cv2.imread('2.png',1)

    fig = plt.figure()
    ax0 = fig.add_subplot(121)
    ax0.set_title('原图')
    ax0.imshow(img[...,::-1],vmin=0,vmax=255)

    ax2 = fig.add_subplot(122)  # 设置第二幅图

    # 添加滑动条
    plt.subplots_adjust(bottom=0.3)   # [0.25,0.1,0.45,0.03]
    s1 = plt.axes([0.25,0.1,0.45,0.03],facecolor='lightgoldenrodyellow')
    slider1 = Slider(s1,'base',0.,200.,valfmt='%.f',valinit=50.0,valstep=2) # 0.0,2.0 是参数取值范围
    # 把监控到的gamma变换传入update_gamma函数中去
    slider1.on_changed(update_gamma)
    slider1.reset()
    slider1.set_val(1)

在这里插入图片描述

2.4 gamma变换

在这里插入图片描述

def gamma_line(x,r):
    return x**r

x = np.linspace(0,1,100)
y = gamma_line(x,1)
y_1 = gamma_line(x,2.5)
y_2 = gamma_line(x,0.4)

plt.plot(x,y,'-',label = 'r=1')
plt.plot(x,y_1,'--',label = 'r=2.5')
plt.plot(x,y_2,'-.',label = 'r=0.4')


plt.ylim(0,1)
plt.xlim(0,1)
plt.legend()
plt.title('gamma_line')
plt.xlabel('input intensity level')
plt.ylabel('output intensity level')
plt.show()

2.4.1 基本原理

步骤：
· 归一化
·
·
·


img1 = c*(\frac{img+\epsilon}{255} )^\gamma*255+r

2.4.2 源码


def gamma_convert(img,c,r):
    table = [c * ((i+0.1)/255)**r * 255 for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

2.4.3 样例

import cv2
import numpy as np
import matplotlib.pyplot as plt

def gamma_convert(img,c,r):
    table = [c * ((i+0.1)/255)**r * 255 for i in range(256)]
    table = np.round(np.array(table)).astype(np.uint8)
    return cv2.LUT(img, table)

img = cv2.imread('beijing2.png',1)
img1 = gamma_convert(img,1,0.5)
plt.subplot(121)
plt.title('img')
plt.imshow(img[...,::-1])
plt.subplot(122)
plt.title('img1')
plt.imshow(img1[...,::-1])
plt.show()

在这里插入图片描述

使用滑动条操作

import cv2
import numpy as np
from matplotlib.widgets import Slider,Button,RadioButtons
import matplotlib.pyplot as plt
from PIL import Image   # pip install pillow


def set_chinese():
    import matplotlib as mp
    mp.rcParams['font.sans-serif']=['SimHei']
    mp.rcParams['axes.unicode_minus'] = False

def gamma_convert(img,gamma,eps=0):
    return (255*(((img+eps)/255.)**gamma)).astype(np.uint8)

def update_gamma(val):
    gamma = slider1.val # 得到滑动条数值
    img1 = gamma_convert(img, gamma, eps=0)
    ax2.set_title('gamma=%f'%(gamma))
    ax2.imshow(img1[..., ::-1], vmin=0, vmax=255)


if __name__ == '__main__':
    set_chinese()
    img = cv2.imread('luna_baoguang.png',1)

    fig = plt.figure()
    ax0 = fig.add_subplot(121)
    ax0.set_title('露娜')
    ax0.imshow(img[...,::-1],vmin=0,vmax=255)

    ax2 = fig.add_subplot(122)  # 设置第二幅图

    # 添加滑动条
    plt.subplots_adjust(bottom=0.3)
    s1 = plt.axes([0.25,0.1,0.55,0.03],facecolor='lightgoldenrodyellow')
    slider1 = Slider(s1,'para :gamma',0.0,10.0,valfmt='%.f',valinit=5.0,valstep=0.1) # 0.0,2.0 是参数取值范围
    # 把监控到的gamma变换传入update_gamma函数中去
    slider1.on_changed(update_gamma)
    slider1.reset()
    slider1.set_val(1)

2.5 分段线性变换

在这里插入图片描述

2.5.1 基本原理

2.5.2 源码

def three_line_convert(img,x1,y1,x2,y2):
    if x1==x2 or x2 == 255:
        return None
    m1 = (img<x1)
    m2 = (x1<=img)&(img<=x2)
    m3 = (img>x2)

    img1 = (y1/x1*img)*m1+((y2-y1)/(x2-x1)*(img-x1)+y1)*m2+((255-y2)/(255-x2)*(img-x2)+y2)*m3
    img1 = img1.astype(np.uint8)
    return img1

2.5.3 样例

import cv2
import numpy as np
import matplotlib.pyplot as plt

def three_line_convert(img,x1,y1,x2,y2):
    if x1==x2 or x2 == 255:
        return None
    m1 = (img<x1)
    m2 = (x1<=img)&(img<=x2)
    m3 = (img>x2)

    img1 = (y1/x1*img)*m1+((y2-y1)/(x2-x1)*(img-x1)+y1)*m2+((255-y2)/(255-x2)*(img-x2)+y2)*m3
    img1 = img1.astype(np.uint8)
    return img1

img = cv2.imread('fen3.png',1)
img1 = three_line_convert(img,36,76,178,228)
plt.subplot(121)
plt.title('img')
plt.imshow(img[...,::-1])
plt.subplot(122)
plt.title('img1')
plt.imshow(img1[...,::-1])

在这里插入图片描述

加入滚动条


import cv2
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.widgets import Slider


def three_line_convert(img,x1,y1,x2,y2):
    if x1==x2 or x2 == 255:
        return None
    m1 = (img<x1)
    m2 = (x1<=img)&(img<=x2)
    m3 = (img>x2)

    img1 = (y1/x1*img)*m1+((y2-y1)/(x2-x1)*(img-x1)+y1)*m2+((255-y2)/(255-x2)*(img-x2)+y2)*m3
    # 绘制函数图像
    x_point = np.arange(0,256,1)
    cond2 = [True if(i>=x1 and i<=x2) else False for i in x_point]
    y_point = (y1/x1*x_point)*(x_point<x1)+ \
              ((y2-y1)/(x2-x1)*(x_point-x1)+y1)*cond2+ \
              ((255-y2)/(255-x2)*(x_point-x2)+y2)*(x_point>x2)

    return img1,x_point,y_point

def update_trans(val):
    # 1 读入滑动条的值
    x1,y1 = slider_x1.val,slider_y1.val
    x2, y2 = slider_x2.val, slider_y2.val
    # 2 执行分段线性变换
    img1,x_point,y_point = three_line_convert(img,x1,y1,x2,y2)
    img1 = img1.astype(np.uint8)
    # 3 显示变换结果
    ax2.clear()
    ax2.set_title('result',fontsize=8)
    ax2.imshow(img1[...,::-1],vmin=0,vmax=255)
    # 4 绘制函数
    ax3.clear()
    ax3.annotate('(%d,%d)'%(x1,y1),xy=(x1,y1),xytext=(x1-15, y1+15))
    ax3.annotate('(%d,%d)'%(x2,y2), xy=(x2,y2), xytext=(x2+15, y2-15))
    ax3.set_title('fun', fontsize=8)
    ax3.grid(True,linestyle=':',linewidth=1)
    ax3.plot([x1,x2],[y1,y2],'ro')
    ax3.plot(x_point, y_point, 'g')
    # 显示变换后的直方图
    ax5.clear()
    ax5.grid(True,linestyle=':',linewidth=1)
    ax5.set_title('hist',fontsize=8)
    ax5.set_xlim(0,255)
    ax5.set_ylim(0, 0.06)
    ax5.hist(img1[...,::-1].flatten(),bins=50,density=True,color='r',edgecolor='k')


img = cv2.imread('hua.png',1)  # [x1,y1,x2,y2] [36,76,178,228]
fig = plt.figure()
ax1 = fig.add_subplot(231)
ax2 = fig.add_subplot(232)
ax3 = fig.add_subplot(233)
ax4 = fig.add_subplot(234)
ax5 = fig.add_subplot(235)

ax1.set_title('origin',fontsize=8)
ax1.imshow(img[...,::-1],vmin=0,vmax=255)

ax4.grid(True,linestyle=':',linewidth=1)
ax4.set_title('origin indensity',fontsize=8)
ax4.set_xlim(0,255)
ax4.set_ylim(0,0.06)
ax4.hist(img[...,0].flatten(),bins=50,density=True,color='r',edgecolor='k')

plt.subplots_adjust(bottom=0.3)
x1 = plt.axes([0.25,0.20,0.45,0.03],facecolor = 'lightgoldenrodyellow')
slider_x1 = Slider(x1,'Para_x1',0.,255.,valfmt='%.f',valinit=100,valstep=1)
slider_x1.on_changed(update_trans)

y1 = plt.axes([0.25,0.15,0.45,0.03],facecolor = 'lightgoldenrodyellow')
slider_y1 = Slider(y1,'Para_y1',0.,255.,valfmt='%.f',valinit=0,valstep=1)
slider_y1.on_changed(update_trans)

x2 = plt.axes([0.25,0.1,0.45,0.03],facecolor = 'lightgoldenrodyellow')
slider_x2 = Slider(x2,'Para_x2',0.,255.,valfmt='%.f',valinit=100,valstep=1)
slider_x2.on_changed(update_trans)

y2 = plt.axes([0.25,0.05,0.45,0.03],facecolor = 'lightgoldenrodyellow')
slider_y2 = Slider(y2,'Para_y2',0.,255.,valfmt='%.f',valinit=0,valstep=1)
slider_y2.on_changed(update_trans)