Capture camera for histogram equalization

image enhancement

• The purpose of image enhancement is to improve the visual quality of images in specific application fields
• Image enhancement includes smoothing, sharpening, edge extraction, inversion, denoising, and various filtering processes.
• The purpose is that the processed image is more suitable for a specific application (mainly subjective observation and analysis)
• There is no universal theory and method, subjective evaluation is mainly

Image enhancement falls into two broad categories:

• Spatial domain image enhancement: "Spatial domain" refers to the plane of the image itself.
• Image enhancement in frequency domain: processed on the basis of Fourier transform.

After an image is compressed into a histogram, the spatial information is lost

• Property 1: A particular image has a unique histogram, but not vice versa.

• Property 2: The histogram of a specific object in the image is translation invariant.

• Property 3: The histogram of a specific object in the image is rotation invariant.

• Property 4: The area of ​​the image $ = \displaystyle\int_0^\infty H(D)$

• Property 5: For discrete images, ${\sum }_{D=0}^{255}H(D)=NL\ast NS$

  where NL and NS are the rows and columns of the image, respectively.

• Property 6: If an image consists of two disconnected regions, the histogram of the entire image is the sum of the histograms of the two regions.

Uses of Histograms

1. Basic image processing tools: light equalization, feature expression.
2. Check the reasonableness of the grayscale range used by the image. 【0-255】
3. Image binarization boundary threshold selection.
   

Histogram Equalization Steps for Digital Images

1. Probability:

$p_r(r_k)\frac{n_k}{n},k=0,1,2,.....,L-1$

2. Cumulative distribution function:

$P(r_k)=\sum {}_{j=0}^k{p}_r(r_j)=\sum {}_{j=0}^k\frac{n_k}{n},k=0,1,2,.....,L-1$

3. Grayscale mapping count transformation function:

$s_k=T(r_k)=(L-1)\ast \sum {}_{j=0}^k{p}_r\left(r_j\right)=\sum {}_{j=0}^k\frac{n_k}{n},k=0,1,2,.....,L-1$

4. Will $s_k$, rounded up, if there is the same $[s_k]$ , then merge.

from os import cpu_count
import cv2 as cv
import numpy as np
import sys
import math as m
sys.path.append('./')
class HistogramEqualization:
    def __init__(self):
        pass
    def rgb2hsi(self, img_src):
        # 对于图像不足3通道的,直接返回原图像
        if len(img_src.shape) < 3:
            return img_src

        img = img_src.astype(np.float32)/255                    # 归一化处理
        img_r = img[:, :, 0]          # 获取红色通道图像
        img_g = img[:, :, 1]          # 获取绿色通道图像
        img_b = img[:, :, 2]          # 获取蓝色通道图像
        
        # 执行转换方程
        sum_rgb = img_r + img_g + img_b      # 求各通道像素值之和
        np.where(sum_rgb > 0, sum_rgb, sys.float_info.min)
        # 计算S分量
        S = 1 - (3 * np.minimum(np.minimum(img_r, img_g), img_b)) / sum_rgb
        # 计算H分量
        den = ((0.5 * (img_r + img_r - img_g - img_b)) / (np.sqrt((img_r - img_g) * (img_r - img_g) + (img_r - img_b) * (img_g - img_b)) + sys.float_info.min))
        # 防止求arccos时参数超出区间[-1, 1]
        den[den > 1] = 1
        den[den < -1] = -1
        H = np.arccos(den)
        index = np.where(img_b > img_g)      # 找出B>G的坐标值
        H[index] = 2 * m.pi - H[index]
        H /= 2 * m.pi
        H[S == 0] = 0
        # 计算I分量
        I = sum_rgb / 3

        # 拼接三个颜色通道并返回
        hsi = np.zeros(img.shape, dtype=np.float32)
        hsi[:, :, 0] = H
        hsi[:, :, 1] = S
        hsi[:, :, 2] = I
        return hsi
    
    # HSI色彩空间转换为RGB色彩空间
    def hsi2rgb(self, hsi):
        # 对于图像不足3通道的,直接返回原图像
        if len(hsi.shape) < 3:
            return hsi

        H = hsi[:, :, 0]                          # 提取H分量
        S = hsi[:, :, 1]                          # 提取S分量
        I = hsi[:, :, 2]                          # 提取I分量
        R = np.zeros(H.shape, dtype=np.float32)   # 创建红色通道
        G = np.zeros(H.shape, dtype=np.float32)   # 创建绿色通道
        B = np.zeros(H.shape, dtype=np.float32)   # 创建蓝色通道

        H *= 2 * m.pi                          # 扩充弧度范围[0, 2*pi]
        
        # 色调[0, 2*pi/3)范围内对应红->绿
        boolh = np.where((H >= 0) & (H < 2 * m.pi / 3))                    # 找出符合条件的二维图像数组下标
        # 计算红色通道
        R[boolh] = I[boolh] * (1 + (S[boolh] * np.cos(H[boolh])) / (np.cos(m.pi / 3 - H[boolh]) + sys.float_info.min))
        # 计算蓝色通道
        B[boolh] = I[boolh] * (1 - S[boolh])
        # 计算绿色通道
        G[boolh] = I[boolh] * 3 - (B[boolh] + R[boolh])

        # 色调[2*pi/3, 4*pi/3)范围内对应绿->蓝
        boolh = np.where((H >= 2 * m.pi / 3) & (H < 4 * m.pi / 3))      # 找出符合条件的二维图像数组下标
        H[boolh] -= 2 * m.pi / 3
        # 计算红色通道
        R[boolh] = I[boolh] * (1 - S[boolh])
        # 计算绿色通道
        G[boolh] = I[boolh] * (1 + (S[boolh] * np.cos(H[boolh])) / (np.cos(m.pi / 3 - H[boolh])))
        # 计算蓝色通道
        B[boolh] = I[boolh] * 3 - (R[boolh] + G[boolh])
        
        # 色调[4*pi/3, 2*pi]范围内对应蓝->红
        boolh = np.where((H >= 4 * m.pi / 3) & (H < 2 * m.pi))          # 找出符合条件的二维图像数组下标
        H[boolh] -= 4 * m.pi / 3
        # 计算绿色通道
        G[boolh] = I[boolh] * (1 - S[boolh])
        # 计算蓝色通道
        B[boolh] = I[boolh] * (1 + (S[boolh] * np.cos(H[boolh])) / (np.cos(m.pi / 3 - H[boolh])))
        # 计算绿色通道
        R[boolh] = I[boolh] * 3 - (B[boolh] + G[boolh])

        # 拼接图像
        rgb = np.zeros(hsi.shape, dtype=np.uint8)
        rgb[:, :, 0] = (R * 255).astype(np.uint8)
        rgb[:, :, 1] = (G * 255).astype(np.uint8)
        rgb[:, :, 2] = (B * 255).astype(np.uint8)

        return rgb
    # 遍历每个像素点，把img里面的像素值转换成initImg的下标索引（0-256），并统计img相同像素点的个数
    def toHisgram(self,img,initImg):
        for i in range(img.shape[0]):
            for j in range(img.shape[1]):
                initImg[img[i,j]] +=1
        return initImg
    
    # 进行直方图均衡化，并返回最终图像
    def toHist(self,img):
        init_img =np.zeros(256,np.int32)
        #直方图统计，获得概率
        # hist = self.toHisgram(img,init_img)
        hist,den= np.histogram(img,256,[0,255])
        hist = hist/np.sum(hist) #统计的像素点（0-256）个数除以总数
        cdf = np.zeros(256, dtype=np.float32)
       #累计分布函数
        np.cumsum(hist[0 : 256], dtype=np.float32, out=cdf[0 : 256]) 
        #变换函数
        t =np.zeros(256,np.uint8)
        t[0 : 256] = 255 * cdf[0 : 256]
        #合并
        dstImg = np.zeros(img.shape, dtype=np.uint8)
        dstImg[:,:] = t[img[:,:]]
        return dstImg
        
    #将RGB转换成HSI色彩空间域，返回HSI图像
    def rgbToHsi(self,img):
        r = img[:,:,0]
        g = img[:,:,1]
        b = img[:,:,2]
        r = r.astype(np.float32)
        g = g.astype(np.float32)
        b = b.astype(np.float32)

        I = (r+g+b)/3
        I = I/255
        img_min = np.min(img,axis=-1)
        S = 1 - (3/(r+g+b)*img_min)
        a = 0.5*((r-g)+(r-b))
        botton = ((r-g)**2+((r-b)*(g-b))+ sys.float_info.min)**0.5
        den =a /botton
        den[den>1]=1
        den[den<-1]=-1
        H = np.arccos(den)
        index = np.where(g<b)
        H[index]= 2*m.pi-H[index]
        H /= 2 * m.pi
        H[S == 0] = 0

        hsi = np.zeros([img.shape[0],img.shape[1],img.shape[2]],dtype=np.float32)
        hsi[:,:,0] = H
        hsi[:,:,1] = S
        hsi[:,:,2] = I
        return hsi
    
#   将HSI转换成RGB色彩空间域 ，返回RGB图像
    def hsiToRgb(self,hsi):
        H = hsi[:,:,0]
        S = hsi[:,:,1]
        I = hsi[:,:,2]
        H *=2*m.pi

        rgb = np.zeros(hsi.shape,np.uint8)
        R = np.zeros(H.shape, dtype=np.float32)   
        G = np.zeros(H.shape, dtype=np.float32)   
        B = np.zeros(H.shape, dtype=np.float32)   

        index = np.where((H>=0)&(H<2*m.pi/3))
        R[index] = I[index] * (1+(S[index]*np.cos(H[index]))/(np.cos(m.pi/3-H[index])))
        B[index] = I[index]*(1-S[index])
        G[index] = 3*I[index]-(B[index]+R[index])

        index = np.where((H>=2*m.pi/3)&(H<4*m.pi/3))
        R[index] = I[index]*(1-S[index])
        G[index] = I[index] * (1+(S[index]*np.cos(H[index]-2*m.pi/3))/(np.cos(m.pi-H[index])))
        B[index] = 3*I[index]-(R[index]+G[index])
        
        index = np.where((H>=4*m.pi/3)&(H<2*m.pi))
        B[index] = I[index] * (1+(S[index]*np.cos(H[index]-4*m.pi/3))/(np.cos(5*m.pi/3-H[index])))
        G[index] = I[index]*(1-S[index])
        R[index] = 3*I[index]-(G[index]+B[index])

        rgb[:,:,0] = (255*R).astype(np.uint8)
        rgb[:,:,1] = (255*G).astype(np.uint8)
        rgb[:,:,2] = (255*B).astype(np.uint8)
        return rgb
    # 计算熵,首先统计img像素点的个数，计算每个像素点在img的分布概率，遍历计算p[i]*m.log2(p[i])，乘以-1返回熵
    def solveEntropy(self,img):
        n = img.shape[0] * img.shape[1]

        hist,den= np.histogram(img,256,[0,255])
        p = hist / n
        entropy = 0
        for i in range(0,256):
            if (p[i]==0):
                continue
            entropy += p[i]*m.log2(p[i])
        return -1 * entropy

    #计算图像亮度、对比度、熵值
    def compareResult(self,img,typeName):
        light = np.mean(img)
        contrast = np.std(img)
        entropy = self.solveEntropy(img)
        print(f"{typeName} 亮度为 {np.mean(img)}， 对比度为 {np.std(img)}， 熵为 {self.solveEntropy(img)}\n")
        
    # 主函数 启动摄像头 处理每一帧的图像
    def main(self):
        cap = cv.VideoCapture(0)
        while cap.isOpened():
            ret,frame = cap.read()
            hsi = self.rgb2hsi(frame)
            # 直方图处理HSI亮度I
            I = hsi[:,:,2]
            I *= 255
            self.compareResult(I,"原I")  
            I = I.astype(np.uint8)
            I = self.toHist(I) 
            self.compareResult(I,"直方图均衡化I")  
            hsi[:,:,2] = I/255

            rgb = self.hsiToRgb(hsi)
            
            self.compareResult(frame,"原RGB图")
            self.compareResult(rgb,"I直方图均衡化RGB图")
            cv.imshow("Orgin RGB",frame)
            cv.imshow("ToHist RGB",rgb)
            if cv.waitKey(1)&0xFF == ord('q'):
                break
        cap.release()
    
#执行主函数，实例化HistogramEqualization
if __name__=='__main__':
    HistogramEqualization().main()

    if cv.waitKey(0)&0xFF == 27:
        cv.destroyAllWindows()