公式

HSI彩色模型就是色调（hub）、饱和度（saturation）、亮度（intensity）

• 色调：描述纯色（纯黄色、纯蓝色之类）的颜色属性
• 饱和度：描述一种纯色被白光稀释的程度
• 亮度：即强度（类似灰度级的感觉）

以下公式来源论文《Color image enhancement with exact HSI color model》

RGB转HSI

$$I=\frac{R+G+B}{3}$$
$$\begin{gathered} H=\{\begin{array}{ll}\theta ,& \text{ if }B\le G\\ 360^{\circ }-\theta ,& \text{ if }B>G\end{array} \\ 其中\theta ={\cos }^{-1}\left\{\frac{\frac{1}{2}[(R-G)+(R-B)]}{{\left[(R-G{)}^2+(R-B)(G-B)\right]}^{1/2}}\right\} \end{gathered}$$
$$S=1-\frac{3\min (R,G,B)}{R+G+B}$$

HSI转RGB

• $0^{\circ }\le H<120^{\circ }$
  $$\begin{array}{rl}B& =I(1-S)\\ R& =I\left[1+\frac{S\cos H}{\cos \left(60^{\circ }-H\right)}\right]\\ G& =3I-(R+B)\end{array}$$
• $120^{\circ }\le H<240^{\circ }$
  $$\begin{array}{rl}H& =H-240^{\circ }\\ R& =I(1-S)\\ G& =I\left[1+\frac{S\cos H}{\cos \left(60^{\circ }-H\right)}\right]\\ B& =3I-(R+G)\end{array}$$
• $240^{\circ }\le H<360^{\circ }$
  $$\begin{array}{rl}H& =H-240^{\circ }\\ G& =I(1-S)\\ B& =I\left[1+\frac{S\cos H}{\cos \left(60^{\circ }-H\right)}\right]\\ R& =3I-(G+B)\end{array}$$

RGB转HSI代码

Mat RGB2HSI(const Mat & rgb){
    Mat hsi(rgb.rows, rgb.cols, rgb.type());
    float  H=0, S=0, I=0;
    for(int i=0; i < rgb.rows; i++)
        for(int j=0; j < rgb.cols; j++){
            float B = rgb.at<Vec3b>(i, j)[0] / 255.f,
                  G = rgb.at<Vec3b>(i, j)[1] / 255.f,
                  R = rgb.at<Vec3b>(i, j)[2] / 255.f;

            float num = (R - G + R - B) / 2,
                  den = sqrt((R - G) * (R - G) + (R - B) * (G - B)),
                  theta = acos(num/den);
            if(den == 0) H = 0; // 分母不能为0
            else H = B <= G ? theta / (2 * MY_PI) : 1 - theta / (2 * MY_PI);

            float sum = B + G + R;
            if(sum == 0) S = 0;
            else S = 1 - 3 * min(min(B, G), R) / sum;

            I = sum/3.0;

            hsi.at<Vec3b>(i, j)[0] = H*255;
            hsi.at<Vec3b>(i, j)[1] = S*255;
            hsi.at<Vec3b>(i, j)[2] = I*255;
        }
    return hsi;
}

HSI转RGB代码

Mat HSI2RGB(const Mat & hsi){
    Mat rgb(hsi.rows, hsi.cols, hsi.type());
    float  R=0,G=0,B=0;
    for(int i=0; i < hsi.rows; i++)
        for(int j=0; j < hsi.cols; j++){
            float H = hsi.at<Vec3b>(i, j)[0] / 255.f * 2 * MY_PI,
                    S = hsi.at<Vec3b>(i, j)[1] / 255.f,
                    I = hsi.at<Vec3b>(i, j)[2] / 255.f;

            if(H < 120.f * MY_PI / 180.f){
                B=I*(1-S);
                R=I*(1+ S*cos(H)/cos(60.f* MY_PI / 180.f-H));
                G=3*I-R-B;
            }
            else if(H >= 120.f * MY_PI / 180.f && H < 240 * MY_PI / 180.f){
                H-=(120.f * MY_PI / 180.f);
                R=I*(1-S);
                G=I*(1+ S*cos(H)/cos(60.f* MY_PI / 180.f-H));
                B=3*I-R-G;
            }
            else if(H >= 240.f * MY_PI / 180.f){
                H-=(240.f * MY_PI / 180.f);
                G=I*(1-S);
                B=I*(1+ S*cos(H)/cos(60.f* MY_PI / 180.f-H));
                R=3*I-B-G;
            }
            
            rgb.at<Vec3b>(i, j)[0] = B*255;
            rgb.at<Vec3b>(i, j)[1] = G*255;
            rgb.at<Vec3b>(i, j)[2] = R*255;
        }
    return rgb;
}

示例

#include<iostream>
#include <opencv2/opencv.hpp>
#define MY_PI 3.1415
using namespace std;
using namespace cv;
Mat RGB2HSI(const Mat & rgb);
Mat HSI2RGB(const Mat & hsi);
int main(int argc, char * argv[]){
    Mat img = imread("../image/RGB.jpg");
    imshow("origin", img);
    waitKey();
    
    Mat hsi = RGB2HSI(img);
    imshow("hsi", hsi);
    waitKey();

    Mat rgb=HSI2RGB(hsi);
    imshow("rgb", rgb);
    waitKey();
    return 0;
}