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

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

HSI转RGB

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

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0else 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;
}