基于二维伽马函数的光照不均匀图像自适应校正算法

前言

这是OpenCV图像处理专栏的第十二篇文章，今天为大家介绍一个用于解决光照不均匀的图像自适应校正算法。光照不均匀其实是非常常见的一种状况，为了提升人类的视觉感受或者是为了提升诸如深度学习之类的算法准确性，人们在解决光照不均衡方面已经有大量的工作。一起来看看这篇论文使用的算法吧，论文名为：《基于二维伽马函数的光照不均匀图像自适应校正算法》。

算法原理

论文使用了Retinex的多尺度高斯滤波求取「光照分量」，然后使用了二「维Gamma函数」针对原图的「HSV空间的V(亮度)分量」进行亮度改变，得到结果。原理还是蛮简单的，因为是中文论文，且作者介绍得很清楚，我就不细说了，可以自己看论文，论文地址见附录。本文的重点在于对算法步骤的解读和OpenCV复现。

需要注意的点
文中公式5(二维Gamma变换) 有误，公式5为：
其中$\gamma$的指数应该是$m-I(x,y)$，而不是$I(x,y)-m$，如果使用后者会得到错误结果，应该是作者笔误了。

C++代码

Mat RGB2HSV(Mat src) {
	int row = src.rows;
	int col = src.cols;
	Mat dst(row, col, CV_32FC3);
	for (int i = 0; i < row; i++) {
		for (int j = 0; j < col; j++) {
			float b = src.at<Vec3b>(i, j)[0] / 255.0;
			float g = src.at<Vec3b>(i, j)[1] / 255.0;
			float r = src.at<Vec3b>(i, j)[2] / 255.0;
			float minn = min(r, min(g, b));
			float maxx = max(r, max(g, b));
			dst.at<Vec3f>(i, j)[2] = maxx; //V
			float delta = maxx - minn;
			float h, s;
			if (maxx != 0) {
				s = delta / maxx;
			}
			else {
				s = 0;
			}
			if (r == maxx) {
				h = (g - b) / delta;
			}
			else if (g == maxx) {
				h = 2 + (b - r) / delta;
			}
			else {
				h = 4 + (r - g) / delta;
			}
			h *= 60;
			if (h < 0)
				h += 360;
			dst.at<Vec3f>(i, j)[0] = h;
			dst.at<Vec3f>(i, j)[1] = s;
		}
	}
	return dst;
}

Mat HSV2RGB(Mat src) {
	int row = src.rows;
	int col = src.cols;
	Mat dst(row, col, CV_8UC3);
	float r, g, b, h, s, v;
	for (int i = 0; i < row; i++) {
		for (int j = 0; j < col; j++) {
			h = src.at<Vec3f>(i, j)[0];
			s = src.at<Vec3f>(i, j)[1];
			v = src.at<Vec3f>(i, j)[2];
			if (s == 0) {
				r = g = b = v;
			}
			else {
				h /= 60;
				int offset = floor(h);
				float f = h - offset;
				float p = v * (1 - s);
				float q = v * (1 - s * f);
				float t = v * (1 - s * (1 - f));
				switch (offset)
				{
				case 0: r = v; g = t; b = p; break;
				case 1: r = q; g = v; b = p; break;
				case 2: r = p; g = v; b = t; break;
				case 3: r = p; g = q; b = v; break;
				case 4: r = t; g = p; b = v; break;
				case 5: r = v; g = p; b = q; break;
				default:
					break;
				}
			}
			dst.at<Vec3b>(i, j)[0] = int(b * 255);
			dst.at<Vec3b>(i, j)[1] = int(g * 255);
			dst.at<Vec3b>(i, j)[2] = int(r * 255);
		}
	}
	return dst;
}

Mat work(Mat src) {
	int row = src.rows;
	int col = src.cols;
	Mat now = RGB2HSV(src);
	Mat H(row, col, CV_32FC1);
	Mat S(row, col, CV_32FC1);
	Mat V(row, col, CV_32FC1);
	for (int i = 0; i < row; i++) {
		for (int j = 0; j < col; j++) {
			H.at<float>(i, j) = now.at<Vec3f>(i, j)[0];
			S.at<float>(i, j) = now.at<Vec3f>(i, j)[1];
			V.at<float>(i, j) = now.at<Vec3f>(i, j)[2];
		}
	}
	int kernel_size = min(row, col);
	if (kernel_size % 2 == 0) {
		kernel_size -= 1;
	}
	float SIGMA1 = 15;
	float SIGMA2 = 80;
	float SIGMA3 = 250;
	float q = sqrt(2.0);
	Mat F(row, col, CV_32FC1);
	Mat F1, F2, F3;
	GaussianBlur(V, F1, Size(kernel_size, kernel_size), SIGMA1 / q);
	GaussianBlur(V, F2, Size(kernel_size, kernel_size), SIGMA2 / q);
	GaussianBlur(V, F3, Size(kernel_size, kernel_size), SIGMA3 / q);
	for (int i = 0; i < row; i++) {
		for (int j = 0; j < col; j++) {
			F.at <float>(i, j) = (F1.at<float>(i, j) + F2.at<float>(i, j) + F3.at<float>(i, j)) / 3.0;
		}
	}
	float average = mean(F)[0];
	Mat out(row, col, CV_32FC1);
	for (int i = 0; i < row; i++) {
		for (int j = 0; j < col; j++) {
			float gamma = powf(0.5, (average - F.at<float>(i, j)) / average);
			out.at<float>(i, j) = powf(V.at<float>(i, j), gamma);
		}
	}
	vector <Mat> v;
	v.push_back(H);
	v.push_back(S);
	v.push_back(out);
	Mat merge_;
	merge(v, merge_);
	Mat dst = HSV2RGB(merge_);
	return dst;
}

效果

论文出处：https://wenku.baidu.com/view/3570f2c255270722182ef74e.html