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C++ OpenCV 图像双三次插值算法 C++OpenCV实现图像双三次插值算法详解

怎么今天你又不开心了呢   2021-12-02 我要评论
想了解C++OpenCV实现图像双三次插值算法详解的相关内容吗怎么今天你又不开心了呢在本文为您仔细讲解C++OpenCV图像双三次插值算法的相关知识和一些Code实例欢迎阅读和指正我们先划重点:OpenCV图像双三次插值算法,C++OpenCV图像双三次插值算法下面大家一起来学习吧。

前言

近期在学习一些传统的图像处理算法比如传统的图像插值算法等。传统的图像插值算法包括邻近插值法、双线性插值法和双三次插值法其中邻近插值法和双线性插值法在网上都有很详细的介绍以及用c++编写的代码。但是网上关于双三次插值法的原理介绍虽然很多也有对应的代码但是大多都不是很详细。因此基于自己对原理的理解自己编写了图像双三次插值算法的c++ opencv代码在这里记录一下。

一、图像双三次插值算法原理

首先是原理部分。图像双三次插值的原理就是目标图像的每一个像素都是由原图上相对应点周围的4x4=16个像素经过加权之后再相加得到的。这里的加权用到的就是三次函数这也是图像双三次插值算法名称的由来(个人猜测)。用到的三次函数如下图所示:

最关键的问题是这个三次函数的输入和输出分别代表啥。简单来说输入就是原图对应点周围相对于这点的4x4大小区域的坐标值大小在0~2之间输出就是这些点横坐标或者纵坐标的权重。4个横坐标、4个纵坐标对应相乘就是4x4大小的权重矩阵然后使用此权重矩阵对原图相对应的区域进行相乘并相加就可以得到目标图点的像素。

下图可以帮助大家更好地理解

首先u和v是什么呢?举一个例子对于一幅100x100的灰度图像要将其放大到500x500那么其缩放因子sx=500/100=5sy=500/100=5。现在目标图像是500x500需要用原图的100x100个像素值来填满这500x500个空根据src_x=i/sx和src_y=j/sy可以得到目标像素坐标(ij)所对应的原图像素坐标(src_x, src_y)这个src_x和src_y的小数部分就是上图中的u和v。

理解了u和v就可以利用u和v来计算双三次插值算法的权重了。上面说了三次函数的输入是原图对应点周围相对于这点的4x4大小区域的坐标值对于上面这幅图而言横坐标有四个输入分别是1+uu1-u2-u;纵坐标也有四个输入分别是1+vv1-v2-v根据三次函数算出权重之后两两相乘就是对应的4x4大小的权重矩阵。

知道了怎么求权重矩阵之后就可以遍历整幅图像进行插值了。下面是基于自己对原理的理解编写的c++ opencv代码代码没有做优化但是能够让大家直观地理解图像双三次插值算法。

二、C++ OpenCV代码

1.计算权重矩阵

前面说了权重矩阵就是横坐标的4个输出和纵坐标的4个输出相乘因此只需要求出横坐标和纵坐标相对应的8个输出值就行了。

代码如下:

std::vector<double> getWeight(double c, double a = 0.5)
{
	//c就是u和v横坐标和纵坐标的输出计算方式一样
	std::vector<double> temp(4);
	temp[0] = 1 + c; temp[1] = c; 
	temp[2] = 1 - c; temp[3] = 2 - c;
	
	//y(x) = (a+2)|x|*|x|*|x| - (a+3)|x|*|x| + 1   |x|<=1
	//y(x) = a|x|*|x|*|x| - 5a|x|*|x| + 8a|x| - 4a  1<|x|<2
	std::vector<double> weight(4);
	weight[0] = (a * pow(abs(temp[0]), 3) - 5 * a * pow(abs(temp[0]), 2) + 8 * a * abs(temp[0]) - 4 * a);
	weight[1] = (a + 2) * pow(abs(temp[1]), 3) - (a + 3) * pow(abs(temp[1]), 2) + 1;
	weight[2] = (a + 2) * pow(abs(temp[2]), 3) - (a + 3) * pow(abs(temp[2]), 2) + 1;
	weight[3] = (a * pow(abs(temp[3]), 3) - 5 * a * pow(abs(temp[3]), 2) + 8 * a * abs(temp[3]) - 4 * a);

	return weight;
}

2.遍历插值

代码如下:

void bicubic(cv::Mat& src, cv::Mat& dst, int dst_rows, int dst_cols)
{
	dst.create(dst_rows, dst_cols, src.type());
	double sy = static_cast<double>(dst_rows) / static_cast<double>(src.rows);
	double sx = static_cast<double>(dst_cols) / static_cast<double>(src.cols);
	cv::Mat border;
	cv::copyMakeBorder(src, border, 1, 1, 1, 1, cv::BORDER_REFLECT_101);

	//处理灰度图
	if (src.channels() == 1)
	{
		for (int i = 1; i < dst_rows + 1; ++i)
		{
			int src_y = (i + 0.5) / sy - 0.5; //做了几何中心对齐
			if (src_y < 0) src_y = 0;
			if (src_y > src.rows - 1) src_y = src.rows - 1;
			src_y += 1;
			//目标图像点坐标对应原图点坐标的4个纵坐标
			int i1 = std::floor(src_y);
			int i2 = std::ceil(src_y);
			int i0 = i1 - 1;
			int i3 = i2 + 1;
			double u = src_y - static_cast<int64>(i1);
			std::vector<double> weight_x = getWeight(u);

			for (int j = 1; j < dst_cols + 1; ++j)
			{
				int src_x = (j + 0.5) / sy - 0.5;
				if (src_x < 0) src_x = 0;
				if (src_x > src.rows - 1) src_x = src.rows - 1;
				src_x += 1;
				//目标图像点坐标对应原图点坐标的4个横坐标
				int j1 = std::floor(src_x);
				int j2 = std::ceil(src_x);
				int j0 = j1 - 1;
				int j3 = j2 + 1;
				double v = src_x - static_cast<int64>(j1);
				std::vector<double> weight_y = getWeight(v);

				//目标点像素对应原图点像素周围4x4区域的加权计算(插值)
				double pix = weight_x[0] * weight_y[0] * border.at<uchar>(i0, j0) + weight_x[1] * weight_y[0] * border.at<uchar>(i0, j1)
					+ weight_x[2] * weight_y[0] * border.at<uchar>(i0, j2) + weight_x[3] * weight_y[0] * border.at<uchar>(i0, j3)
					+ weight_x[0] * weight_y[1] * border.at<uchar>(i1, j0) + weight_x[1] * weight_y[1] * border.at<uchar>(i1, j1)
					+ weight_x[2] * weight_y[1] * border.at<uchar>(i1, j2) + weight_x[3] * weight_y[1] * border.at<uchar>(i1, j3)
					+ weight_x[0] * weight_y[2] * border.at<uchar>(i2, j0) + weight_x[1] * weight_y[2] * border.at<uchar>(i2, j1)
					+ weight_x[2] * weight_y[2] * border.at<uchar>(i2, j2) + weight_x[3] * weight_y[2] * border.at<uchar>(i2, j3)
					+ weight_x[0] * weight_y[3] * border.at<uchar>(i3, j0) + weight_x[1] * weight_y[3] * border.at<uchar>(i3, j1)
					+ weight_x[2] * weight_y[3] * border.at<uchar>(i3, j2) + weight_x[3] * weight_y[3] * border.at<uchar>(i3, j3);
				if (pix < 0) pix = 0;
				if (pix > 255)pix = 255;

				dst.at<uchar>(i - 1, j - 1) = static_cast<uchar>(pix);
			}
		}
	}
	//处理彩色图像
	else if (src.channels() == 3)
	{
		for (int i = 1; i < dst_rows + 1; ++i)
		{
			int src_y = (i + 0.5) / sy - 0.5;
			if (src_y < 0) src_y = 0;
			if (src_y > src.rows - 1) src_y = src.rows - 1;
			src_y += 1;
			int i1 = std::floor(src_y);
			int i2 = std::ceil(src_y);
			int i0 = i1 - 1;
			int i3 = i2 + 1;
			double u = src_y - static_cast<int64>(i1);
			std::vector<double> weight_y = getWeight(u);

			for (int j = 1; j < dst_cols + 1; ++j)
			{
				int src_x = (j + 0.5) / sy - 0.5;
				if (src_x < 0) src_x = 0;
				if (src_x > src.rows - 1) src_x = src.rows - 1;
				src_x += 1;
				int j1 = std::floor(src_x);
				int j2 = std::ceil(src_x);
				int j0 = j1 - 1;
				int j3 = j2 + 1;
				double v = src_x - static_cast<int64>(j1);
				std::vector<double> weight_x = getWeight(v);

				cv::Vec3b pix;

				pix[0] = weight_x[0] * weight_y[0] * border.at<cv::Vec3b>(i0, j0)[0] + weight_x[1] * weight_y[0] * border.at<cv::Vec3b>(i0, j1)[0]
					+ weight_x[2] * weight_y[0] * border.at<cv::Vec3b>(i0, j2)[0] + weight_x[3] * weight_y[0] * border.at<cv::Vec3b>(i0, j3)[0]
					+ weight_x[0] * weight_y[1] * border.at<cv::Vec3b>(i1, j0)[0] + weight_x[1] * weight_y[1] * border.at<cv::Vec3b>(i1, j1)[0]
					+ weight_x[2] * weight_y[1] * border.at<cv::Vec3b>(i1, j2)[0] + weight_x[3] * weight_y[1] * border.at<cv::Vec3b>(i1, j3)[0]
					+ weight_x[0] * weight_y[2] * border.at<cv::Vec3b>(i2, j0)[0] + weight_x[1] * weight_y[2] * border.at<cv::Vec3b>(i2, j1)[0]
					+ weight_x[2] * weight_y[2] * border.at<cv::Vec3b>(i2, j2)[0] + weight_x[3] * weight_y[2] * border.at<cv::Vec3b>(i2, j3)[0]
					+ weight_x[0] * weight_y[3] * border.at<cv::Vec3b>(i3, j0)[0] + weight_x[1] * weight_y[3] * border.at<cv::Vec3b>(i3, j1)[0]
					+ weight_x[2] * weight_y[3] * border.at<cv::Vec3b>(i3, j2)[0] + weight_x[3] * weight_y[3] * border.at<cv::Vec3b>(i3, j3)[0];
				pix[1] = weight_x[0] * weight_y[0] * border.at<cv::Vec3b>(i0, j0)[1] + weight_x[1] * weight_y[0] * border.at<cv::Vec3b>(i0, j1)[1]
					+ weight_x[2] * weight_y[0] * border.at<cv::Vec3b>(i0, j2)[1] + weight_x[3] * weight_y[0] * border.at<cv::Vec3b>(i0, j3)[1]
					+ weight_x[0] * weight_y[1] * border.at<cv::Vec3b>(i1, j0)[1] + weight_x[1] * weight_y[1] * border.at<cv::Vec3b>(i1, j1)[1]
					+ weight_x[2] * weight_y[1] * border.at<cv::Vec3b>(i1, j2)[1] + weight_x[3] * weight_y[1] * border.at<cv::Vec3b>(i1, j3)[1]
					+ weight_x[0] * weight_y[2] * border.at<cv::Vec3b>(i2, j0)[1] + weight_x[1] * weight_y[2] * border.at<cv::Vec3b>(i2, j1)[1]
					+ weight_x[2] * weight_y[2] * border.at<cv::Vec3b>(i2, j2)[1] + weight_x[3] * weight_y[2] * border.at<cv::Vec3b>(i2, j3)[1]
					+ weight_x[0] * weight_y[3] * border.at<cv::Vec3b>(i3, j0)[1] + weight_x[1] * weight_y[3] * border.at<cv::Vec3b>(i3, j1)[1]
					+ weight_x[2] * weight_y[3] * border.at<cv::Vec3b>(i3, j2)[1] + weight_x[3] * weight_y[3] * border.at<cv::Vec3b>(i3, j3)[1];
				pix[2] = weight_x[0] * weight_y[0] * border.at<cv::Vec3b>(i0, j0)[2] + weight_x[1] * weight_y[0] * border.at<cv::Vec3b>(i0, j1)[2]
					+ weight_x[2] * weight_y[0] * border.at<cv::Vec3b>(i0, j2)[2] + weight_x[3] * weight_y[0] * border.at<cv::Vec3b>(i0, j3)[2]
					+ weight_x[0] * weight_y[1] * border.at<cv::Vec3b>(i1, j0)[2] + weight_x[1] * weight_y[1] * border.at<cv::Vec3b>(i1, j1)[2]
					+ weight_x[2] * weight_y[1] * border.at<cv::Vec3b>(i1, j2)[2] + weight_x[3] * weight_y[1] * border.at<cv::Vec3b>(i1, j3)[2]
					+ weight_x[0] * weight_y[2] * border.at<cv::Vec3b>(i2, j0)[2] + weight_x[1] * weight_y[2] * border.at<cv::Vec3b>(i2, j1)[2]
					+ weight_x[2] * weight_y[2] * border.at<cv::Vec3b>(i2, j2)[2] + weight_x[3] * weight_y[2] * border.at<cv::Vec3b>(i2, j3)[2]
					+ weight_x[0] * weight_y[3] * border.at<cv::Vec3b>(i3, j0)[2] + weight_x[1] * weight_y[3] * border.at<cv::Vec3b>(i3, j1)[2]
					+ weight_x[2] * weight_y[3] * border.at<cv::Vec3b>(i3, j2)[2] + weight_x[3] * weight_y[3] * border.at<cv::Vec3b>(i3, j3)[2];

				for (int i = 0; i < src.channels(); ++i)
				{
					if (pix[i] < 0) pix = 0;
					if (pix[i] > 255)pix = 255;
				}
				dst.at<cv::Vec3b>(i - 1, j - 1) = static_cast<cv::Vec3b>(pix);
			}
		}	
	}	
}

3. 测试及结果

int main()
{
	cv::Mat src = cv::imread("C:\\Users\\Echo\\Pictures\\Saved Pictures\\bilateral.png");
	cv::Mat dst;
	bicubic(src, dst, 309/0.5, 338/0.5);
	cv::imshow("gray", dst);
	cv::imshow("src", src);
	cv::waitKey(0);
}

彩色图像(放大两倍)


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