双线性插值运算实现

﹏ヽ暗。殇╰゛Y 2022-03-01 20:52 282阅读 0赞

一、原理

双线性插值  
在数学上，双线性插值是有两个变量的插值函数的线性插值扩展，其核心思想是在两个方向分别进行一次线性插值\[1\]。见下图：

![è¿éåå¾çæè¿°][SouthEast]

假如我们想得到未知函数 f 在点 P = (x, y) 的值，假设我们已知函数 f 在 Q11 = (x1, y1)、Q12 = (x1, y2), Q21 = (x2, y1) 以及 Q22 = (x2, y2) 四个点的值。最常见的情况，f就是一个像素点的像素值。首先在 x 方向进行线性插值，得到

![SouthEast 1][]

![è¿éåå¾çæè¿°][SouthEast 2]  
然后在 y 方向进行线性插值，得到

![è¿éåå¾çæè¿°][SouthEast 3]

综合起来就是双线性插值最后的结果：

![è¿éåå¾çæè¿°][SouthEast 4]![SouthEast 5][]  
由于图像双线性插值只会用相邻的4个点，因此上述公式的分母都是1。opencv中的源码如下，用了一些优化手段，比如用整数计算代替float（下面代码中的\*2048就是变11位小数为整数，最后有两个连乘，因此>>22位），以及源图像和目标图像几何中心的对齐   
SrcX=(dstX+0.5)\* (srcWidth/dstWidth) -0.5   
SrcY=(dstY+0.5) \* (srcHeight/dstHeight)-0.5，

二、C++代码

uchar InterBilinear(float x,float y,cv::Mat &src)
    {
    	int x_L = cvFloor(x) - 1;
    	int x_R = cvFloor(x) + 1;
    	int y_T = cvFloor(y) - 1;
    	int y_B = cvFloor(y) + 1;
    
    	if (x_L <= 0) x_L = 0;
    	else if (x_L >= src.cols - 1) x_L = src.cols - 1;
    	if (x_R <= 0) x_R = 0;
    	else if (x_R > src.cols - 1) x_R = src.cols - 1;
    		
    	if (y_T <= 0) y_T = 0;
    	else if (y_T > src.rows - 1) y_T = src.rows - 1;
    	if (y_B <= 0) y_B = 0;
    	else if (y_B > src.rows - 1) y_B = src.rows - 1;
    
    	uchar grayTopL = src.at<uchar>(x_L, y_T);//左上角
    	uchar grayTopR = src.at<uchar>(x_R, y_T);//右上角
    	uchar grayBottonL = src.at<uchar>(x_L, y_B);//左下角
    	uchar grayBottonR = src.at<uchar>(x_R, y_B);//右下角
    	//1、计算X方向插值
    	float HLscale = 0.f, HRscale = 0.f, VTscale = 0.f, VBscale=0.f;
    	HLscale = 1 - (x - x_L) / (x_R - x_L);
    	HRscale = 1 - (x_R - x) / (x_R - x_L);
    	VTscale = 1 - (y - y_T) / (y_B - y_T);
    	VBscale = 1 - (y_B-y) / (y_B - y_T);
    	uchar Hpixel1= static_cast<uchar>(grayTopL*HLscale + grayTopR*HRscale);
    	uchar Hpixel2 = static_cast<uchar>(grayBottonL*HLscale + grayBottonR*HRscale);
    	//计算Y方向插值
    	uchar Vpixel = static_cast<uchar>(Hpixel1*VTscale + Hpixel2*VBscale);
    	return Vpixel;
    }
    
    void ImageZoom(cv::Mat &srcimg, cv::Mat &dst, float scale)
    {
    	cv::Mat resultimg, grayimg;
    	if (scale <= 1e-6)
    	{
    		cout << "Illegal Parameter!" << endl;
    		return;
    	}
    	if (!srcimg.data)
    	{
    		cout << "Image Is Null!" << endl;
    		return;
    	}
    	
    	grayimg = srcimg.clone();
    	int new_width = static_cast<int>(scale*srcimg.cols);
    	int new_height = static_cast<int>(scale*srcimg.rows);
    	getgrayMat(grayimg);
    	resultimg.create(cv::Size(new_width, new_height), grayimg.depth());
    	for (int i0 = 0; i0 < new_height; i0++)
    	{
    		for (int j0 = 0; j0 < new_width; j0++)
    		{
    				float j1 = (j0+0.1f) / scale;
    				float i1 = (i0+0.1f )/ scale;
    				if (j1 <= 1e-6)
    					j1 = 0.f;
    				if (i1 <= 1e-6)
    					i1 = 0.f;
    				uchar Interval=InterBilinear(i1, j1, grayimg);
    				resultimg.at<uchar>(i0, j0) = Interval;
    		}
    	}
    	dst = resultimg.clone();
    	resultimg.release();
    }

[SouthEast]: /images/20220302/92724e708c1940e7aa8a3734e28478d2.png
[SouthEast 1]: /images/20220302/9f7dcd32ee2e471187c842971dcf8614.png
[SouthEast 2]: /images/20220302/1258b64b541b45af939ff024e193396f.png
[SouthEast 3]: /images/20220302/3408fdf57a4d4114bc4da88c3ef156ee.png
[SouthEast 4]: https://img-blog.csdn.net/20170324225222878?watermark/2/text/aHR0cDovL2Jsb2cuY3Nkbi5uZXQveGJpbndvcmxk/font/5a6L5L2T/fontsize/400/fill/I0JBQkFCMA==/dissolve/70/gravity/SouthEast
[SouthEast 5]: /images/20220302/eea144a9cb92447f88d5838a504c21ec.png