数字图像的缩放及opencv中的实现

比眉伴天荒 2022-06-12 06:19 278阅读 0赞

**1. 数字图像的缩放**

常用的数字图像的缩放的方式有最近邻插值、双线性插值、双三次插值。

最近邻插值就是把目标图像的像素点映射到原图像中，那个像素离得最近，就把目标图像中的像素值取为该点的值。

双线性插值是指考虑两个方向（X & Y），四个像素点来计算目标图像中的像素值。和最近邻相比，每个双线性不仅考虑了两个方向，并且每个方向上考虑了目标像素与原像素点的距离的加权。双线性内插法的计算比最邻近点法复杂，计算量较大，但没有灰度不连续的缺点，结果基本令人满意。它具有低通滤波性质，使高频分量受损，图像轮廓可能会有一点模糊。

关于最近邻和双线性插值的原理可以参考下面两篇博客，里面的讲解通俗易懂。

[http://blog.csdn.net/andrew659/article/details/4818988][http_blog.csdn.net_andrew659_article_details_4818988]

[http://blog.csdn.net/qq\_20823641/article/details/52221442][http_blog.csdn.net_qq_20823641_article_details_52221442]

双三次插值则可以看成是考虑了更大范围(16“邻域”)的一种加权来计算目标像素点的像素值。相比双线性计算量更大了，当然也取得了更平滑的边缘。

**2.opencv中图像缩放API**

opencv中提供了resize()来对图像进行缩放。但是其提供了五种插值方式供选择，除了刚刚提到的三种还有INTER\_AERE（区域插值）和INTER\_LANCZOS4（兰索斯插值）。下面是官方文档。根据官方文档，对于缩小图像，一般情况下最好用CV\_INTER\_AREA，而对于放大图像，一般情况下最好用CV\_INTER\_CUBIC（效率不高，慢） 或 CV\_INTER\_LINEAR（效率较高，速度较快）。

C++: void resize(InputArray src, OutputArray dst, Size dsize, double fx=0, double fy=0, intinterpolation=INTER\_LINEAR )

<table style="border-collapse:collapse; margin:20px -.5em 10px; border:0px; color:rgb(0,0,0); font-family:'Open Sans','Lucida Grande','Lucida Sans Unicode',Geneva,Verdana,sans-serif; font-size:14px; line-height:18.2px; text-align:justify"> 
 <tbody> 
 <tr> 
 <th style="text-align:left; padding:1px 8px 1px 5px; border:0px!important"> Parameters:</th> 
 <td style="padding:1px 8px 1px 5px; text-align:left; border:0px!important"> 
 <ul style="margin:0px; padding-left:1em"> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">src&nbsp;– input image.</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">dst&nbsp;– output image; it has the size&nbsp;dsize&nbsp;(when it is non-zero) or the size computed fromsrc.size(),&nbsp;fx, and&nbsp;fy; the type of&nbsp;dst&nbsp;is the same as of&nbsp;src.</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">dsize&nbsp;– output image size; if it equals zero, it is computed as: 
 <div> 
 <img src="http://docs.opencv.org/3.0-beta/_images/math/35ed0468ed221de8a5f35516bceafda9788cd015.png" alt="\texttt{dsize = Size(round(fx*src.cols), round(fy*src.rows))}" style="border:0px"> 
 </div> Either&nbsp;dsize&nbsp;or both&nbsp;fx&nbsp;and&nbsp;fy&nbsp;must be non-zero. </li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">fx&nbsp;– scale factor along the horizontal axis; when it equals 0, it is computed as 
 <div> 
 <img src="http://docs.opencv.org/3.0-beta/_images/math/68bc15bc90b1ec313d34f5d72485fa04c51f5c3e.png" alt="\texttt{(double)dsize.width/src.cols}" style="border:0px"> 
 </div> </li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">fy&nbsp;– scale factor along the vertical axis; when it equals 0, it is computed as 
 <div> 
 <img src="http://docs.opencv.org/3.0-beta/_images/math/af495c626474d56d29d356d581a18f143109e972.png" alt="\texttt{(double)dsize.height/src.rows}" style="border:0px"> 
 </div> </li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">interpolation&nbsp;– interpolation method: 
 <ul style="margin:0px; padding-left:1em"> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">INTER_NEAREST&nbsp;- a nearest-neighbor interpolation</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">INTER_LINEAR&nbsp;- a bilinear interpolation (used by default)</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">INTER_AREA&nbsp;- resampling using pixel area relation. It may be a preferred method for image decimation, as it gives moire’-free results. But when the image is zoomed, it is similar to theINTER_NEAREST&nbsp;method.</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">INTER_CUBIC&nbsp;- a bicubic interpolation over 4x4 pixel neighborhood</li> 
 <li style="text-align:justify; line-height:18.2px; margin:0px">INTER_LANCZOS4&nbsp;- a Lanczos interpolation over 8x8 pixel neighborhood</li> 
 </ul> </li> 
 </ul> </td> 
 </tr> 
 </tbody> 
</table>

fx & fy默认值为0，interpolation 默认值为1（INTER\_LINEAR），INTER\_NEAREST==0，INTER\_CUBIC==2, INTER\_AREA==3，INTER\_LANCZOS4==4

下面用for循环代替cv::resize函数来说明其详细的插值实现过程，其中部分代码摘自于cv::resize函数中的源代码。

每种插值算法的前部分代码是相同的，如下：

cv::Mat matSrc, matDst1, matDst2;  
      
    matSrc = cv::imread("lena.jpg", 2 | 4);  //载入无损的源图像
    matDst1 = cv::Mat(cv::Size(800, 1000), matSrc.type(), cv::Scalar::all(0));  
    matDst2 = cv::Mat(matDst1.size(), matSrc.type(), cv::Scalar::all(0));  
      
    double scale_x = (double)matSrc.cols / matDst1.cols;//x方向的缩放因子  
    double scale_y = (double)matSrc.rows / matDst1.rows;//y方向的缩放因子

2.1、最近邻：公式，

![20131215165908937][]

for (int i = 0; i < matDst1.cols; ++i)//以目标图像为基准，映射到源图像中 
 { 
 int sx = cvFloor(i * scale_x); //向下取整
 sx = std::min(sx, matSrc.cols - 1); //防止超出源图像的边界
 for (int j = 0; j < matDst1.rows; ++j) 
 { 
 int sy = cvFloor(j * scale_y); 
 sy = std::min(sy, matSrc.rows - 1); //防止超出源图像的边界 
 matDst1.at<cv::Vec3b>(j, i) = matSrc.at<cv::Vec3b>(sy, sx); 
 } 
 } 
 cv::imwrite("nearest_1.jpg", matDst1); 
 
 cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 0); 
 cv::imwrite("nearest_2.jpg", matDst2);

2.2、双线性：由相邻的四像素(2\*2)计算得出，公式，

![20131215170323218][]

char* dataDst = matDst1.data; 
 int stepDst = matDst1.step;//每一行像素数据所占的字节数 
 uchar* dataSrc = matSrc.data; 
 int stepSrc = matSrc.step; 
 int iWidthSrc = matSrc.cols; 
 int iHiehgtSrc = matSrc.rows; 
 
 for (int j = 0; j < matDst1.rows; ++j) 
 { 
 float fy = (float)((j + 0.5) * scale_y - 0.5); 
 int sy = cvFloor(fy); //sy为fy的整数部分（向下取整）
 fy -= sy; //fy更新为fy的小数部分
 sy = std::min(sy, iHeihgtSrc - 2); //防止sy越上界
 sy = std::max(0, sy); //防止sy越下界
 
 short cbufy[2]; 
 cbufy[0] = cv::saturate_cast<short>((1.f - fy) * 2048); 
 cbufy[1] = 2048 - cbufy[0]; 
 
 for (int i = 0; i < matDst1.cols; ++i) 
 { 
 float fx = (float)((i + 0.5) * scale_x - 0.5); 
 int sx = cvFloor(fx);//sx为fx的整数部分（向下取整） 
 fx -= sx;//fx更新为fx的小数部分 
 
 if (sx < 0) { 
 fx = 0, sx = 0; 
 } 
 if (sx >= iWidthSrc - 1) { 
 fx = 0, sx = iWidthSrc - 2; 
 } 
 
 short cbufx[2]; 
 cbufx[0] = cv::saturate_cast<short>((1.f - fx) * 2048); 
 cbufx[1] = 2048 - cbufx[0]; 
 
 //由于cbufx[0]和cbufy[1]都放大了2048（2^11）倍，这里右移是为了还原，
 		//这样先乘后右移的操作在图像处理中很常见，主要是为了简化计算 
 		for (int k = 0; k < matSrc.channels(); ++k) 
 { 
 *(dataDst+ j*stepDst + 3*i + k) = (*(dataSrc + sy*stepSrc + 3*sx + k) * cbufx[0] * cbufy[0] + 
 *(dataSrc + (sy+1)*stepSrc + 3*sx + k) * cbufx[0] * cbufy[1] + 
 *(dataSrc + sy*stepSrc + 3*(sx+1) + k) * cbufx[1] * cbufy[0] + 
 *(dataSrc + (sy+1)*stepSrc + 3*(sx+1) + k) * cbufx[1] * cbufy[1]) >> 22; 
 } 
 } 
 } 
 cv::imwrite("linear_1.jpg", matDst1); 
 
 cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 1); //调用resize()中的双线性插值
 cv::imwrite("linear_2.jpg", matDst2);

2.3 双三次

![这里写图片描述][20161009182301788]

下面的代码中a取-0.75

2.4 基于像素区域关系：共分三种情况，图像放大时类似于最近邻插值，图像缩小(x轴、y轴同时缩小)又分两种情况，此情况下可以避免波纹出现。

看了[fengbingchun][]的博客，但是感觉这一段有问题，等什么时候自己把源代码翻出来看看吧

2.5  兰索斯插值：由相邻的8\*8像素计算得出，公式类似于双线性

int iscale_x = cv::saturate_cast<int>(scale_x); 
 int iscale_y = cv::saturate_cast<int>(scale_y); 
 
 for (int j = 0; j < matDst1.rows; ++j) 
 { 
 float fy = (float)((j + 0.5) * scale_y - 0.5); 
 int sy = cvFloor(fy); 
 fy -= sy; 
 sy = std::min(sy, matSrc.rows - 5); 
 sy = std::max(3, sy); 
 
 const double s45 = 0.70710678118654752440084436210485; 
 const double cs[][2] = {
 {1, 0}, {-s45, -s45}, {0, 1}, {s45, -s45}, {-1, 0}, {s45, s45}, {0, -1}, {-s45, s45}}; 
 float coeffsY[8]; 
 
 if (fy < FLT_EPSILON) 
 	{ 
 for (int t = 0; t < 8; t++) 
 coeffsY[t] = 0; 
 coeffsY[3] = 1; 
 } 
 	else 
 	{ 
 float sum = 0; 
 double y0 = -(fy + 3) * CV_PI * 0.25, s0 = sin(y0), c0 = cos(y0); 
 
 for (int t = 0; t < 8; ++t) 
 { 
 double dy = -(fy + 3 -t) * CV_PI * 0.25; 
 coeffsY[t] = (float)((cs[t][0] * s0 + cs[t][1] * c0) / (dy * dy)); 
 sum += coeffsY[t]; 
 } 
 
 sum = 1.f / sum; 
 for (int t = 0; t < 8; ++t) 
 coeffsY[t] *= sum; 
 } 
 
 short cbufY[8]; 
 cbufY[0] = cv::saturate_cast<short>(coeffsY[0] * 2048); 
 cbufY[1] = cv::saturate_cast<short>(coeffsY[1] * 2048); 
 cbufY[2] = cv::saturate_cast<short>(coeffsY[2] * 2048); 
 cbufY[3] = cv::saturate_cast<short>(coeffsY[3] * 2048); 
 cbufY[4] = cv::saturate_cast<short>(coeffsY[4] * 2048); 
 cbufY[5] = cv::saturate_cast<short>(coeffsY[5] * 2048); 
 cbufY[6] = cv::saturate_cast<short>(coeffsY[6] * 2048); 
 cbufY[7] = cv::saturate_cast<short>(coeffsY[7] * 2048); 
 
 for (int i = 0; i < matDst1.cols; ++i) 
 { 
 float fx = (float)((i + 0.5) * scale_x - 0.5); 
 int sx = cvFloor(fx); 
 fx -= sx; 
 
 if (sx < 3)
 		{ 
 fx = 0, sx = 3; 
 } 
 if (sx >= matSrc.cols - 5) 
 		{ 
 fx = 0, sx = matSrc.cols - 5; 
 } 
 
 float coeffsX[8]; 
 
 if (fx < FLT_EPSILON) 
 		{ 
 for ( int t = 0; t < 8; t++ ) 
 coeffsX[t] = 0; 
 coeffsX[3] = 1; 
 } 
 		else 
 		{ 
 float sum = 0; 
 double x0 = -(fx + 3) * CV_PI * 0.25, s0 = sin(x0), c0 = cos(x0); 
 
 for (int t = 0; t < 8; ++t) 
 { 
 double dx = -(fx + 3 -t) * CV_PI * 0.25; 
 coeffsX[t] = (float)((cs[t][0] * s0 + cs[t][1] * c0) / (dx * dx)); 
 sum += coeffsX[t]; 
 } 
 
 sum = 1.f / sum; 
 for (int t = 0; t < 8; ++t) 
 coeffsX[t] *= sum; 
 } 
 
 short cbufX[8]; 
 cbufX[0] = cv::saturate_cast<short>(coeffsX[0] * 2048); 
 cbufX[1] = cv::saturate_cast<short>(coeffsX[1] * 2048); 
 cbufX[2] = cv::saturate_cast<short>(coeffsX[2] * 2048); 
 cbufX[3] = cv::saturate_cast<short>(coeffsX[3] * 2048); 
 cbufX[4] = cv::saturate_cast<short>(coeffsX[4] * 2048); 
 cbufX[5] = cv::saturate_cast<short>(coeffsX[5] * 2048); 
 cbufX[6] = cv::saturate_cast<short>(coeffsX[6] * 2048); 
 cbufX[7] = cv::saturate_cast<short>(coeffsX[7] * 2048); 
 
 for (int k = 0; k < matSrc.channels(); ++k) 
 { 
 matDst1.at<cv::Vec3b>(j, i)[k] = abs((matSrc.at<cv::Vec3b>(sy-3, sx-3)[k] * cbufX[0] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-3)[k] * cbufX[0] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx-3)[k] * cbufX[0] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-3)[k] * cbufX[0] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx-3)[k] * cbufX[0] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-3)[k] * cbufX[0] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx-3)[k] * cbufX[0] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-3)[k] * cbufX[0] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx-2)[k] * cbufX[1] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-2)[k] * cbufX[1] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx-2)[k] * cbufX[1] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-2)[k] * cbufX[1] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx-2)[k] * cbufX[1] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-2)[k] * cbufX[1] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx-2)[k] * cbufX[1] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-2)[k] * cbufX[1] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx-1)[k] * cbufX[2] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx-1)[k] * cbufX[2] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx-1)[k] * cbufX[2] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx-1)[k] * cbufX[2] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx-1)[k] * cbufX[2] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx-1)[k] * cbufX[2] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx-1)[k] * cbufX[2] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx-1)[k] * cbufX[2] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx)[k] * cbufX[3] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx)[k] * cbufX[3] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx)[k] * cbufX[3] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx)[k] * cbufX[3] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx)[k] * cbufX[3] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx)[k] * cbufX[3] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx)[k] * cbufX[3] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx)[k] * cbufX[3] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx+1)[k] * cbufX[4] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+1)[k] * cbufX[4] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx+1)[k] * cbufX[4] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+1)[k] * cbufX[4] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx+1)[k] * cbufX[4] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+1)[k] * cbufX[4] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx+1)[k] * cbufX[4] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+1)[k] * cbufX[4] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx+2)[k] * cbufX[5] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+2)[k] * cbufX[5] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx+2)[k] * cbufX[5] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+2)[k] * cbufX[5] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx+2)[k] * cbufX[5] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+2)[k] * cbufX[5] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx+2)[k] * cbufX[5] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+2)[k] * cbufX[5] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx+3)[k] * cbufX[6] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+3)[k] * cbufX[6] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx+3)[k] * cbufX[6] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+3)[k] * cbufX[6] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx+3)[k] * cbufX[6] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+3)[k] * cbufX[6] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx+3)[k] * cbufX[6] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+3)[k] * cbufX[6] * cbufY[7] + 
 
 matSrc.at<cv::Vec3b>(sy-3, sx+4)[k] * cbufX[7] * cbufY[0] + matSrc.at<cv::Vec3b>(sy-2, sx+4)[k] * cbufX[7] * cbufY[1] + 
 matSrc.at<cv::Vec3b>(sy-1, sx+4)[k] * cbufX[7] * cbufY[2] + matSrc.at<cv::Vec3b>(sy, sx+4)[k] * cbufX[7] * cbufY[3] + 
 matSrc.at<cv::Vec3b>(sy+1, sx+4)[k] * cbufX[7] * cbufY[4] + matSrc.at<cv::Vec3b>(sy+2, sx+4)[k] * cbufX[7] * cbufY[5] + 
 matSrc.at<cv::Vec3b>(sy+3, sx+4)[k] * cbufX[7] * cbufY[6] + matSrc.at<cv::Vec3b>(sy+4, sx+4)[k] * cbufX[7] * cbufY[7] ) >> 22);// 4194304 
 } 
 } 
 } 
 cv::imwrite("Lanczos_1.jpg", matDst1); 
 
 cv::resize(matSrc, matDst2, matDst1.size(), 0, 0, 4); 
 cv::imwrite("Lanczos_2.jpg", matDst2);

[http_blog.csdn.net_andrew659_article_details_4818988]: http://blog.csdn.net/andrew659/article/details/4818988
[http_blog.csdn.net_qq_20823641_article_details_52221442]: http://blog.csdn.net/qq_20823641/article/details/52221442
[20131215165908937]: /images/20220612/ec1be04aa5a2471d96afd32cf78dd6f4.png
[20131215170323218]: /images/20220612/6c12d2806d6d473987f6f12c5012d16c.png
[20161009182301788]: /images/20220612/0278abb466494ba6be79d940c11828cb.png
[fengbingchun]: http://my.csdn.net/fengbingchun