图像卷积回顾与计算优化(待续)

小灰灰 2022-09-20 15:03 147阅读 0赞

卷积及其计算方法是《信号与系统》与《数字信号处理》课程的一个核心知识点，谈及应用，我倒是能用的过来，在图像中简单地说就是掩模相乘，不过上次师兄谈及一个卷积优化方法，我想了想居然只想到行列分开这个。现在只能重新复习一下知识点。

学图像的应该都知道，卷积运算在图像处理领域应用相当广泛，例如在图像滤波、增强、分析等处理时都要用到卷积运算，它实质上是一种矩阵运算，其特点是运算量大，并且数据复用率高。

**下面首先来回顾一下一维卷积：**

**卷积定义**：

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![SouthEast 1][]

而在图像处理中，用得主要是离散二维卷积

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**OpenCV中的卷积函数**

filter2D——对图像作卷积运算.

> C++: void filter2D(InputArray src, OutputArray dst, int ddepth, InputArray kernel, Point anchor=Point(-1,-1), double delta=0, int borderType=BORDER\_DEFAULT )
> 
> C: void cvFilter2D(const CvArr\* src, CvArr\* dst, const CvMat\* kernel, CvPoint anchor=cvPoint(-1,-1) )  
>

参数：

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 <th style="font-family:'Microsoft YaHei',微软雅黑!important; text-align:left; padding:1px 8px 1px 5px; border:0px!important"> &nbsp;</th> 
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 <ul style="margin:0px; padding-left:1em"> 
 <li style="text-align:justify; margin:0px">src&nbsp;– 输入图像.</li> 
 <li style="text-align:justify; margin:0px">dst&nbsp;–与输入图像大小相同通道数相同的输出图像 .</li> 
 <li style="text-align:justify; margin:0px">ddepth&nbsp;– 
 <dl style="margin-bottom:15px">
 desired depth of the destination image; if it is negative, it will be the same as&nbsp; 
 src.depth(); the following combinations of&nbsp; 
 src.depth()&nbsp;and 
 ddepth&nbsp;are supported: 
 <dd style="margin-top:1em; margin-bottom:1em; margin-left:30px"> 
 <ul style="margin:0px; padding-left:1em"> 
 <li style="text-align:justify; margin:0px">src.depth()&nbsp;=&nbsp;CV_8U,&nbsp;ddepth&nbsp;= -1/CV_16S/CV_32F/CV_64F</li> 
 <li style="text-align:justify; margin:0px">src.depth()&nbsp;=&nbsp;CV_16U/CV_16S,&nbsp;ddepth&nbsp;= -1/CV_32F/CV_64F</li> 
 <li style="text-align:justify; margin:0px">src.depth()&nbsp;=&nbsp;CV_32F,&nbsp;ddepth&nbsp;= -1/CV_32F/CV_64F</li> 
 <li style="text-align:justify; margin:0px">src.depth()&nbsp;=&nbsp;CV_64F,&nbsp;ddepth&nbsp;= -1/CV_64F</li> 
 </ul> 
 </dd> 
 </dl> when&nbsp;ddepth=-1, the output image will have the same depth as the source. </li> 
 <li style="text-align:justify; margin:0px">kernel&nbsp;– convolution kernel (or rather a correlation kernel), a single-channel floating point matrix; if you want to apply different kernels to different channels, split the image into separate color planes using<a href="http://docs.opencv.org/modules/core/doc/operations_on_arrays.html#void%20split%28const%20Mat&amp;%20src,%20Mat*%20mvbegin%29" title="void split(const Mat&amp; src, Mat* mvbegin)" style="color:rgb(0,144,217); text-decoration:none" rel="nofollow">split()</a>&nbsp;and process them individually.</li> 
 <li style="text-align:justify; margin:0px">anchor&nbsp;– anchor of the kernel that indicates the relative position of a filtered point within the kernel; the anchor should lie within the kernel; default value (-1,-1) means that the anchor is at the kernel center.</li> 
 <li style="text-align:justify; margin:0px">delta&nbsp;– optional value added to the filtered pixels before storing them in&nbsp;dst.</li> 
 <li style="text-align:justify; margin:0px">borderType&nbsp;– pixel extrapolation method (see<a href="http://docs.opencv.org/modules/imgproc/doc/filtering.html?highlight=filter2d#int%20borderInterpolate%28int%20p,%20int%20len,%20int%20borderType%29" title="int borderInterpolate(int p, int len, int borderType)" style="color:rgb(0,144,217); text-decoration:none" rel="nofollow">borderInterpolate()</a>&nbsp;for details)</li> 
 </ul> </td> 
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</table>

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**Matlab中的卷积及例子**

**线性卷积与圆周卷积的区别**

[SouthEast]: /images/20220828/22ce72572791454e8886ff1c898fab2b.png
[SouthEast 1]: /images/20220828/a1cbe62551364519959b282ef95247cf.png
[SouthEast 2]: /images/20220828/5502baae134144189e3e540e23b18ac2.png
[SouthEast 3]: /images/20220828/5d56694fa6c8499f82be70eafbd21538.png