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<h1>OpenCV图像处理篇之图像平滑</h1>
<h4>2014-09-18 / xiahouzuoxin</h4>
<h4>Tags: OpenCV</h4>
转载请注明出处: <a href="http://xiahouzuoxin.github.io/notes/">http://xiahouzuoxin.github.io/notes/</a>
<div id="TOC">
<ul>
<li><a href="#图像平滑算法">图像平滑算法</a></li>
<li><a href="#程序分析及结果">程序分析及结果</a></li>
</ul>
</div>
<!---title:OpenCV图像处理篇之图像平滑-->
<!---keywords:OpenCV-->
<!---date:2014-09-18-->
<h2 id="图像平滑算法">图像平滑算法</h2>
<p>图像平滑与图像模糊是同一概念，主要用于图像的去噪。平滑要使用滤波器，为不改变图像的相位信息，一般使用线性滤波器，其统一形式如下：</p>
<p><img src="https://latex.codecogs.com/png.latex? \Large g(i,j)=\sum_{k,l}f(i+k,j+l)h(k,l)"></p>
<p>其中h称为滤波器的核函数，说白了就是权值。不同的核函数代表不同的滤波器，有不同的用途。</p>
<p>在图像处理中，常见的滤波器包括：</p>
<ol style="list-style-type: decimal">
<li><p>归一化滤波器（Homogeneous blur）</p>
<p>也是__均值滤波器__，用输出像素点核窗口内的像素均值代替输出点像素值。</p></li>
<li><p>高斯滤波器（Guassian blur）</p>
<p>是实际中最常用的滤波器，高斯滤波是将输入数组的每一个像素点与 高斯内核 卷积将卷积和当作输出像素值。高斯核相当于对输出像素的邻域赋予不同的权值，输出像素点所在位置的权值最大（对应高斯函数的均值位置）。二维高斯函数为，</p>
<p><img src="https://latex.codecogs.com/png.latex? \Large G(x,y) = Ae^{\frac{-(x-u_x)^2}{2\delta_x^2}+\frac{-(y-y_x)^2}{2\delta_y^2}"></p></li>
<li><p>中值滤波器（median blur）</p>
<p>中值滤波将图像的每个像素用邻域(以当前像素为中心的正方形区域)像素的中值代替。对椒盐噪声最有效的滤波器，去除跳变点非常有效。</p></li>
<li><p>双边滤波器（Bilatrial blur）</p>
<p>为避免滤波器平滑图像去噪的同时使边缘也模糊，这种情况下使用双边滤波器。关于双边滤波器的解释参见<a href="http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html" class="uri">http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MANDUCHI1/Bilateral_Filtering.html</a></p></li>
</ol>
<p>下面的程序将先给标准Lena图像添加椒盐噪声，分别使用4种不同的滤波器进行平滑操作，请注意观察不同滤波器对椒盐噪声的去噪效果！</p>
<h2 id="程序分析及结果">程序分析及结果</h2>
<pre class="sourceCode c"><code class="sourceCode c"><span class="co">/*</span>
<span class="co"> * FileName : image_smoothing.cpp</span>
<span class="co"> * Author : xiahouzuoxin @163.com</span>
<span class="co"> * Version : v1.0</span>
<span class="co"> * Date : Wed 17 Sep 2014 08:30:25 PM CST</span>
<span class="co"> * Brief : </span>
<span class="co"> * </span>
<span class="co"> * Copyright (C) MICL,USTB</span>
<span class="co"> */</span>
<span class="ot">#include "cv.h"</span>
<span class="ot">#include "imgproc/imgproc.hpp"</span>
<span class="ot">#include "highgui/highgui.hpp"</span>
using namespace std;
using namespace cv;
<span class="dt">const</span> <span class="dt">int</span> MAX_KERNEL_LENGTH = <span class="dv">10</span>;
<span class="dt">const</span> <span class="dt">char</span> *wn_name = <span class="st">"Smoothing"</span>;
<span class="dt">static</span> <span class="dt">void</span> salt(Mat &I, <span class="dt">int</span> n);
<span class="dt">static</span> <span class="dt">void</span> disp_caption(<span class="dt">const</span> <span class="dt">char</span> *wn_name, Mat src, <span class="dt">const</span> <span class="dt">char</span> *caption);
<span class="dt">static</span> <span class="dt">void</span> disp_image(<span class="dt">const</span> <span class="dt">char</span> *wn_name, Mat I);
<span class="co">/*</span>
<span class="co"> * @brief </span>
<span class="co"> * @inputs </span>
<span class="co"> * @outputs </span>
<span class="co"> * @retval </span>
<span class="co"> */</span>
<span class="dt">int</span> main(<span class="dt">int</span> argc, <span class="dt">char</span> *argv[])
{
<span class="kw">if</span> (argc<<span class="dv">2</span>) {
cout<<<span class="st">"Usage: ./image_smoothing [file name]"</span><<endl;
<span class="kw">return</span> -<span class="dv">1</span>;
}
Mat I = imread(argv[<span class="dv">1</span>], CV_LOAD_IMAGE_GRAYSCALE);
salt(I, <span class="dv">6000</span>);
imshow(wn_name, I);
waitKey(<span class="dv">0</span>);
Mat dst; <span class="co">// Result</span>
<span class="co">/* Homogeneous blur */</span>
disp_caption(wn_name, I, <span class="st">"Homogeneous blur"</span>);
<span class="kw">for</span> (<span class="dt">int</span> i=<span class="dv">1</span>; i<MAX_KERNEL_LENGTH; i+=<span class="dv">2</span>) {
blur(I, dst, Size(i, i), Point(-<span class="dv">1</span>,-<span class="dv">1</span>));
disp_image(wn_name, dst);
}
<span class="co">/* Guassian blur */</span>
disp_caption(wn_name, I, <span class="st">"Gaussian blur"</span>);
<span class="kw">for</span> (<span class="dt">int</span> i=<span class="dv">1</span>; i<MAX_KERNEL_LENGTH; i+=<span class="dv">2</span>) {
GaussianBlur(I, dst, Size(i, i), <span class="dv">0</span>, <span class="dv">0</span>);
disp_image(wn_name, dst);
}
<span class="co">/* Median blur */</span>
disp_caption(wn_name, I, <span class="st">"Median blur"</span>);
<span class="kw">for</span> (<span class="dt">int</span> i=<span class="dv">1</span>; i<MAX_KERNEL_LENGTH; i+=<span class="dv">2</span>) {
medianBlur(I, dst, i);
disp_image(wn_name, dst);
}
<span class="co">/* Bilatrial blur */</span>
disp_caption(wn_name, I, <span class="st">"Bilatrial blur"</span>);
<span class="kw">for</span> (<span class="dt">int</span> i=<span class="dv">1</span>; i<MAX_KERNEL_LENGTH; i+=<span class="dv">2</span>) {
bilateralFilter(I, dst, i, i*<span class="dv">2</span>, i/<span class="dv">2</span>);
disp_image(wn_name, dst);
}
waitKey(<span class="dv">0</span>);
<span class="kw">return</span> <span class="dv">0</span>;
}
<span class="co">/*</span>
<span class="co"> * @brief 显示提示文字（滤波方法）</span>
<span class="co"> * @inputs </span>
<span class="co"> * @outputs </span>
<span class="co"> * @retval </span>
<span class="co"> */</span>
<span class="dt">static</span> <span class="dt">void</span> disp_caption(<span class="dt">const</span> <span class="dt">char</span> *wn_name, Mat src, <span class="dt">const</span> <span class="dt">char</span> *caption)
{
Mat dst = Mat::zeros(src.size(), src.type());
putText(dst, caption, Point(src.cols/<span class="dv">4</span>, src.rows/<span class="dv">2</span>), CV_FONT_HERSHEY_COMPLEX, <span class="dv">1</span>, Scalar(<span class="dv">255</span>,<span class="dv">255</span>,<span class="dv">255</span>));
imshow(wn_name, dst);
waitKey(<span class="dv">0</span>);
}
<span class="co">/*</span>
<span class="co"> * @brief 显示图像</span>
<span class="co"> * @inputs </span>
<span class="co"> * @outputs </span>
<span class="co"> * @retval </span>
<span class="co"> */</span>
<span class="dt">static</span> <span class="dt">void</span> disp_image(<span class="dt">const</span> <span class="dt">char</span> *wn_name, Mat I)
{
imshow(wn_name, I);
waitKey(<span class="dv">1000</span>);
}
<span class="co">/*</span>
<span class="co"> * @brief 添加椒盐噪声</span>
<span class="co"> * @inputs </span>
<span class="co"> * @outputs </span>
<span class="co"> * @retval </span>
<span class="co"> */</span>
<span class="dt">static</span> <span class="dt">void</span> salt(Mat &I, <span class="dt">int</span> n=<span class="dv">3000</span>)
{
<span class="kw">for</span> (<span class="dt">int</span> k=<span class="dv">0</span>; k<n; k++) {
<span class="dt">int</span> i = rand() % I.cols;
<span class="dt">int</span> j = rand() % I.rows;
<span class="kw">if</span> (I.channels()) {
I.at<uchar>(j,i) = <span class="dv">255</span>;
} <span class="kw">else</span> {
I.at<Vec3b>(j,i)[<span class="dv">0</span>] = <span class="dv">255</span>;
I.at<Vec3b>(j,i)[<span class="dv">1</span>] = <span class="dv">255</span>;
I.at<Vec3b>(j,i)[<span class="dv">2</span>] = <span class="dv">255</span>;
}
}
}</code></pre>
<p>上面程序的逻辑非常清晰：</p>
<ol style="list-style-type: decimal">
<li><p>读入灰度图，并添加椒盐噪声（6000个噪声点）：</p>
<pre class="sourceCode c"><code class="sourceCode c">Mat I = imread(argv[<span class="dv">1</span>], CV_LOAD_IMAGE_GRAYSCALE);
salt(I, <span class="dv">6000</span>);</code></pre>
<div class="figure">
<img src="../images/OpenCV图像处理篇之图像平滑/LenaNoise.PNG" alt="LenaNoise" /><p class="caption">LenaNoise</p>
</div></li>
<li><p><code>disp_caption</code>和<code>disp_image</code>函数分别是用于显示提示文字和平滑过程中的变化图像的，平滑过程中图像的变化如下图：</p>
<div class="figure">
<img src="../images/OpenCV图像处理篇之图像平滑/blur.gif" alt="blur" /><p class="caption">blur</p>
</div>
<p>注意观察上面的图，中值滤波（Median Blur）对椒盐噪声的效果最好！</p></li>
<li><p>四种滤波方法分别使用到4个OpenCV函数，这些函数的声明都在<code>imgproc.hpp</code>中，这些函数的前2个参数都是原图像和滤波后图像。</p>
<p>归一化滤波器<code>blur</code>的第3个参数为滤波核窗口的大小，Size(i,i)表示ixi大小的窗口。</p>
<p>高斯滤波器<code>GaussianBlur</code>第3个参数也是滤波核窗口的大小，第4、第5个参数分辨表示x方向和y方向的δ。</p>
<p>中值滤波器<code>medianBlur</code>第3个参数是滤波器的长度，该滤波器的窗口为正方形。</p>
<p>双边滤波器的函数原型如下：</p>
<pre><code>//! smooths the image using bilateral filter
CV_EXPORTS_W void bilateralFilter( InputArray src, OutputArray dst, int d,
double sigmaColor, double sigmaSpace,
int borderType=BORDER_DEFAULT );</code></pre></li>
<li><p>本程序使用的Makefile文件为：</p>
<pre><code>TARG=image_smoothing
SRC=image_smoothing.cpp
LIB=-L/usr/local/lib/
INC=-I/usr/local/include/opencv/ -I/usr/local/include/opencv2
CFLAGS=
$(TARG):$(SRC)
g++ -g -o $@ ${CFLAGS} $(LIB) $(INC) \
-lopencv_core -lopencv_highgui -lopencv_imgproc \
$^
.PHONY:clean
clean:
-rm $(TARG) tags -f </code></pre></li>
</ol>
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