图像去噪之非局部均值算法-原理和实现 - 好文

1、基本原理

是一种空间域滤波，和高斯模糊、均值滤波类似，当前像素点的值时通过周围像素的加权平均得到。不同之处在于权值计算策略不同，也就是下面公式中w计算方式不同；

2、权重策略

以上图为例，对其去噪；对于帽子边缘的一个像素点，相比于高斯模糊或者均值模糊，用附近帽子边缘的像素点求均值更能好。那么计算机如何知道哪些像素也同样的是帽子边缘的像素？帽子边缘具有相似的结构，如果我们在每个像素周围画一个方框，方框内像素的欧式距离越小，说明结构越相似，中间的像素越是处于相同的结构位置，对应权重要更大，这个框的大小称kernel
size。对多大范围内(B(p,r))的像素求加权平均，在这个算法中成为search size;

距离计算公式：

距离越小，越相似，权重越大

3、实现代码
#include <iostream> #include <opencv2/core/core.hpp> #include
<opencv2/highgui/highgui.hpp> #include <opencv2/imgproc/imgproc.hpp> #include
<opencv2/photo.hpp> using namespace std; using namespace cv; int distance2(Mat
m1, Mat m2) { Mat dst; absdiff(m1, m2, dst);int sum = 0; for (int j = 0; j <
dst.rows; j++) {for (int i = 0; i < dst.cols; i++) { sum += dst.at<uchar>(j,i)
* dst.at<uchar>(j, i); } }return sum; } void nlmean(Mat src, Mat &dst, double h,
double sigma, int halfKernelSize, int halfSearchSize) { Mat boardSrc;
dst.create(src.rows, src.cols, CV_8UC1);int boardSize = halfKernelSize +
halfSearchSize; copyMakeBorder(src, boardSrc, boardSize, boardSize, boardSize,
boardSize, BORDER_REFLECT);double h2 = h*h; double sigma2 = 2 * sigma*sigma; int
rows = src.rows;int cols = src.cols; int lookupTableSize = 256 * 256 *(2*
halfKernelSize +1)*(2* halfKernelSize+1); double *lookupTable = new double
[lookupTableSize];for (int i = 0; i < lookupTableSize; i++) { if(i<sigma2)
lookupTable[i] =1; else lookupTable[i] = exp(-i/ h2/(2* halfKernelSize+1) /(2*
halfKernelSize+1)); } for (int j = boardSize; j < boardSize+ rows; j++) { for (
int i = boardSize; i < boardSize+cols; i++) { Mat patchA=boardSrc( Range(j -
halfKernelSize, j + halfKernelSize), Range (i - halfKernelSize, i +
halfKernelSize));double w = 0; double p = 0; double sumw = 0; for (int sr =
-halfSearchSize; sr <= halfSearchSize; sr++) {for (int sc = -halfSearchSize; sc
<= halfSearchSize; sc++) { Mat patchB = boardSrc(Range(j+sr - halfKernelSize,
j+sr + halfKernelSize), Range(i +sc- halfKernelSize, i+sc + halfKernelSize));int
d2 = distance2(patchA, patchB); w = lookupTable[d2]; p +=
boardSrc.at<uchar>(j+sr, i+sc)*w; sumw += w; } } dst.at<uchar>(j - boardSize, i
- boardSize) = saturate_cast<uchar>(p / sumw); } }delete[]lookupTable; } int
main() { Mat src = imread("lena.png", IMREAD_GRAYSCALE); Mat dst; Mat cvdst;
fastNlMeansDenoising(src, cvdst,3, 7, 10); namedWindow("src"); imshow("src",
src); imshow("cvdst", cvdst); nlmean(src, dst, 3, 5, 3, 10); imshow("mydst",
dst); Mat diff; absdiff(src, dst, diff); imshow("diff", diff); waitKey(0); }
4、效果：

原图

opencv自带函数实现效果

我的实现效果

4、论文链接
http://www.ipol.im/pub/art/2011/bcm_nlm/?utm_source=doi
<http://www.ipol.im/pub/art/2011/bcm_nlm/?utm_source=doi>

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