Bilateral Filtering for Gray and Color Images
双边滤波器:保留边界的平滑滤波器。 在局部上,就是在灰度值差异不大的区域平滑,在灰度值差异比较大的边界地区保留边界。所以双边滤波器作用于每个像素的同时,必然会受到领域像素点的距离、灰度值差的权重影响。
已知低通滤波可以表示为:
range filter可以表示为:(range filter 试选定一个数值范围,再做滤波的一个操作)
所以,双边滤波器的定义是:
其中,k(x)是归一化(normalize)函数,
( f 表示原图像,h 表示处理后的图像 x 表示 h 中某个像素点位置,ξ 表示 f 中x位置像素点的邻域像素,f(ξ)表示该像素点的灰度值,c表示低通滤波, s表示range filter)
其中,
//Filters.h
#ifndef FILTERS_H
#define FILTERS_H
#include "opencv2/imgproc.hpp"
#include "opencv2/highgui.hpp"
#include "opencv2/core.hpp"
#include <iostream>
#include <cmath>
//Bilateral Filtering
//sigmaD == sigmaSpace, sigmaR == sigmaColor
cv::Mat BilateralFilter(cv::Mat inputImg, int filterSize, double sigmaD, double sigmaR);
cv::Mat fastBilateralFilter(cv::Mat inputImg, int filterSize, double sigmaD, double sigmaR);
#endif // ! FILTERS_H
//Filters.cpp
#include "Filters.h"
double SpaceFactor(int x1, int y1, int x2, int y2, double sigmaD) {
double absX = pow(abs(x1 - x2), 2);
double absY = pow(abs(y1 - y2), 2);
return exp(-(absX + absY) / (2 * pow(sigmaD, 2)));
}
double ColorFactor(int x, int y, double sigmaR) {
double distance = abs(x - y) / sigmaR;
return exp(-0.5 * pow(distance, 2));
}
cv::Mat BilateralFilter(cv::Mat inputImg, int filterSize, double sigmaD, double sigmaR) {
int len; //must be odd number
cv::Mat gray; // must be 1-channel image
cv::Mat LabImage; // if channels == 3
if (filterSize % 2 != 1 || filterSize <= 0) {
std::cerr << "Filter Size must be a positive odd number!" << std::endl;
return inputImg;
}
len = filterSize / 2;
if (inputImg.channels() >= 3) {
cv::cvtColor(inputImg, LabImage, cv::COLOR_BGR2Lab);
gray = cv::Mat::zeros(LabImage.size(), CV_8UC1);
for (int i = 0; i < LabImage.rows; i++) {
for (int j = 0; j < LabImage.cols; j++) {
gray.ptr<uchar>(i)[j] = LabImage.ptr<uchar>(i, j)[0];
}
}
}
else if(inputImg.channels() == 1){
inputImg.copyTo(gray);
}
else {
std::cerr << "the count of input image's channel can not be 2!" << std::endl;
return inputImg;
}
cv::Mat resultGrayImg = cv::Mat::zeros(gray.size(), CV_8UC1);
for (int i = 0; i < gray.rows; i++) {
for (int j = 0; j < gray.cols; j++) {
double k = 0;
double f = 0;
for (int r = i - len; r <= i + len; r++) {
for (int c = j - len; c <= j + len; c++) {
if (r < 0 || c < 0 || r >= gray.rows || c >= gray.cols)
continue;
f = f + gray.ptr<uchar>(r)[c] * SpaceFactor(i, j, r, c, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(r)[c], sigmaD);
k += SpaceFactor(i, j, r, c, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(r)[c], sigmaD);
}
}
int value = f / k;
if (value < 0) value = 0;
else if (value > 255) value = 255;
resultGrayImg.ptr<uchar>(i)[j] = (uchar)value;
}
}
cv::Mat resultImg;
if (inputImg.channels() >= 3) {
for (int i = 0; i < LabImage.rows; i++) {
for (int j = 0; j < LabImage.cols; j++) {
LabImage.ptr<uchar>(i, j)[0] = resultGrayImg.ptr<uchar>(i)[j];
}
}
cv::cvtColor(LabImage, resultImg, cv::COLOR_Lab2BGR);
}
else {
resultGrayImg.copyTo(resultImg);
}
return resultImg;
}
cv::Mat fastBilateralFilter(cv::Mat inputImg, int filterSize, double sigmaD, double sigmaR) {
int len; //must be odd number
cv::Mat gray; // must be 1-channel image
cv::Mat LabImage; // if channels == 3
if (filterSize % 2 != 1 || filterSize <= 0) {
std::cerr << "Filter Size must be a positive odd number!" << std::endl;
return inputImg;
}
len = filterSize / 2;
if (inputImg.channels() >= 3) {
cv::cvtColor(inputImg, LabImage, cv::COLOR_BGR2Lab);
gray = cv::Mat::zeros(LabImage.size(), CV_8UC1);
for (int i = 0; i < LabImage.rows; i++) {
for (int j = 0; j < LabImage.cols; j++) {
gray.ptr<uchar>(i)[j] = LabImage.ptr<uchar>(i, j)[0];
}
}
}
else if (inputImg.channels() == 1) {
inputImg.copyTo(gray);
}
else {
std::cerr << "the count of input image's channel can not be 2!" << std::endl;
return inputImg;
}
cv::Mat resultGrayImg = cv::Mat::zeros(gray.size(), CV_8UC1);
for (int i = 0; i < gray.rows; i++) {
for (int j = 0; j < gray.cols; j++) {
double k = 0;
double f = 0;
double sum = 0;
for (int r = i - len; r <= i + len; r++) {
if (r < 0 || r >= gray.rows)
continue;
f = f + gray.ptr<uchar>(r)[j] * SpaceFactor(i, j, r, j, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(r)[j], sigmaD);
k += SpaceFactor(i, j, r, j, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(r)[j], sigmaD);
}
sum = f / k;
f = k = 0.0;
for (int c = j - len; c <= j + len; c++) {
if (c < 0 || c >= gray.cols)
continue;
f = f + gray.ptr<uchar>(i)[c] * SpaceFactor(i, j, i, c, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(i)[c], sigmaD);
k += SpaceFactor(i, j, i, c, sigmaD) * ColorFactor(gray.ptr<uchar>(i)[j], gray.ptr<uchar>(i)[c], sigmaD);
}
int value = (sum + f / k) / 2;
if (value < 0) value = 0;
else if (value > 255) value = 255;
resultGrayImg.ptr<uchar>(i)[j] = (uchar)value;
}
}
cv::Mat resultImg;
if (inputImg.channels() >= 3) {
for (int i = 0; i < LabImage.rows; i++) {
for (int j = 0; j < LabImage.cols; j++) {
LabImage.ptr<uchar>(i, j)[0] = resultGrayImg.ptr<uchar>(i)[j];
}
}
cv::cvtColor(LabImage, resultImg, cv::COLOR_Lab2BGR);
}
else {
resultGrayImg.copyTo(resultImg);
}
return resultImg;
}
//main.cpp
#include <iostream>
#include <time.h>
#include "Filters.h"
using namespace std;
int main() {
cv::Mat img = cv::imread("Capture.jpg", cv::IMREAD_UNCHANGED);
clock_t begin_time = clock();
cv::Mat result = BilateralFilter(img, 15, 12.5, 50);
std::cout << float(clock() - begin_time) / CLOCKS_PER_SEC << std:: endl;
cv::imshow("original", result);
cv::waitKey(0);
cv::imwrite("original.jpg", result);
begin_time = clock();
result = fastBilateralFilter(img, 15, 12.5, 50);
std::cout << float(clock() - begin_time) / CLOCKS_PER_SEC << std::endl;
cv::imshow("fast", result);
cv::waitKey(0);
cv::imwrite("fast.jpg", result);
begin_time = clock();
cv::bilateralFilter(img, result, 15, 50, 12.5);
std::cout << float(clock() - begin_time) / CLOCKS_PER_SEC << std::endl;
cv::imshow("opencv", result);
cv::waitKey(0);
cv::imwrite("opencv.jpg", result);
system("pause");
return 0;
}
运行结果:
46.889s 5.694s 0.202s
二维算子降成两个一维算子之后,速度加快了一些,但是还是不如opencv的快,效果也比它差一些(No more reinventing the wheel...)
从左至右:“小雀斑”帅气原图、BilateralFilter处理结果、fastBilateralFilter处理结果、opencv接口处理结果
原文链接: https://www.cnblogs.com/cheermyang/p/6637186.html
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