【C++】双边滤波器（bilateral filter）

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