C++?OpenCV實(shí)現(xiàn)boxfilter方框?yàn)V波的方法詳解

更新時(shí)間：2022年10月13日 11:34:34 作者：拜陽

box?filter的作用很簡單，即對(duì)局部區(qū)域求平均，并把值賦給某個(gè)點(diǎn)，一般我們賦給區(qū)域中心。本文將用C++實(shí)現(xiàn)boxfilter方框?yàn)V波，需要的可以了解一下

box filter簡單解釋

box filter的作用很簡單，即對(duì)局部區(qū)域求平均，并把值賦給某個(gè)點(diǎn)，一般我們賦給區(qū)域中心。用公式表達(dá)如下：

其中patch是以(row,col)為中心的一塊區(qū)域。

為了跟后面的公式及程序?qū)?yīng)，我們做如下定義：

r：patch的半徑。半徑在寬高方向可以不相等，但是本文目的不在于對(duì)半徑的處理，所以簡單起見設(shè)為相等。
n：patch的長度，等于(2∗r+1）。
(rows,cols)：圖像的尺寸，行數(shù)和列數(shù)。
(row,col)：對(duì)完整圖像的索引。
(i,j)：對(duì)圖像patch的索引
k：對(duì)通道的索引。

1. 暴力實(shí)現(xiàn)——四循環(huán)

外層兩個(gè)循環(huán)是關(guān)于完整圖像(row,col)的循環(huán)，內(nèi)層兩個(gè)循環(huán)是關(guān)于圖像patch(i,j)的循環(huán)。

注意：如果圖像是多通道的話實(shí)際上還有一個(gè)通常維度的循環(huán)，但是通道數(shù)不是本文優(yōu)化的重心，所以本文不再贅述這個(gè)因素，后文也不再提，并且在計(jì)算量的估計(jì)中也會(huì)把這個(gè)因素省略掉。

這個(gè)實(shí)現(xiàn)比較簡單，需要做的計(jì)算有：

rows∗cols∗n∗n次加法，內(nèi)層循環(huán)的計(jì)算量o(n²)，非常大。
rows∗cols次除法：除法為了求平均

2. 行列分離

patch的平均可以進(jìn)行行列分離，也就是先對(duì)行方向做平均，并緩存結(jié)果，再對(duì)緩存的結(jié)果做列方向的平均。以公式的形式表達(dá)如下：

舉個(gè)例子展開寫會(huì)容易理解，比如3*3的patch，共9個(gè)數(shù)：

這種方式的計(jì)算量：

2∗rows∗cols∗n次加法，相對(duì)于暴力版本，內(nèi)層循環(huán)降低了一個(gè)數(shù)量級(jí)的算力，變成o(n)了
2∗rows∗cols次除法

3. 行列分離優(yōu)化版

第二種實(shí)現(xiàn)可以對(duì)求和做進(jìn)一步優(yōu)化。在單個(gè)維度做求和時(shí)，可以對(duì)當(dāng)前一維patch的和做一個(gè)緩存，當(dāng)中心點(diǎn)移動(dòng)后，減去彈出像素的值，加上新增像素的值，這樣就避免了重復(fù)性求和操作。

這種方案需要對(duì)patch的和做一個(gè)初始化和緩存，該方案的計(jì)算量為：

2∗rows∗cols次減法，2∗rows∗cols次加法，內(nèi)層循環(huán)的計(jì)算變?yōu)閛(1)了，進(jìn)一步降低了一個(gè)數(shù)量級(jí)算力。
2∗rows∗cols次除法

代碼

上面做計(jì)算量估計(jì)的時(shí)候沒有考慮邊界條件，在具體代碼實(shí)現(xiàn)的時(shí)候需要仔細(xì)處理邊界，防止數(shù)組訪問越界。

代碼同時(shí)跟opencv做了個(gè)效果和性能的對(duì)比，第三種方式雖然仍然比opencv慢，但性能基本處于同一量級(jí)了，opencv可能還做了一些其他跟算法無關(guān)的優(yōu)化，比如指令集、并行化之類的。

注意：下面為了方便比較，opencv boxFilter的邊界處理參數(shù)選擇BORDER_CONSTANT。即使是邊界處patch不滿覆蓋的情況下，opencv仍然除以n² ，也就是說除以的數(shù)字有點(diǎn)大了，所以邊界會(huì)逐漸發(fā)黑，特別是kernel_size（對(duì)應(yīng)于radius）比較大時(shí)候視覺效果更明顯。

#include <opencv2/opencv.hpp>
#include <iostream>
#include <vector>
#include <string>
#include <ctime>


using namespace std;
using namespace cv;


Mat BoxFilter_1(const Mat& image, int radius);
Mat BoxFilter_2(const Mat& image, int radius);
Mat BoxFilter_3(const Mat& image, int radius);


int main()
{
    clock_t time_beg;
    clock_t time_end;

    Mat image = imread("lena_std.bmp", IMREAD_UNCHANGED);
    image.convertTo(image, CV_32FC3);
    image /= 255.0f;

    int radius = 9;
    int ksize = radius * 2 + 1;

    Mat image_box_filter_cv;
    time_beg = clock();
    boxFilter(image, image_box_filter_cv, -1, Size(ksize, ksize), Point(-1, -1), true, BORDER_CONSTANT);
    time_end = clock();
    cout << "box-filter-cv time cost: " << time_end - time_beg << endl;

    Mat image_box_filter_1 = BoxFilter_1(image, radius);
    Mat image_box_filter_2 = BoxFilter_2(image, radius);
    Mat image_box_filter_3 = BoxFilter_3(image, radius);

    

    namedWindow("original_image", 1);
    imshow("original_image", image);
    namedWindow("cv_box_filter", 1);
    imshow("cv_box_filter", image_box_filter_cv);
    namedWindow("box_filter-1", 1);
    imshow("box_filter-1", image_box_filter_1);
    namedWindow("box_filter-2", 1);
    imshow("box_filter-2", image_box_filter_2);
    namedWindow("box_filter-3", 1);
    imshow("box_filter-3", image_box_filter_3);

    Mat diff;
    cv::absdiff(image_box_filter_2, image_box_filter_3, diff);
    namedWindow("diff", 1);
    imshow("diff", 50 * diff);

    waitKey(0);
    destroyAllWindows();

    return 0;
}


Mat BoxFilter_1(const Mat& image, int radius)
{
    int cols = image.cols;
    int rows = image.rows;
    int channels = image.channels();
    int row_bound = rows - 1;
    int col_bound = cols - 1;
    Mat result(rows, cols, CV_32FC3);

    clock_t time_beg;
    clock_t time_end;
    time_beg = clock();

    for (int row = 0; row < rows; ++row) {
        int row_beg = max(row - radius, 0);
        int row_end = min(row + radius, row_bound);
        for (int col = 0; col < cols; ++col) {
            int col_beg = max(col - radius, 0);
            int col_end = min(col + radius, col_bound);

            vector<float> sums(channels, 0.0f);
            int count = 0;
            for (int i = row_beg; i <= row_end; ++i) {
                for (int j = col_beg; j <= col_end; ++j) {
                    count++;
                    for (int k = 0; k < channels; ++k) {
                        sums[k] += image.at<Vec3f>(i, j)[k];
                    }
                }
            }

            for (int k = 0; k < channels; ++k) {
                result.at<Vec3f>(row, col)[k] = sums[k] / static_cast<float>(count);

                // opencv BORDER_CONSTANT:
                /*float COUNT = (float)(2 * radius + 1) * (2 * radius + 1);
                result.at<Vec3f>(row, col)[k] = sums[k] / COUNT;*/
            }
        }
    }
    result = cv::max(cv::min(result, 1.0), 0.0);
    time_end = clock();
    cout << "box-filter-1 time cost: " << time_end - time_beg << endl;

    return result;
}


Mat BoxFilter_2(const Mat& image, int radius)
{
    int cols = image.cols;
    int rows = image.rows;
    int channels = image.channels();
    int row_bound = rows - 1;
    int col_bound = cols - 1;
    Mat result(rows, cols, CV_32FC3);

    clock_t time_beg;
    clock_t time_end;
    time_beg = clock();

    // compute mean for row-wise
    Mat row_result(rows, cols, CV_32FC3);
    for (int row = 0; row < rows; ++row) {
        for (int col = 0; col < cols; ++col) {
            int col_beg = max(col - radius, 0);
            int col_end = min(col + radius, col_bound);

            vector<float> sums(channels, 0.0f);
            int count = 0;
            for (int j = col_beg; j <= col_end; ++j) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += image.at<Vec3f>(row, j)[k];
                }
            }
            for (int k = 0; k < channels; ++k) {
                row_result.at<Vec3f>(row, col)[k] = sums[k] / static_cast<float>(count);
            }
        }
    }

    // compute mean for column-wise
    for (int col = 0; col < cols; ++col) {
        for (int row = 0; row < rows; ++row) {
            int row_beg = max(row - radius, 0);
            int row_end = min(row + radius, row_bound);

            vector<float> sums(channels, 0.0f);
            int count = 0;
            for (int i = row_beg; i <= row_end; ++i) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += row_result.at<Vec3f>(i, col)[k];
                }
            }
            for (int k = 0; k < channels; ++k) {
                result.at<Vec3f>(row, col)[k] = sums[k] / static_cast<float>(count);
            }
        }
    }
    result = cv::max(cv::min(result, 1.0), 0.0);
    time_end = clock();
    cout << "box-filter-2 time cost: " << time_end - time_beg << endl;

    return result;
}


Mat BoxFilter_3(const Mat& image, int radius)
{
    int cols = image.cols;
    int rows = image.rows;
    int channels = image.channels();
    Mat result(rows, cols, CV_32FC3);

    clock_t time_beg;
    clock_t time_end;
    time_beg = clock();

    // compute mean for row-wise
    Mat row_result(rows, cols, CV_32FC3);
    for (int row = 0; row < rows; ++row) {
        // initialize sums for row
        vector<float> sums(channels, 0.0f);
        int count = 0;
        for (int col = 0; col < radius; ++col) {
            if (col < cols) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += image.at<Vec3f>(row, col)[k];
                }
            }
        }
        // process row
        for (int col = 0; col < cols; ++col) {
            int left = col - radius - 1;
            int right = col + radius;
            if (left >= 0) {
                count--;
                for (int k = 0; k < channels; ++k) {
                    sums[k] -= image.at<Vec3f>(row, left)[k];
                }
            }
            if (right < cols) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += image.at<Vec3f>(row, right)[k];
                }
            }
            for (int k = 0; k < channels; ++k) {
                row_result.at<Vec3f>(row, col)[k] = sums[k] / static_cast<float>(count);
            }
        }
    }

    // compute mean for column-wise
    for (int col = 0; col < cols; ++col) {
        // initialize sums for column
        vector<float> sums(channels, 0.0f);
        int count = 0;
        for (int row = 0; row < radius; ++row) {
            if (row < rows) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += row_result.at<Vec3f>(row, col)[k];
                }
            }
        }
        // process column
        for (int row = 0; row < rows; ++row) {
            int up = row - radius - 1;
            int down = row + radius;
            if (up >= 0) {
                count--;
                for (int k = 0; k < channels; ++k) {
                    sums[k] -= row_result.at<Vec3f>(up, col)[k];
                }
            }
            if (down < rows) {
                count++;
                for (int k = 0; k < channels; ++k) {
                    sums[k] += row_result.at<Vec3f>(down, col)[k];
                }
            }
            for (int k = 0; k < channels; ++k) {
                result.at<Vec3f>(row, col)[k] = sums[k] / static_cast<float>(count);
            }
        }
    }
    result = cv::max(cv::min(result, 1.0), 0.0);
    time_end = clock();
    cout << "box-filter-3 time cost: " << time_end - time_beg << endl;

    return result;
}

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