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C++ OpenCV boxfilter方框滤波
box filter简单解释
box filter的作用很简单，即对局部区域求平均，并把值赋给某个点，一般我们赋给区域中心。用公式表达如下：
其中patch是以(row,col)为中心的一块区域。
为了跟后面的公式及程序对应，我们做如下定义：
- r：patch的半径。半径在宽高方向可以不相等，但是本文目的不在于对半径的处理，所以简单起见设为相等。
- n：patch的长度，等于(2∗r+1）。
- (rows,cols)：图像的尺寸，行数和列数。
- (row,col)：对完整图像的索引。
- (i,j)：对图像patch的索引
- k：对通道的索引。
1. 暴力实现——四循环
外层两个循环是关于完整图像(row,col)的循环，内层两个循环是关于图像patch(i,j)的循环。
注意：如果图像是多通道的话实际上还有一个通常维度的循环，但是通道数不是本文优化的重心，所以本文不再赘述这个因素，后文也不再提，并且在计算量的估计中也会把这个因素省略掉。
这个实现比较简单，需要做的计算有：
- rows∗cols∗n∗n次加法，内层循环的计算量o(n2)，非常大。
- rows∗cols次除法：除法为了求平均
2. 行列分离
patch的平均可以进行行列分离，也就是先对行方向做平均，并缓存结果，再对缓存的结果做列方向的平均。以公式的形式表达如下：
举个例子展开写会容易理解，比如3*3的patch，共9个数：
这种方式的计算量：
- 2∗rows∗cols∗n次加法，相对于暴力版本，内层循环降低了一个数量级的算力，变成o(n)了
- 2∗rows∗cols次除法
3. 行列分离优化版
第二种实现可以对求和做进一步优化。在单个维度做求和时，可以对当前一维patch的和做一个缓存，当中心点移动后，减去弹出像素的值，加上新增像素的值，这样就避免了重复性求和操作。
这种方案需要对patch的和做一个初始化和缓存，该方案的计算量为：
- 2∗rows∗cols次减法，2∗rows∗cols次加法，内层循环的计算变为o(1)了，进一步降低了一个数量级算力。
- 2∗rows∗cols次除法
代码
上面做计算量估计的时候没有考虑边界条件，在具体代码实现的时候需要仔细处理边界，防止数组访问越界。
代码同时跟opencv做了个效果和性能的对比，第三种方式虽然仍然比opencv慢，但性能基本处于同一量级了，opencv可能还做了一些其他跟算法无关的优化，比如指令集、并行化之类的。
注意：下面为了方便比较，opencv boxFilter的边界处理参数选择BORDER_CONSTANT。即使是边界处patch不满覆盖的情况下，opencv仍然除以n2 ，也就是说除以的数字有点大了，所以边界会逐渐发黑，特别是kernel_size（对应于radius）比较大时候视觉效果更明显。
#include#include #include #include #include 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 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 (i, j)[k]; } } } for (int k = 0; k < channels; ++k) { result.at (row, col)[k] = sums[k] / static_cast (count); // opencv BORDER_CONSTANT: /*float COUNT = (float)(2 * radius + 1) * (2 * radius + 1); result.at (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 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 (row, j)[k]; } } for (int k = 0; k < channels; ++k) { row_result.at (row, col)[k] = sums[k] / static_cast (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 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 (i, col)[k]; } } for (int k = 0; k < channels; ++k) { result.at (row, col)[k] = sums[k] / static_cast (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 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 (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 (row, left)[k]; } } if (right < cols) { count++; for (int k = 0; k < channels; ++k) { sums[k] += image.at (row, right)[k]; } } for (int k = 0; k < channels; ++k) { row_result.at (row, col)[k] = sums[k] / static_cast (count); } } } // compute mean for column-wise for (int col = 0; col < cols; ++col) { // initialize sums for column vector 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 (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 (up, col)[k]; } } if (down < rows) { count++; for (int k = 0; k < channels; ++k) { sums[k] += row_result.at (down, col)[k]; } } for (int k = 0; k < channels; ++k) { result.at (row, col)[k] = sums[k] / static_cast (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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