双边滤波原理与C++实现

一、原理

双边滤波（Bilateral filter）是一种可以去噪保边的滤波器。之所以可以达到此效果，是因为滤波器是由两个函数构成：一个函数是由几何空间距离决定滤波器系数，另一个由像素差值决定滤波器系数。

原理示意图如下：

双边滤波器中，输出像素的值依赖于邻域像素的值的加权组合，

权重系数w(i,j,k,l)取决于定义域核

和值域核

的乘积

二、C++实现

2.1 OpenCV调用方法：

cvSmooth(m_iplImg, dstImg, CV_BILATERAL, 2 * r + 1, 0, sigma_r, sigma_d);

2.2 MATLAB版代码：

http://www.mathworks.com/matlabcentral/fileexchange/12191-bilateral-filtering/content/Bilateral%20Filtering/bfilter2.m

调用方法参见资料[1]

2.3 C++代码

void CImageObj::Bilateral_Filter(int r, double sigma_d, double sigma_r)
{
	int i, j, m, n, k;
	int nx = m_width, ny = m_height;
	int w_filter = 2 * r + 1; // 滤波器边长

	double gaussian_d_coeff = -0.5 / (sigma_d * sigma_d);
	double gaussian_r_coeff = -0.5 / (sigma_r * sigma_r);

	double** d_metrix = NewDoubleMatrix(w_filter, w_filter);  // spatial weight
	double r_metrix[256];  // similarity weight

	// copy the original image
	double* img_tmp = new double[m_nChannels * nx * ny];
	for (i = 0; i < ny; i++)
		for (j = 0; j < nx; j++)
			for (k = 0; k < m_nChannels; k++)
			{
				img_tmp[i * m_nChannels * nx + m_nChannels * j + k] = m_imgData[i * m_nChannels * nx + m_nChannels * j + k];
			}

	// compute spatial weight
	for (i = -r; i <= r; i++)
		for (j = -r; j <= r; j++)
		{
			int x = j + r;
			int y = i + r;

			d_metrix[y][x] = exp((i * i + j * j) * gaussian_d_coeff);
		}

	// compute similarity weight
	for (i = 0; i < 256; i++)
	{
		r_metrix[i] = exp(i * i * gaussian_r_coeff);
	}

	// bilateral filter
	for (i = 0; i < ny; i++)
		for (j = 0; j < nx; j++)
		{
			for (k = 0; k < m_nChannels; k++)
			{
				double weight_sum, pixcel_sum;
				weight_sum = pixcel_sum = 0.0;

				for (m = -r; m <= r; m++)
					for (n = -r; n <= r; n++)
					{
						if (m*m + n*n > r*r) continue;

						int x_tmp = j + n;
						int y_tmp = i + m;

						x_tmp = x_tmp < 0 ? 0 : x_tmp;
						x_tmp = x_tmp > nx - 1 ? nx - 1 : x_tmp;   // 边界处理，replicate
						y_tmp = y_tmp < 0 ? 0 : y_tmp;
						y_tmp = y_tmp > ny - 1 ? ny - 1 : y_tmp;

						int pixcel_dif = (int)abs(img_tmp[y_tmp * m_nChannels * nx + m_nChannels * x_tmp + k] - img_tmp[i * m_nChannels * nx + m_nChannels * j + k]);
						double weight_tmp = d_metrix[m + r][n + r] * r_metrix[pixcel_dif];  // 复合权重

						pixcel_sum += img_tmp[y_tmp * m_nChannels * nx + m_nChannels * x_tmp + k] * weight_tmp;
						weight_sum += weight_tmp;
					}

				pixcel_sum = pixcel_sum / weight_sum;
				m_imgData[i * m_nChannels * nx + m_nChannels * j + k] = (uchar)pixcel_sum;

			} // 一个通道

		} // END ALL LOOP

	UpdateImage();
	DeleteDoubleMatrix(d_metrix, w_filter, w_filter);
	delete[] img_tmp;
}

性能方面，跟OpenCV处理速度有差距，有兴趣的，可以自己研究OpenCV版本的源代码

三、效果图

四、参考资料

资料[4]是MIT的学习资料，最全面，包括课件、论文、代码等，涵盖原理、改进、应用、与PDE的联系等等，最值得一看。

[1] 双边滤波器的原理及实现[Rachel-Zhang]

[2]【OpenCV】邻域滤波：方框、高斯、中值、双边滤波

[3] Bilateral Filtering(双边滤波) for SSAO

[4] MIT学习资料