opecv c++计算图像的曲率

公式

$\kappa =\frac{z_{xx}\cdot z_y^2-2\cdot z_x\cdot z_y\cdot z_{xy}+z_{yy}\cdot z_x^2}{(z_x^2+z_y^2+1{)}^{3/2}}$

其中：
$z_x=\frac{\partial z}{\partial x}$
$z_y=\frac{\partial z}{\partial y}$
$z_{xx},z_{yy},z_{xy}$ 分别为 ( z ) 关于 ( x ) 和 ( y ) 的二阶导数和交叉导数。

代码

void computeCurvature(const cv::Mat& depth_map, cv::Mat& curvature_map)
{cv::Mat gradient_x, gradient_y;cv::Mat gradient_xx, gradient_yy, gradient_xy;// 计算一阶导数Sobel(depth_map, gradient_x, CV_64F, 1, 0, 3);Sobel(depth_map, gradient_y, CV_64F, 0, 1, 3);// 计算二阶导数Sobel(gradient_x, gradient_xx, CV_64F, 1, 0, 3);Sobel(gradient_y, gradient_yy, CV_64F, 0, 1, 3);Sobel(gradient_x, gradient_xy, CV_64F, 0, 1, 3);// 计算曲率cv::Mat denominator = gradient_x.mul(gradient_x) + gradient_y.mul(gradient_y) + cv::Mat::ones(depth_map.size(), CV_64F);cv::pow(denominator, 1.5, denominator);curvature_map = (gradient_xx.mul(gradient_y.mul(gradient_y)) - 2.0 * gradient_x.mul(gradient_y.mul(gradient_xy)) + gradient_yy.mul(gradient_x.mul(gradient_x))) / denominator;
}