关于非线性优化雅可比矩阵的疑惑？ch6和ch7
作者: MaZhaoYong创建于 2024年12月21日更新于 2024年12月21日
- In chapter 6, the handwritten Gauss-Newton method for curve fitting is given, in which the error term e(x) is used to derive the optimization variable x, resulting in the Jacobian matrix J, and the incremental equation JJ^TΔx = -Je is successfully used for calculation. The code is as follows: “H += inv_sigma * inv_sigma * J * J.transpose(); b += -inv_sigma * inv_sigma * error * J;”
- However, in chapter 7, the handwritten Gauss-Newton method for pnp’s ba is given, in which the error term e(x) is used to derive the optimization variable x, resulting in the transpose of the Jacobian matrix J^T, and then when the incremental equation is inserted into the program, J^T is first transformed. The code is as follows: “H += J.transpose() * J; b += -J.transpose() * e;”
- My question is why the two methods are the same, in which the error term e(x) is used to derive the optimization variable x, and the first method results in the Jacobian matrix J, while the second method results in the transpose of the Jacobian matrix J^T.
内容来源: gaoxiang12/slambook