levenberg-marquardt algorithm
时间: 2023-05-02 20:03:40 浏览: 51
B'levenberg-Marquardt算法是一种非线性最小二乘优化算法,适用于求解复杂的非线性问题,特别是在数据噪声较大的情况下。该算法利用了Levenberg(1944年)和Marquardt(1963年)的思想,通过在牛顿法和梯度下降法之间进行平衡来快速优化相关参数。该算法具有收敛速度快、精度高、参数调整灵活等优点,在很多领域得到广泛应用,如信号处理、图像处理、机器学习、计算机视觉等。
相关问题
Levenberg-Marquardt pytorch
Levenberg-Marquardt (LM) is a widely used optimization algorithm for nonlinear least squares problems. In PyTorch, LM can be implemented using the `torch.autograd.functional` module. Here's an example of how to use LM to fit a curve to data:
```python
import torch
from torch.autograd.functional import jacobian
# Define the model
def model(x, params):
a, b, c = params
return a * torch.sin(b * x) + c
# Define the objective function
def objective(params):
y_pred = model(x, params)
residuals = y - y_pred
return torch.sum(residuals ** 2)
# Generate some data
x = torch.linspace(-1, 1, 100)
y = 2 * torch.sin(3 * x) + 0.5 * torch.randn(100)
# Initialize the parameters
params = torch.tensor([1.0, 1.0, 1.0], requires_grad=True)
# Set up the LM optimizer
optimizer = torch.optim.LBFGS([params])
# Train the model
for i in range(100):
def closure():
optimizer.zero_grad()
loss = objective(params)
loss.backward()
return loss
optimizer.step(closure)
# Print the final parameters
print(params)
```
In this example, we define a model that takes an input `x` and a set of parameters `params`, and returns a prediction `y_pred`. We then define an objective function that measures the difference between the predicted values and the actual values (`y` in this case). We generate some random data, initialize the parameters, and set up the LM optimizer. Finally, we train the model by minimizing the objective function using the LM optimizer. The final parameters are printed out.
Levenberg-Marquardt对相机标定结果进行优化的代码(matlab)
以下是一个简单的Matlab代码示例,使用Levenberg-Marquardt算法对相机标定结果进行优化:
```matlab
% 读入标定结果
load('calibration_results.mat', 'cameraParams', 'imagePoints', 'worldPoints');
% 定义优化函数
fun = @(x) reprojectionError(x, imagePoints, worldPoints);
% 初始矩阵
x0 = cameraParams.IntrinsicMatrix(:);
% Levenberg-Marquardt优化函数
options = optimoptions(@lsqnonlin, 'Algorithm', 'levenberg-marquardt');
[x, ~, ~, ~] = lsqnonlin(fun, x0, [], [], options);
% 更新相机参数
cameraParams.IntrinsicMatrix = reshape(x, [3, 3]);
cameraParams.FocalLength = [cameraParams.IntrinsicMatrix(1,1) cameraParams.IntrinsicMatrix(2,2)];
cameraParams.PrincipalPoint = [cameraParams.IntrinsicMatrix(1,3) cameraParams.IntrinsicMatrix(2,3)];
% 定义重投影误差函数
function [errors] = reprojectionError(x, imagePoints, worldPoints)
% 将向量形式的内部矩阵转换为矩阵形式
intrinsics = reshape(x, [3, 3]);
% 计算重投影误差
[R, t] = extrinsics(imagePoints, worldPoints, intrinsics);
reprojectedPoints = worldToImage(cameraParams, R, t, worldPoints);
errors = imagePoints - reprojectedPoints;
end
```
注意,此代码需要标定结果的.mat文件,其中包含相机参数、图像点和世界点。此外,还需要定义一个重投影误差函数,用于计算相机参数优化后的重投影误差。最终,代码使用Levenberg-Marquardt算法对内部矩阵进行优化,并更新相机参数。