Scipy least_square with jacobian

Question

我正在尝试使用 scipy 复制相机校准优化。

该算法在没有雅可比的情况下工作正常（优化收敛于最优结果）。 然而，当添加雅可比函数时，最小二乘函数几乎没有迭代并在不收敛的情况下停止。

import numpy as np
from scipy.optimize import least_squares
# Camera projection function
def project(params,points_2D, points_3D):
    """
    This function takes in 3D points and camera parameters,
    and returns the projected 2D points.
    """
    fx, fy, cx, cy = params
    X, Y, Z = points_3D
    x = fx * X / Z + cx
    y = -fy * Y / Z + cy
    return np.array([x, y])
# Jacobian function
def jacobian(params,points_2D, points_3D):
    fx, fy, cx, cy = params
    X, Y, Z = points_3D
    nb_pts = points_3D.shape[1]
    J = np.zeros((2*nb_pts,4))
    for i in range(nb_pts):
        J[2*i:2*i+2, :] = np.array([
            [X[i]/Z[i], 0, 1, 0],
            [0, Y[i]/Z[i], 0, 1]
        ])
    return J
# Residual function for least_squares
def residuals(params, points_2D, points_3D):
    """This function computes the residuals, i.e., the difference between the observed 2D points and the projected 2D points."""
    projected_points = project(params,points_2D,points_3D)
    return ((projected_points - points_2D.T)**2).flatten()


# Initial guess for the camera parameters
params0 = np.array([1050, 1000, 320, 240]) # Optimal parameters are [1000, 1000, 320, 240]


# Example 3D points
points_3D = np.array([
    [0, 0, 3],
    [20/100, 0, 2],
    [0, -1/100, 1]
])

# Example 2D points
points_2D = np.array([
    [320, 240],
    [420, 240],
    [320, 250]
])
pts = residuals(params0,points_2D,points_3D.T)
print(pts)
# Perform optimization
result = least_squares(residuals, params0, jac=jacobian, args=(points_2D, points_3D.T), verbose=1)
# Print the optimized camera parameters
print(result.x)
pts2 = residuals(result.x,points_2D,points_3D.T)
print(pts2)

知道我做错了什么吗？