PyTorch实现OpenCV鱼眼相机投影存在微小偏差问题排查

拥有3台已标定的鱼眼相机和1台普通相机，需在PyTorch中实现OpenCV的projectPoints()与fisheye.projectPoints()函数，以支持反向传播操作。目前已完成大部分实现，但鱼眼相机的投影结果与OpenCV输出存在微小偏差，投影点呈现类似拉伸的差异。已尝试重写代码、检查参数顺序、切换32/64位精度等操作，问题仍未解决，现寻求问题原因及解决方法。

def distort(self, points):
    x = points[:, 0]
    y = points[:, 1]
    r = torch.sqrt(torch.square(x) + torch.square(y))
    theta = torch.atan(r)
    theta2 = theta**2
    theta4 = theta2**2
    theta6 = theta2**3
    theta8 = theta4**2
    D_mx = self.get_D()
    theta_d = theta * (1 + 
                       (D_mx[0].item() * theta2) +
                       (D_mx[1].item() * theta4) +
                       (D_mx[2].item() * theta6) +
                       (D_mx[3].item() * theta8)
                       )
    x_dist = (theta_d / r) * x
    y_dist = (theta_d / r) * y
    dist_pts = torch.stack((x_dist,y_dist), dim=1)
    return dist_pts
    
def project_world(self, points, distort=None):
    utils.check_tensor(points, shape=[points.shape[0],3], dtype=torch.double)
    points = points.view(-1,3,1)
    camera_points = torch.matmul(self.get_R_mx(), points).view(-1,3) + self.get_T_vec().view(3)
    return self.project(camera_points, distort=distort)
        
def project(self, points, distort=None):
    utils.check_tensor(points, shape=[points.shape[0], 3])
    points = points[:, :2] / points[:,2:3]
    if distort is not None:
        points = self.distort(points)
    elif self.should_distort:
        points = self.distort(points)
    points = points.view(-1, 2, 1)
    projected = torch.matmul(self.get_K()[:2,:2], points).view(-1, 2) + self.get_K()[:2,2]
    utils.check_tensor(projected, shape=[projected.shape[0],2])
    return projected

内容的提问来源于stack exchange，提问作者pattyhoops