<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def moments(I_xy_input, x, y):
 """ compute quadrupole moments from a light distribution :param I_xy: light distribution :param x: x-coordinates of I_xy :param y: y-coordinates of I_xy :return: Q_xx, Q_xy, Q_yy """

    I_xy = copy.deepcopy(I_xy_input)
    background = np.minimum(0, np.min(I_xy))
    I_xy -= background
    x_ = np.sum(I_xy * x)
    y_ = np.sum(I_xy * y)
    r = (np.max(x) - np.min(x)) / 3.
    mask = mask_util.mask_sphere(x, y, center_x=x_, center_y=y_, r=r)
    Q_xx = np.sum(I_xy * mask * (x - x_) ** 2)
    Q_xy = np.sum(I_xy * mask * (x - x_) * (y - y_))
    Q_yy = np.sum(I_xy * mask * (y - y_) ** 2)
    return Q_xx, Q_xy, Q_yy, background / np.mean(I_xy)