mat = np.array(
    [[ 65.481, 128.553, 24.966 ],
     [-37.797, -74.203, 112.0  ],
     [  112.0, -93.786, -18.214]])
mat_inv = np.linalg.inv(mat)
offset = np.array([16, 128, 128])

def rgb2ycbcr(rgb_img):
    ycbcr_img = np.zeros(rgb_img.shape)
    for x in range(rgb_img.shape[0]):
        for y in range(rgb_img.shape[1]):
            ycbcr_img[x, y, :] = np.round(np.dot(mat, rgb_img[x, y, :] * 1.0 / 255) + offset)
    return ycbcr_img

def ycbcr2rgb(ycbcr_img):
    rgb_img = np.zeros(ycbcr_img.shape, dtype=np.uint8)
    for x in range(ycbcr_img.shape[0]):
        for y in range(ycbcr_img.shape[1]):
            [r, g, b] = ycbcr_img[x,y,:]
            rgb_img[x, y, :] = np.maximum(0, np.minimum(255, np.round(np.dot(mat_inv, ycbcr_img[x, y, :] - offset) * 255.0)))
    return rgb_img