import numpy as np

arr = np.random.randint(0, 256, (200, 200), dtype=np.uint8)

def func(arr1d):
    kernel = np.ones(3) / 3
    return np.convolve(arr1d, kernel, mode='same')

first_pass = np.apply_along_axis(func, axis=0, arr=arr)
final_result = np.apply_along_axis(func, axis=1, arr=first_pass)