Write a function that saves the image as a specified file: $(15\backslash \%)$

$-$ In the parameter lists, it supplies an image filename and output filename

$-$ Load the image and convert it to the grayscale

$-$ Blur the image

$-$ Run the Sobel edge detection algorithm on the blurred image, with applying both vertical and horizontal filters.

$-$ Run the Canny edge detection algorithm on the blurred image

$-$ Stack the three images in a column

$-$ Save the result as the specified output filename. Do not show the plots.

This problem is about image processing and data visualization.

Note: There are multiple ways in stacking images. You may consider plt $.$ subplot, or cv$2.$vconcat.

Code:

$```$

#

import numpy as np

import cv$2$

import matplotlib.pyplot as plt

# Problem $2$

def problem$\_2($image$\_$filename, output$="$q$2.$jpg$")$:

# write your logic here

plt$.$savefig$($output$)$ # do not show the plt

$```$