Demonstrate the running of the following python code:

import cv$2$

import numpy as np

from scipy.spatial.distance import cdist

from skimage.transform import ProjectiveTransform, warp

import kornia.feature

import kornia.geometry.transform

image$1=$ cv$2.$imread$(\text{'}$path$\_$to$\_$your$\_$first$\_$image.jpg$\text{'})$

image$2=$ cv$2.$imread$(\text{'}$path$\_$to$\_$your$\_$second$\_$image.jpg$\text{'})$

gray$1=$ cv$2.$cvtColor$($image$1,$ cv$2.$COLOR$\_$BGR$2$GRAY$)$

gray$2=$ cv$2.$cvtColor$($image$2,$ cv$2.$COLOR$\_$BGR$2$GRAY$)$

sift $=$ cv$2.$SIFT$\_$create$()$

keypoints$1,$ descriptors$1=$ sift.detectAndCompute$($gray$1,$ None$)$

keypoints$2,$ descriptors$2=$ sift.detectAndCompute$($gray$2,$ None$)$

distances $=$ cdist$($descriptors$1,$ descriptors$2,$ 'sqeuclidean'$)$

threshold $=0\mathrm{.}5$

matches $=[]$

# Iterate through distance matrix to select matches below the threshold

for i$,$ row in enumerate$($distances$)$:

for j$,$ distance in enumerate$($row$)$:

if distance $<$ threshold:

matches.append$(($i$,$ j$))$

import numpy as np

import cv$2$

def estimate$\_$affine$\_$transform$($matched$\_$points$1,$ matched$\_$points$2)$:

$"""$

Estimate an affine transformation using a set of matched points.

$"""$

# Using cv$2.$getAffineTransform requires exactly $3$ points.

# The points need to be reshaped as $(3,2).$

if matched$\_$points$1.$shape$[0]!=3$ or matched$\_$points$2.$shape$[0]!=3$:

raise ValueError$("$Exactly $3$ points are required"$)$

transform $=$ cv$2.$getAffineTransform$($np$.$float$32($matched$\_$points$1),$ np$.$float$32($matched$\_$points$2))$

return transform

def ransac$($keypoints$1,$ keypoints$2,$ matches, num$\_$iterations$=1000,$ distance$\_$threshold$=3\mathrm{.}0)$:

$"""$

Perform RANSAC to find the best affine transformation.

:param keypoints$1$: Keypoints from the first image.

:param keypoints$2$: Keypoints from the second image.

:param matches: Matched pairs of keypoints indices.

:param num$\_$iterations: Number of RANSAC iterations.

:param distance$\_$threshold: Threshold to consider a point as an inlier.

:return: The best affine transformation and the mask of inliers.

$"""$

max$\_$inliers $=[]$

best$\_$transform $=$ None

for $\_$ in range$($num$\_$iterations$)$:

# Randomly select $3$ matches

sampled$\_$matches $=$ np$.$random.choice$($matches$,3,$ replace$=$False$)$

# Extract the matched keypoints' coordinates

pts$1=$ np$.$float$32([$keypoints$1[$m$[0]].$pt for m in sampled$\_$matches$])$

pts$2=$ np$.$float$32([$keypoints$2[$m$[1]].$pt for m in sampled$\_$matches$])$

# Estimate affine transform from $3$ pairs of matched points

M $=$ estimate$\_$affine$\_$transform$($pts$1,$ pts$2)$

# Transform all keypoints from the first image to the second image's coordinate system

pts$1\_$transformed $=$ cv$2.$transform$($np$.$array$([$keypoints$1[$m$[0]].$pt for m in matches$]).$reshape$(-1,1,2),$ M$)$

# Calculate distances between actual and transformed points

distances $=$ np$.$sqrt$($np$.$sum$(($pts$1\_$transformed $-$ np$.$array$([$keypoints$2[$m$[1]].$pt for m in matches$]).$reshape$(-1,1,2))**2,$ axis$=2)).$flatten$()$

# Determine inliers $($where distance is below threshold$)$

inliers $=$ distances $<$ distance$\_$threshold

# Update best transformation if current one has more inliers

if sum$($inliers$)>$ len$($max$\_$inliers$)$:

max$\_$inliers $=$ inliers

best$\_$transform $=$ M

return best$\_$transform, max$\_$inliers

mosaic$[$:height$1,$ :width$1]=$ image$1$

mosaic$[$:height$2,$ :width$2]=$ np$.$maximum$($mosaic$[$:height$2,$ :width$2],$ warped$\_$image$)$

# Display the color mosaic result

cv$2.$imshow$(\text{'}$Mosaic$\text{'},$ mosaic$)$

Make whatever changes needed $($preferably minor$)$ to run it and show said changes in the code.