# import necessary packages

# reading$/$writing image files

from skimage import io

from skimage import color

# displaying images and plots

import matplotlib as mpl

import matplotlib.pyplot as plt

# array operations

import numpy as np

# mathematical calculations

import math

# data frame operations

import pandas as pd

# STEP $1$ Quantize the image with $32$ so that there are only $8$ intensity levels

# ADD YOUR CODE HERE

# display the quantized image

def my$\_$imgLuminance$($imgRGB$)$:

# make sure it is a color image

dim$\_$img $=$ imgRGB.shape$[2]$

assert dim$\_$img $>=3$

# get the luminance data

if dim$\_$img $==3$:

imgLum $=$ color.rgb$2$gray$($imgRGB$)$

else:

# ignore the alpha channel

imgLum $=$ color.rgb$2$gray$($imgRGB$[$:$,$:$,0$:$3])$

imgLum $=$ np$.$round$($imgLum $*255,0)$

imgLum $=$ np$.$minimum$($imgLum$,255)$

imgLum $=$ np$.$maximum$($imgLum$,0)$

imgLum $=$ imgLum.astype$(\text{'}$uint$8\text{'})$

return imgLum

def my$\_$Histogram$($img$,$ nBit$)$:

nLevel $=2**$nBit

valMax $=0$

for i in range$(8-$nBit,$8)$:

valMax $+=2**$i

imgQuan $=$ img & valMax

hist $=$ np$.$zeros$(($nLevel$,),$ dtype$=$int$)$

valMin $=2**(8-$nBit$)$

for n in range$($nLevel$)$:

hist$[$n$]=$ np$.$count$\_$nonzero$($imgQuan$==$n$*$valMin$)$

return hist, imgQuan, nLevel

if imgRGB.ndim $>=3$:

imgLum $=$ my$\_$imgLuminance$($imgRGB$)$

else:

imgLum $=$ imgRGB

nBit $=3$

histLum, imgLumQuan, numLevel $=$ my$\_$Histogram$($imgLum$,$ nBit$)$

print$("----------------------")$

print$("$Level:$",$ nLevel$)$

print$("----------------------")$

plt$.$figure$($figsize$=(5,5))$

plt$.$subplot$(1,1,1)$

plt$.$title$(\text{'}$Quantize Image'$)$

plt$.$imshow$($imgLumQuan$,$ cmap$=$'gray'$)$

plt$.$axis$(\text{'}$off$\text{'})$

plt$.$show$()$

plt$.$close$()$

# STEP $2$ Define a vector source by combining two consecutive pixels

# and calculate the probabilities of these vector symbols

# ADD YOUR CODE HERE

# notes:

# since each pixel has $8$ intensity levels, there will be $8$x$8=64$ symbols in the vector source.

# the symbols for the vector source could be represented as $"$aa$,$ ab$,$ ac$,...,$ hf$,$ fg$,$ hh$."$

# there are a total of $512*512/2=131,072$ sample vectors in the input image to calculate the histogram

# calculate the histogram of the vector symbols

# obtain the pdf by normalizing the histogram

# plot the pdf of this vector source