Modified in running, tests successful

%% Cell type:code id:14f74f21 tags:

``` python

import numpy as np

from matplotlib import pyplot as plt

from itertools import product

import os

import sys

from PIL import Image

from scipy.optimize import minimize,linprog

# import time

# import seaborn as sns

from sklearn.neighbors import KernelDensity

# import pandas as pd

from collections import Counter

import numpy.linalg as la

```

%% Cell type:code id:c16af61f tags:

``` python

def file_extractor(dirname="images"):

    files = os.listdir(dirname)

    scenes = []

    for file in files:

        if file == '.DS_Store':

            continue

        else:

            scenes.append(os.path.join(dirname, file))

    return scenes

def image_extractor(scenes):

    image_folder = []

    for scene in scenes:

        files = os.listdir(scene)

        for file in files:

            if file[-5:] != ".tiff" or file[-7:] == "_6.tiff":

                continue

            else:

                image_folder.append(os.path.join(scene, file))

    return image_folder #returns a list of file paths to .tiff files in the specified directory given in file_extractor

def im_distribution(images, num):

    """

    Function that extracts tiff files from specific cameras and returns a list of all

    the tiff files corresponding to that camera. i.e. all pictures labeled "_7.tiff" or otherwise

    specified camera numbers.

    Parameters:

        images (list): list of all tiff files, regardless of classification. This is NOT a list of directories but

        of specific tiff files that can be opened right away. This is the list that we iterate through and

        divide.

        num (str): a string designation for the camera number that we want to extract i.e. "14" for double digits

        of "_1" for single digits.

    Returns:

        tiff (list): A list of tiff files that have the specified designation from num. They are the files extracted

        from the 'images' list that correspond to the given num.

    """

    tiff = []

    for im in images:

        if im[-7:-5] == num:

            tiff.append(im)

    return tiff

```

%% Cell type:code id:53786325 tags:

``` python

def predict_pix(tiff_image_path, difference = True):

    """

    This function predict the pixel values excluding the boundary.

    Using the 4 neighbor pixel values and MSE to predict the next pixel value

    (-1,1) (0,1) (1,1)  => relative position of the 4 other given values

    (-1,0) (0,0)        => (0,0) is the one we want to predict

    take the derivative of mean square error to solve for the system of equation

    A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]])

    A @ [a, b, c] = [-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3] where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)

    and the predicted pixel value is c.

    Input:

    tiff_image_path (string): path to the tiff file

    Return:

    image   ndarray(512 X 640): original image

    predict ndarray(325380,): predicted image excluding the boundary

    diff.   ndarray(325380,): IF difference = TRUE, difference between the min and max of four neighbors exclude the boundary

                            ELSE: the residuals of the four nearest pixels to a fitted hyperplane

    error   ndarray(325380,): difference between the original image and predicted image

    A       ndarray(3 X 3): system of equation

    """

    image_obj = Image.open(tiff_image_path)    #Open the image and read it as an Image object

    image_array = np.array(image_obj)[1:,:].astype(int)    #Convert to an array, leaving out the first row because the first row is just housekeeping data

    # image_array = image_array.astype(int)

    A = np.array([[3,0,-1],[0,3,3],[1,-3,-4]]) # the matrix for system of equation

    # where z0 = (-1,1), z1 = (0,1), z2 = (1,1), z3 = (-1,0)

    z0 = image_array[0:-2,0:-2]   # get all the first pixel for the entire image

    z1 = image_array[0:-2,1:-1]   # get all the second pixel for the entire image

    z2 = image_array[0:-2,2::]    # get all the third pixel for the entire image

    z3 = image_array[1:-1,0:-2]   # get all the forth pixel for the entire image

    # calculate the out put of the system of equation

    y0 = np.ravel(-z0+z2-z3)

    y1 = np.ravel(z0+z1+z2)

    y2 = np.ravel(-z0-z1-z2-z3)

    y = np.vstack((y0,y1,y2))

    # use numpy solver to solve the system of equations all at once

    #predict = np.floor(np.linalg.solve(A,y)[-1])

    predict = np.round(np.round((np.linalg.solve(A,y)[-1]),1))

    #Matrix system of points that will be used to solve the least squares fitting hyperplane

    points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])

    # flatten the neighbor pixlels and stack them together

    z0 = np.ravel(z0)

    z1 = np.ravel(z1)

    z2 = np.ravel(z2)

    z3 = np.ravel(z3)

    neighbor = np.vstack((z0,z1,z2,z3)).T

    if difference:

        # calculate the difference

        diff = np.max(neighbor,axis = 1) - np.min(neighbor, axis=1)

    else:

        #Compute the best fitting hyperplane using least squares

        #The res is the residuals of the four points used to fit the hyperplane (summed distance of each of the

        #points to the hyperplane), it is a measure of gradient

        f, diff, rank, s = la.lstsq(points, neighbor.T, rcond=None)

        diff = diff.astype(int)

    # calculate the error

    error = np.ravel(image_array[1:-1,1:-1])-predict

    return image_array, predict, diff, error, A

```

%% Cell type:code id:6b965751 tags:

``` python

"""

this huffman encoding code is found online

https://favtutor.com/blogs/huffman-coding

"""

class NodeTree(object):

    def __init__(self, left=None, right=None):

        self.left = left

        self.right = right

    def children(self):

        return self.left, self.right

    def __str__(self):

        return self.left, self.right

def huffman_code_tree(node, binString=''):

    '''

    Function to find Huffman Code

    '''

    if type(node) is str:

        return {node: binString}

    (l, r) = node.children()

    d = dict()

    d.update(huffman_code_tree(l, binString + '0'))

    d.update(huffman_code_tree(r, binString + '1'))

    return d

def make_tree(nodes):

    '''

    Function to make tree

    :param nodes: Nodes

    :return: Root of the tree

    '''

    while len(nodes) > 1:

        (key1, c1) = nodes[-1]

        (key2, c2) = nodes[-2]

        nodes = nodes[:-2]

        node = NodeTree(key1, key2)

        nodes.append((node, c1 + c2))

        #reverse True, decending order

        #There is a huge memory leak here, no idea how or why

        nodes = sorted(nodes, key=lambda x: x[1], reverse=True)

    return nodes[0][0]

```

%% Cell type:code id:b7561883 tags:

``` python

def huffman(tiff_image_path, num_bins=4, difference = True):

    """

    This function is used to encode the error based on the difference

    and split the difference into different bins

    Input:

    tiff_image_path     (string): path to the tiff file

    num_bins            (int): number of bins

    Return:

    huffman_encoding_list  list    (num_bins + 1): a list of dictionary

    image_array            ndarray (512, 640): original image

    new_error              ndarray (512, 640): error that includes the boundary

    diff                   ndarray (510, 638): difference of min and max of the 4 neighbors

    boundary               ndarray (2300,): the boundary values after subtracting the very first pixel value

    predict                ndarray (325380,): the list of predicted values

    bins                   list    (num_bins - 1,): a list of threshold to cut the bins

    A                      ndarray (3 X 3): system of equation

    """

    # get the image_array, etc

    image_array, predict, diff, error, A = predict_pix(tiff_image_path, difference)

    # calculate the number of points that will go in each bin

    data_points_per_bin = diff.size // num_bins

    # sort the difference and create the bins

    sorted_diff = np.sort(diff.copy())

    bins = [sorted_diff[i*data_points_per_bin] for i in range(1,num_bins)]

    # get the boundary

    boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))

    # take the difference of the boundary with the very first pixel

    boundary = boundary - image_array[0,0]

    #boundary is 1dim, so boundary[0] is just the first element

    boundary[0] = image_array[0,0]

    # huffman encode the boundary

    bound_vals_as_string = [str(i) for i in boundary]

    freq = dict(Counter(bound_vals_as_string))

    freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)

    node = make_tree(freq)

    huffman_encoding_dict = huffman_code_tree(node)

    # create a list of huffman table

    huffman_encoding_list = [huffman_encoding_dict]

    n = len(bins)

    # loop through different bins

    for i in range (0,n):

        # the first bin

        if i == 0 :

            # get the point within the bin and huffman huffman_encoding_dict

            mask = diff <= bins[i]

            line_as_string = [str(i) for i in error[mask].astype(int)]

            freq = dict(Counter(line_as_string))

            freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)

            node = make_tree(freq)

            huffman_encoding_dict = huffman_code_tree(node)

            huffman_encoding_list.append(huffman_encoding_dict)

        # the middle bins

        else:

            # get the point within the bin and huffman huffman_encoding_dict

            mask = diff > bins[i-1]

            new_error = error[mask]

            mask2 = diff[mask] <= bins[i]

            line_as_string = [str(i) for i in new_error[mask2].astype(int)]

            freq = dict(Counter(line_as_string))

            freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)

            node = make_tree(freq)

            huffman_encoding_dict = huffman_code_tree(node)

            huffman_encoding_list.append(huffman_encoding_dict)

    # the last bin

    # get the point within the bin and huffman huffman_encoding_dict

    mask = diff > bins[-1]

    line_as_string = [str(i) for i in error[mask].astype(int)]

    freq = dict(Counter(line_as_string))

    freq = sorted(freq.items(), key=lambda x: x[1], reverse=True)

    node = make_tree(freq)

    huffman_encoding_dict = huffman_code_tree(node)

    huffman_encoding_list.append(huffman_encoding_dict)

    # create a error matrix that includes the boundary (used in encoding matrix)

    new_error = np.copy(image_array)

    new_error[1:-1,1:-1] = np.reshape(error,(510, 638))

    keep = new_error[0,0]

    new_error[0,:] = new_error[0,:] - keep

    new_error[-1,:] = new_error[-1,:] - keep

    new_error[1:-1,0] = new_error[1:-1,0] - keep

    new_error[1:-1,-1] = new_error[1:-1,-1] - keep

    new_error[0,0] = keep

    # huffman_encoding_list = list(set(huffman_encoding_list))

    diff = np.reshape(diff,(510,638))

    # return the huffman dictionary

    return huffman_encoding_list, image_array, new_error, diff, boundary, predict, bins, A

```

%% Cell type:code id:2eb774d2 tags:

``` python

def encoder(error, list_dic, diff, bound, bins):

    """

    This function encode the matrix with huffman coding tables

    Input:

    error     (512, 640): a matrix with all the errors

    list_dic  (num_dic + 1,): a list of huffman coding table

    bound     (2300,): the boundary values after subtracting the very first pixel value

    bins       (num_bins - 1,): a list of threshold to cut the bins

    Return:

    encoded   (512, 640): encoded matrix

    """

    # copy the error matrix (including the boundary)

    encoded = np.copy(error).astype(int).astype(str).astype(object)

    #diff = np.reshape(diff,(510,638))

    # loop through all the pixel to encode

    for i in range(encoded.shape[0]):

        for j in range(encoded.shape[1]):

            if i == 0 or i == encoded.shape[0]-1 or j == 0 or j == encoded.shape[1]-1:

                encoded[i][j] = list_dic[0][encoded[i][j]]

            elif diff[i-1][j-1] <= bins[0]:

                encoded[i][j] = list_dic[1][encoded[i][j]]

            elif diff[i-1][j-1] <= bins[1] and diff[i-1][j-1] > bins[0]:

                encoded[i][j] = list_dic[2][encoded[i][j]]

            elif diff[i-1][j-1] <= bins[2] and diff[i-1][j-1] > bins[1]:

                encoded[i][j] = list_dic[3][encoded[i][j]]

            else:

                encoded[i][j] = list_dic[4][encoded[i][j]]

    return encoded

```

%% Cell type:code id:8eeb40d0 tags:

``` python

def decoder(A, encoded_matrix, list_dic, bins, use_diff):

    """

    This function decodes the encoded_matrix.

    Input:

    A               (3 X 3): system of equation

    list_dic        (num_dic + 1,): a list of huffman coding table

    encoded_matrix  (512, 640): encoded matrix

    bins            (num_bins - 1,): a list of threshold to cut the bins

    Return:

    decode_matrix   (512, 640): decoded matrix

    """

    # change the dictionary back to list

    # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins

    the_keys0 = list(list_dic[0].keys())

    the_values0 = list(list_dic[0].values())

    the_keys1 = list(list_dic[1].keys())

    the_values1 = list(list_dic[1].values())

    the_keys2 = list(list_dic[2].keys())

    the_values2 = list(list_dic[2].values())

    the_keys3 = list(list_dic[3].keys())

    the_values3 = list(list_dic[3].values())

    the_keys4 = list(list_dic[4].keys())

    the_values4 = list(list_dic[4].values())

    #Matrix system of points that will be used to solve the least squares fitting hyperplane

    points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]])

    decode_matrix = np.zeros((512,640))

    # loop through all the element in the matrix

    for i in range(decode_matrix.shape[0]):

        for j in range(decode_matrix.shape[1]):

            # if it's the very first pixel on the image

            if i == 0 and j == 0:

                decode_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])])

                print(encoded_matrix[i][j])

                print(the_values0.index(encoded_matrix[i,j]))

                print(int(the_keys0[the_values0.index(encoded_matrix[i,j])]))

            # if it's on the boundary (any of the 4 edges)

            elif i == 0 or i == decode_matrix.shape[0]-1 or j == 0 or j == decode_matrix.shape[1]-1:

                decode_matrix[i][j] = int(the_keys0[the_values0.index(encoded_matrix[i,j])]) + decode_matrix[0][0]

            # if not the boundary

            else:

                # predict the image with the known pixel value

                z0 = decode_matrix[i-1][j-1]

                z1 = decode_matrix[i-1][j]

                z2 = decode_matrix[i-1][j+1]

                z3 = decode_matrix[i][j-1]

                y0 = int(-z0+z2-z3)

                y1 = int(z0+z1+z2)

                y2 = int(-z0-z1-z2-z3)

                y = np.vstack((y0,y1,y2))

                if use_diff:

                    difference = max(z0,z1,z2,z3) - min(z0,z1,z2,z3)

                else:

                    f, difference, rank, s = la.lstsq(points, [z0,z1,z2,z3], rcond=None)

                    difference = difference.astype(int)

                predict = np.round(np.round(np.linalg.solve(A,y)[-1][0],1))

                # add on the difference by searching the dictionary

                # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins

                if difference <= bins[0]:

                    decode_matrix[i][j] = int(the_keys1[the_values1.index(encoded_matrix[i,j])]) + int(predict)

                elif difference <= bins[1] and difference > bins[0]:

                    decode_matrix[i][j] = int(the_keys2[the_values2.index(encoded_matrix[i,j])]) + int(predict)

                elif difference <= bins[2] and difference > bins[1]:

                    decode_matrix[i][j] = int(the_keys3[the_values3.index(encoded_matrix[i,j])]) + int(predict)

                else:

                    decode_matrix[i][j] = int(the_keys4[the_values4.index(encoded_matrix[i,j])]) + int(predict)

    return decode_matrix.astype(int)

```

%% Cell type:code id:f959fe93 tags:

``` python

def compress_rate(image_array, new_error, diff, bound, huffman_encoding_list, bins):

    '''

    This function is used to calculate the compression rate.

    Input:

    image_array      (512, 640): original_core image

    new_error  (512, 640): error that includes the boundary

    diff       (510, 638): difference of min and max of the 4 neighbors

    bound      (2300,): the boundary values after subtracting the very first pixel value

    huffman_encoding_list   (num_dic + 1,): a list of huffman coding table

    bins       (num_bins - 1,): a list of threshold to cut the bins

    Return:

    compression rate

    '''

    # the bits for the original image

    o_len = 0

    # the bits for the compressed image

    c_len = 0

    # initializing the varible

    #this was unused

    # im = np.reshape(image,(512, 640))

    real_boundary = np.hstack((image_array[0,:],image_array[-1,:],image_array[1:-1,0],image_array[1:-1,-1]))

    #Bryce's notes: Why are they all reshaped?

    original_core = image_array[1:-1,1:-1].reshape(-1)

    diff = diff.reshape(-1)

    error = new_error[1:-1,1:-1].reshape(-1)

    # calculate the bit for boundary

    for i in range(0,len(bound)):

        o_len += len(bin(real_boundary[i])[2:])

        c_len += len(huffman_encoding_list[0][str(bound[i])])

    # calculate the bit for the pixels inside the boundary

    for i in range(0,len(original_core)):

        # for the original image

        o_len += len(bin(original_core[i])[2:])

        # check the difference and find the coresponding huffman table

        # !!!!!WARNING!!!! has to change this part, eveytime you change the number of bins

        if diff[i] <= bins[0]:

            c_len += len(huffman_encoding_list[1][str(int(error[i]))])

        elif diff[i] <= bins[1] and diff[i] > bins[0]:

            c_len += len(huffman_encoding_list[2][str(int(error[i]))])

        elif diff[i] <= bins[2] and diff[i] > bins[1]:

            c_len += len(huffman_encoding_list[3][str(int(error[i]))])

        else:

            c_len += len(huffman_encoding_list[4][str(int(error[i]))])

    return c_len/o_len

```

%% Cell type:code id:3e0e9742 tags:

``` python

scenes = file_extractor()

images = image_extractor(scenes)

list_dic, image, new_error, diff, bound, predict, bins, A = huffman(images[0], 4, False)

encoded_matrix = encoder(new_error, list_dic, diff, bound, bins)

reconstruct_image = decoder(A, encoded_matrix, list_dic, bins, False)

print(np.allclose(image, reconstruct_image))

print(len(list_dic))

```

%% Output

    11100100000

    499

    22275

    True

    5

%% Cell type:code id:004e8ba8 tags:

``` python

compress_rate(image, new_error, diff, bound, list_dic, bins)

```

%% Output

    0.4232928466796875

%% Cell type:code id:a282f9e6 tags:

``` python

print(sys.getsizeof(encoded_matrix))

print(sys.getsizeof(reconstruct_image))

```