new compression

%% Cell type:code id: 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

from sklearn.neighbors import KernelDensity

from collections import Counter

import numpy.linalg as la

```

%% Cell type:code id: 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: 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

```

%% Cell type:code id: 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]

def decode_string(huffman_string, the_keys, the_values):

    for i in range(len(huffman_string)):

        try:

            return (int(the_keys[the_values.index(huffman_string[:i+1])]),huffman_string[i+1:])

        except:

            pass

```

%% Cell type:code id: tags:

``` python

def make_dictionary(tiff_image_path_list, 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

    """

    list_of_all_vals = []

    huffman_encoding_list = []

    for i in range(num_bins+1):

        list_of_all_vals.append([])

    for i, tiff_image_path in enumerate(tiff_image_path_list):

        # get the image_array, etc

        image_array, predict, diff, error= 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 = [12,60,180]

        # 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

        for j in boundary:

            list_of_all_vals[0].append(str(j))

        # create a list of huffman table

        n = len(bins)

        # loop through different bins

        for k in range (0,n):

            # the first bin

            if k == 0 :

                # get the point within the bin and huffman huffman_encoding_dict

                mask = diff <= bins[k]

                for j in error[mask].astype(int):

                    list_of_all_vals[k+1].append(str(j))

            # the middle bins

            else:

                # get the point within the bin and huffman huffman_encoding_dict

                mask = diff > bins[k-1]

                new_error = error[mask]

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

                for j in new_error[mask2].astype(int):

                    list_of_all_vals[k+1].append(str(j))

        # the last bin

        # get the point within the bin and huffman huffman_encoding_dict

        mask = diff > bins[-1]

        for j in error[mask].astype(int):

            list_of_all_vals[-1].append(str(j))

    for item in list_of_all_vals:

        freq = dict(Counter(item))

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

        node = make_tree(freq)

        huffman_encoding_list.append(huffman_code_tree(node))

        # 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,bins

```

%% Cell type:code id: 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= 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)]

    bins = [12,60,180]

    # 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

```

%% Cell type:code id: 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

    """

    returnable_encode = ""

    # 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:

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

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

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

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

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

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

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

            else:

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

    return returnable_encode

```

%% Cell type:code id: tags:

``` python

# def bitstring_to_bytes(s):

#     v = int(s, 2)

#     b = bytearray()

#     while v:

#         b.append(v & 0xff)

#         v >>= 8

#     return bytes(b[::-1])

def bitstring_to_bytes(input_string):

    int_array = []

    length_of_string = len(input_string)

    while length_of_string >= 8:

        int_array.append(int(input_string[:8],2))

        input_string = input_string[8:]

        length_of_string = len(input_string)

    if length_of_string > 0:

        int_array.append(int(input_string,2))

    print(int_array[-12:])

        zerobuffer = ""

        for _ in range(8-length_of_string):

            zerobuffer += "0"

        int_array.append(int(input_string+zerobuffer,2))

    # print(int_array[0:20])

    # print(int_array[-12:])

    return bytes(int_array)

```

%% Cell type:code id: tags:

``` python

def decoder(encoded_string, 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

    """

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

    # change the dictionary back to list

    # !!!!!WARNING!!!! has to change this part, everytime 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:

                colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)

                decode_matrix[i][j] = colorvalue

            # 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:

                colorvalue, encoded_string = decode_string(encoded_string,the_keys=the_keys0, the_values=the_values0)

                decode_matrix[i][j] = colorvalue + 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]