predic_pix_lstsq added

%% 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 time

```

%% 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[-4:] == ".jp4" or file[-7:] == "_6.tiff":

            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:aceba613 tags:

``` python

def predict_pix(tiff_image):

    """

    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 (string): path to the tiff file

    Return:

    image   (512 X 640): original image

    predict (325380,): predicted image exclude the boundary

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

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

    A       (3 X 3): system of equation

    """

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

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

    image = image.astype(int)

    print(image.shape)

    # use

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

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

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

    z3 = image[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))

    # 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

    # calculate the difference

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

    # calculate the error

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

    return image, predict, diff, error, A

```

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

``` python

"""

this huffman coding 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))

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

    return nodes[0][0]

```

%% Cell type:code id:b7561883 tags:

``` python

def huffman(image, num_bins=4):

    """

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

    and split the difference into different bins

    Input:

    image    (string): path to the tiff file

    num_bins (int): number of bins

    Return:

    list_dic   (num_bins + 1): a list of dictionary

    image      (512, 640): original image

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

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

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

    predict    (325380,): the list of predicted values

    bins       (num_bins)

    A       (3 X 3): system of equation

    """

    # get the prediction error and difference

    image, predict, diff, error, A = predict_pix(image)

    # get the number of points in each bins

    data_points_per_bin = len(diff) // num_bins

    # sort the difference and create the bins

    sorted_diff = diff.copy()

    sorted_diff.sort()

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

    # get the boundary

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

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

    boundary = boundary - image[0,0]

    boundary[0] = image[0,0]

    # huffman encode the boundary

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

    freq = dict(Counter(string))

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

    node = make_tree(freq)

    encode = huffman_code_tree(node)

    # create a list of huffman table

    list_dic = [encode]

    n = len(bins)

    # loop through different bins

    for i in range (0,n):

        # the fisrt bin

        if i == 0 :

            # get the point within the bin and huffman encode

            mask = diff <= bins[i]

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

            freq = dict(Counter(string))

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

            node = make_tree(freq)

            encode = huffman_code_tree(node)

            list_dic.append(encode)

        # the middle bins

        else:

            # get the point within the bin and huffman encode

            mask = diff > bins[i-1]

            new_error = error[mask]

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

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

            freq = dict(Counter(string))

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

            node = make_tree(freq)

            encode = huffman_code_tree(node)

            list_dic.append(encode)

    # the last bin

    # get the point within the bin and huffman encode

    mask = diff > bins[-1]

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

    freq = dict(Counter(string))

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

    node = make_tree(freq)

    encode = huffman_code_tree(node)

    list_dic.append(encode)

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

    new_error = np.copy(image)

    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

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

    # return the huffman dictionary

    return list_dic, image, new_error, diff, boundary, predict, bins, A

```

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

``` python

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

    # 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):

    """

    Function that accecpts the prediction matrix A for the linear system,

    the encoded matrix of error values, and the encoding dicitonary.

    """

    # 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())

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

    # loop through all the element in the matrix

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

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

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

            if i == 0 and j == 0:

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

            # if it's on the boundary

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

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

            # if not the boundary

            else:

                # predict the image with the known pixel value

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

                z1 = error_matrix[i-1][j]

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

                z3 = error_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))

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

                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]:

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

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

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

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

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

                else:

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

    return error_matrix.astype(int)

```

%% Cell type:code id:f959fe93 tags:

``` python

def compress_rate(image, error, diff, bound, list_dic, bins):

    # the bits for the original image

    o_len = 0

    # the bits for the compressed image

    c_len = 0

    # initializing the varible

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

    real_b = np.hstack((im[0,:],im[-1,:],im[1:-1,0],im[1:-1,-1]))

    original = im[1:-1,1:-1].reshape(-1)

    diff = diff.reshape(-1)

    # calculate the bit for boundary

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

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

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

    # calculate the bit for the pixels inside the boundary

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

        # for the original image

        o_len += len(bin(original[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(list_dic[1][str(int(error[i]))])

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

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

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

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

        else:

            c_len += len(list_dic[5][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)

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

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

print(np.allclose(image, reconstruct_image))

print(len(list_dic))

```

%% Output

    (512, 640)

    True

    5

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

``` python

print(bins)

```

%% Output

    [26, 40, 62]

%% Cell type:code id:a282f9e6 tags:

``` python

def predict_pix_lstsq(tiff_list):

    """

    Predict the next pixel using a fit hyperplane of the four closest pixels.

    The gradient measure in this function is the summed distance to the fitted hyperplane

    of each of the four points, aka the residual from the least squares function. The previous

    predict_pix function uses the difference between the minimal and maximal pixels of the surrounding

    four.

    """

    image = tiff_list

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

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

    image = image.astype(int)

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

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

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

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

    z3 = image[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.round(np.round((np.linalg.solve(A,y)[-1]),1)) #round the solution to the nearest integer so that encoding/decoding is easier

    points = np.array([[-1,-1,1], [-1,0,1], [-1,1,1], [0,-1,1]]) #Matrix system of points that will be used to solve the least squares fitting hyperplane

    # flatten the neighbor pixels 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

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

    # calculate the difference

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

    # flatten the image to a vector

    image = np.ravel(image[1:-1,1:-1])

    error = image-predict

    return image, predict, res, error, A, diff

```

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

``` python

import numpy as np

from matplotlib import pyplot as plt

from itertools import product