Merge branch 'master' of https://git.elphel.com/nathaniel/image-compression

%% Cell type:code id:dbef8759 tags:

``` python

import numpy as np

from prediction_MSE_Scout import file_extractor, image_extractor, im_distribution

from matplotlib import pyplot as plt

from itertools import product

import os

import sys

from PIL import Image

from scipy.optimize import minimize

from time import time

from numpy import linalg as la

from scipy.stats import gaussian_kde

import seaborn as sns

import pywt

from collections import Counter

```

%% Cell type:code id:9ed20f84 tags:

``` python

def plot_hist(tiff_list, i=0):

    """

    This function is the leftovers from the first attempt to plot histograms.

    As it stands it needs some work in order to function again. We will

    fix this later. 1/25/22

    """

    image = tiff_list[i]

    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_int = image.astype(int)

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

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

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

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

    z3 = image_int[1:-1,0:-2]   # get all the fourth 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.linalg.solve(A,y)[-1]

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

    #predict = []

    # 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

    # calculate the difference

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

    diff = np.pad(diff.reshape(510,638), pad_width=1)

    # flatten the image to a vector

    small_image = image_int[1:-1,1:-1]

    #Reshape the predictions to be a 2D array

    predict = np.pad(predict.reshape(510,638), pad_width=1)

    """predict[0,:] = image[0,:]

    predict[:,0] = image[:,0]

    predict[:,-1] = image[:,-1]

    predict[-1,:] = image[-1,:]"""

    #Calculate the error between the original image and our predictions

    #Note that we only predicted on the inside square of the original image, excluding

    #The first row, column and last row, column

    #error = (image_int - predict).astype(int) #Experiment

    #this one works

    error = image_int - predict

    return predict, diff, image_int, error, A

```

%% Cell type:code id:ba2881d9 tags:

``` python

scenes = file_extractor()

images = image_extractor(scenes)

num_images = im_distribution(images, "11")

```

%% Cell type:code id:11e95c34 tags:

``` python

predict, diff, im, err, A = plot_hist(num_images, 0)

```

%% Cell type:code id:434e4d2f tags:

``` python

def reconstruct(error, A):

    """

    Function that reconstructs the original image

    from the error matrix and using the predictive

    algorithm developed in the encoding.

    Parameters:

        error (array): matrix of errors computed in encoding. Same

                       shape as the original image (512, 640) in this case

        A (array): Matrix used for the system of equations to create predictions

    Returns: cd cdcd

        image (array): The reconstructed image

    """

    new_e = error.copy()

    rows, columns = new_e.shape

    for r in range(1, rows-1):

        for c in range(1, columns-1):

            z0, z1, z2, z3 = new_e[r-1][c-1], new_e[r-1][c], new_e[r-1][c+1], new_e[r][c-1]

            y = np.vstack((-z0+z2-z3, z0+z1+z2, -z0-z1-z2-z3))

            #Real solution that works, DO NOT DELETE

            #new_e[r][c] = int(np.ceil(new_e[r][c] + np.linalg.solve(A,y)[-1]))

            new_e[r][c] = np.round(new_e[r][c] + np.linalg.solve(A,y)[-1], 1)

    return new_e.astype(int)

```

%% Cell type:code id:bf427edd tags:

%% Cell type:code id:4f4a5a35 tags:

``` python

new_error = reconstruct(err, A)

```

%% Output

    -19

    [22286.]

    22285.0

    [22266.]

    22266.999999999996

%% Cell type:code id:5edcf208 tags:

%% Cell type:code id:6d95ffce tags:

``` python

first = []

second = []

third = []

fourth = []

for i in range(1,diff.shape[0]-1):

    for j in range(1,diff.shape[1]-1):

        if diff[i][j] <= 50:

            first.append(np.abs(err[i][j]))

        elif diff[i][j] > 50 and diff[i][j] <= 100:

            second.append(np.abs(err[i][j]))

        elif diff[i][j] > 100 and diff[i][j] <= 200:

            third.append(np.abs(err[i][j]))

        else:

            fourth.append(np.abs(err[i][j]))

```

%% Cell type:code id:953375c5 tags:

%% Cell type:code id:1c848109 tags:

``` python

plt.hist(first)

plt.show()

print(np.max(first))

plt.hist(second)

plt.show()

print(np.max(second))

plt.hist(third)

plt.show()

print(np.max(third))

plt.hist(fourth)

plt.show()

print(np.max(fourth))

```

%% Output

    124

    181

    216

    251

%% Cell type:code id:90387cb9 tags:

%% Cell type:code id:139938e3 tags:

``` python

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:e477d0c8 tags:

``` python

def enc_experiment(images, plot=True):

    origin, predict, diff, error, A = plot_hist(images, 2)

    image = Image.open(images[0])    #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)

    new_error = np.copy(image)

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

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

    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

    new_error = np.ravel(new_error)

    if plot:

        plt.hist(new_error[1:],bins=100)

        plt.show()

    #ab_error = np.abs(new_error)

    #string = [str(i) for i in ab_error]

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

    #string = [str(i) for i in np.arange(0,5)] + [str(i) for i in np.arange(0,5)] + [str(i) for i in np.arange(0,2)]*2

    freq = dict(Counter(string))

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

    node = make_tree(freq)

    encoding_dict = huffman_code_tree(node)

    #encoded = ["1"+encoding[str(-i)] if i < 0 else "0"+encoding[str(i)] for i in error]

    #print(time.time()-start)

    encoded = new_error.reshape((512,640)).copy().astype(str)

    #encoded = np.zeros_like(new_error.reshape((512,640))).astype(str)

    print(encoded)

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

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

            if i == 0 and j == 0:

                encoded[i][j] = encoded[i][j]

            else:

                #print(encoding_dict[encoded[i][j]])

                encoded[i][j] = encoding_dict[encoded[i][j]]

                #print(encoded[i][j])

    return encoding_dict, encoded, new_error.reshape((512,640))

    #print(encoding)

```

%% Cell type:code id:fd8e96a5 tags:

``` python

encode_dict, encoding, error = enc_experiment(images, plot=False)

```

%% Output

    15

    [['22541' '-10' '14' ... '32' '48' '33']

     ['7' '67' '-21' ... '-1' '-1' '77']

     ['7' '-15' '-3' ... '10' '-45' '58']

     ...

     ['49' '82' '-2' ... '-64' '5' '151']

     ['27' '-33' '18' ... '47' '-16' '208']

     ['17' '0' '-5' ... '138' '207' '226']]

%% Cell type:code id:7ebd8dd8 tags:

``` python

print(encoding[0][100])

print(error[0][100])

print(encode_dict['92'])

```

%% Output

    11110111110

    92

    11110111110001

%% Cell type:code id:a6a579b7 tags:

``` python

def decoder(A, encoded_matrix, encoding_dict):

    """

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

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

    """

    error_matrix = encoded_matrix.copy()

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

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

            if i == 0 and j == 0:

                error_matrix[i][j] = encoded_matrix[i][j]

            else:

                error_matrix[i][j] = encoding_dict.

```