信息论 哈夫曼编码 与 菲诺编码的实现（对一幅BMP格式的灰度图像（个人 证件照片）进行二元霍夫曼编码和译码。并进行编码效率的计算，对一幅BMP格式的灰度图像进行二 元Fano编码、译码 ）

原始图片

灰度处理

编码生成的码表：noldList:

解码后图片

编码结果

fano编码实现

源码：

哈夫曼编码实现

#Writen by james ruslin


import json
from math import log
from tkinter import *
from PIL import Image
pixelFrequen = {} #全局 字典
nodeList = []
codeList = {}
E1 = NONE
E2 = NONE


class node:
    def __init__(self, leftChild=None, rightChild=None, father=None, value=0, count=None):
        self.leftChild = leftChild
        self.rightChild = rightChild
        self.father = father
        self.value = value
        self.count = count

def calculater(p):
    return -log(p, 2)*p


def efficient(image):
    row = image.size[0]
    col = image.size[1]
    allnumber = row*col
    h = 0
    for key in pixelFrequen.keys():
        h += calculater(pixelFrequen[key] / allnumber)
    L = 0
    for key in pixelFrequen.keys():
        L += len(codeList[str(key)]) * pixelFrequen[key] / allnumber
    R = h/L
    return R


def toGray(string):
    im = Image.open(string)
    im = im.convert('L')
    im.save('C:/Users/user/Desktop/newGray.bmp')
    return im       #返回图片‘对象’


def counter(list):
    global pixelFrequen
    for i in list:
        if i in pixelFrequen.keys():
            pixelFrequen[i] += 1
        else:
            pixelFrequen[i] = 1


def leafNodes(pixelValue): #通过组合数组，构造叶子
    for i in range(len(pixelValue)):
        nodeList.append(node(value=pixelValue[i][1], count=str(pixelValue[i][0])))

    return nodeList


def sortNodes(nodeList):
    nodeList = sorted(nodeList, key=lambda node: node.value) #按照node.value对node排序
    return nodeList

def huffmanTree(nodeList):
    nodeList = sortNodes(nodeList)
    while len(nodeList) != 1:
        left = nodeList[0]
        right = nodeList[1]
        new = node()
        new.leftChild = left
        new.rightChild = right
        left.father = new
        right.father = new
        new.value = left.value + right.value
        nodeList.remove(left)
        nodeList.remove(right)
        nodeList.append(new)
        nodeList = sortNodes(nodeList)
    return nodeList


def huffmanCoder(image):
    width = image.size[0]
    height = image.size[1]
    imMatrix = image.load()
    list = []
    for i in range(width):
        for j in range(height):
            list.append(imMatrix[i, j])

    counter(list)
    global pixelFrequen
    pixel = pixelFrequen
    pixel = sorted(pixel.items(), key=lambda item: item[1])  #以列表返回可遍历的(键, 值) 元组数组。
    leafList = leafNodes(pixel)
    head = huffmanTree(leafList)[0]  #leafList里的结点相互连接，形成树
    global codeList
    for i in leafList:
        codingNode = i
        codeList.setdefault(i.count, "")
        while codingNode != head:
            if codingNode == codingNode.father.leftChild:
                codeList[i.count] = '0' + codeList[i.count]
            else:
                codeList[i.count] = '1' + codeList[i.count]
            codingNode = codingNode.father
    result = ''
    for i in range(width):
        for j in range(height):
            for key, value in codeList.items():
                if str(imMatrix[i, j]) == key:
                    result = result + value

    file = open('C:/Users/user/Desktop/result.txt', 'w')
    file.write(result)
    file1 = open('C:/Users/user/Desktop/codeList.json', 'w')
    jsObj = json.dumps(codeList)
    file1.write(jsObj)
    print("编码结果已写入文件")


def decode(width, height):
    file = open('C:/Users/user/Desktop/result.txt', 'r')
    codeGet = file.readlines()[0].strip('\n')
    len = codeGet.__len__()
    pixelReturn = []
    global codeList

    i = 0
    current = ""
    current += codeGet[0]
    flag = 0
    while i < len:
        for key in codeList.keys():
            if current == codeList[key]:
                pixelReturn.append(key)
                flag = 1
                break
        if flag == 1:
            if i == len - 1:
                break
            else:
                i = i + 1
                current = codeGet[i]
                flag = 0
        else:
            i += 1
            if i < len:
                current += codeGet[i]
            else:
                break

    c = Image.new('L', (width, height))
    t = 0
    for i in range(width):
        for j in range(height):
            c.putpixel((i, j), (int(pixelReturn[t])))
            t = t + 1
    c.save('C:/Users/user/Desktop/ReturnedHuffman.bmp')

def core():
    global E1
    global E2
    root = Tk(className='刘畅2017212184')
    root.geometry("600x600+100+0")  # 800宽度，800高度，x,y坐标，左上角
    label = Label(root)
    label['text'] = '二元huffman编码'
    label.pack()
    L1 = Label(root, text="图像文件的位置:")
    L1.place(x=130, y=100, width=100, height=50)
    E1 = Entry(root, bd=5)
    E1.place(x=270, y=100, width=300, height=40)

    L2 = Label(root, text="编码效率为:")
    L2.place(x=130, y=200, width=100, height=50)
    E2 = Text(root)
    E2.place(x=270, y=200, width=150, height=40)

    button = Button(root, text='开始编码', command=main)
    # 收到消息执行go函数
    button.place(x=250, y=400, width=70, height=50)
    root.mainloop()


def main():
        global E1
        global E2
        string = E1.get()
        print(string)
        image = toGray(string)
        huffmanCoder(image)
        row = image.size[0]
        col = image.size[1]

        decode(image.size[0], image.size[1])
        e = efficient(image)
        E2.insert(INSERT, str(e))
core() 

fano编码实现

# Writen by Liu
import copy
from math import log
from tkinter import *
from PIL import Image
import json


pixelFrequent = {}#键为像素值，键值为数量
nodeList = []   #存放结点
codeList = {}   #键为像素值，键值为码字
E1 = NONE
E2 = NONE


class Node:

    def __init__(self, leftChild = None, rightChild = None, father = None, value = 0, count = None):
        self.leftChild = leftChild
        self.rightChild = rightChild
        self.father = father
        self.value = value
        self.count = count


def calculater(p):
    return -log(p, 2)*p


def efficient(image):
    row = image.size[0]
    col = image.size[1]
    allnumber = row * col
    h = 0
    for key in pixelFrequent.keys():
        h += calculater(pixelFrequent[key]/allnumber)
    L = 0
    for key in pixelFrequent.keys():
        L += len(codeList[key])*pixelFrequent[key]/allnumber
    R = h/L
    return R


def toGray(string):
    im = Image.open(string)
    im = im.convert('L')
    im.save('C:/Users/user/Desktop/newGray.bmp')
    return im       # 返回图片‘对象’


def counter(list):  # 对像素字典初始化，键为像素，键值为其对应的数量
    global pixelFrequent
    for i in list:
        if i in pixelFrequent.keys():
            pixelFrequent[i] += 1
        else:
            pixelFrequent[i] = 1


def leafNode(pixelValueList):
    for i in range(len(pixelValueList)):
        nodeList.append(Node(value = pixelValueList[i][1], count = pixelValueList[i][0]))
    return nodeList


def sortNode(codeList):
    codeList = sorted(codeList, key=lambda Node: Node.value)
    return codeList


def initcodeList(list):  # list = pixelFrequent(keys())  #初始化编码表，键值为空串
    global codeList
    length = len(list)
    for i in range(length):
        codeList.setdefault(list[i], "")


def sortList(list):  # 通过字典的键值进行字典的访问排序
    global pixelFrequent
    Templist = sorted(pixelFrequent.items(), key=lambda item: item[1])
    length = len(Templist)
    for i in range(length):
        list.append(Templist[i][0])
    return list


def FanoProgress(paralist):  # list = pixelFrequent(keys())，对list排序 ，对编码表进行更新，递归
    list = copy.copy(paralist)
    global pixelFrequent
    global codeList
    value_all = 0
    length = len(list)
    if length == 1:
        return 0
    for i in range(length):
        value_all += pixelFrequent[list[i]]
    count1 = 0
    count2 = 0

    for i in range(int((length*2)/3)):
        count1 += pixelFrequent[list[i]]

    distance = 0
    distance2 = 0
    if value_all - 2 * count1 > 0:
        while True:
            count1 = count1 + pixelFrequent[list[int((length*2)/3)+distance]]
            distance += 1
            if value_all - 2 * count1 <= 0:
                count2 = count1 - pixelFrequent[list[int((length*2)/3)+distance - 1]]
                break

        if abs(value_all - 2 * count1) > abs(value_all - 2 * count2):
            distance -= 1
        else:
            distance -= 0


        listlower = copy.copy(list)
        listHigher = copy.copy(list)



        for i in range(int((length*2)/3) + distance):
            codeList[list[i]] = codeList[list[i]] + '1'
            listHigher.remove(list[i])
        for j in range(int((length*2)/3) + distance, length):
            codeList[list[j]] = codeList[list[j]] + '0'
            listlower.remove(list[j])
        FanoProgress(listlower)
        FanoProgress(listHigher)

    elif value_all - 2 * count1 < 0:
        while True:
            count1 = count1 - pixelFrequent[list[int((length*2)/3) - distance2-1]]
            distance2 += 1
            if value_all - 2 * count1 >= 0:
                count2 = count1 + pixelFrequent[list[int((length*2)/3) - distance2]]

                break
        if abs(value_all - 2 * count1) > abs(value_all - 2 * count2):
            distance2 -= 1
        else:
            distance2 -= 0


        listlower = copy.copy(list)
        listHigher = copy.copy(list)



        for i in range(int((length*2)/3) - distance2):
            codeList[list[i]] += '1'
            listHigher.remove(list[i])
        for j in range(int((length*2)/3) - distance2, length):
            codeList[list[j]] += '0'
            listlower.remove(list[j])
        FanoProgress(listlower)
        FanoProgress(listHigher)

    else:


        listlower = copy.copy(list)
        listHigher = copy.copy(list)



        for i in range(int((length*2)/3)):
            codeList[list[i]] += '1'
            listHigher.remove(list[i])
        for j in range(int((length*2)/3), length):
            codeList[list[j]] += '0'
            listlower.remove(list[j])
        FanoProgress(listlower)
        FanoProgress(listHigher)


def Fanocoder(im):  # 读取像素列表，对应编码表进行编码
    imMatrix = im.load()
    width = im.size[0]
    height = im.size[1]

    pixelList = []
    for i in range(width):
        for j in range(height):
            pixelList.append(imMatrix[i, j])
    counter(pixelList)
    list = []
    list = sortList(list)
    initcodeList(list)
    FanoProgress(list)
    result = ""  # 编码结果，对每个像素点进行Fano编码
    for i in range(width):
        for j in range(height):
            for key, values in codeList.items():
                if imMatrix[i, j] == key:
                    result = result + values
    file = open('C:/Users/user/Desktop/FanoResult.txt', 'w')
    file.write(result)
    file1 = open('C:/Users/user/Desktop/FanoCodeList.json', 'w')
    jsObj = json.dumps(codeList)
    file1.write(jsObj)
    print("编码结果已写入文件")


def decode(width, height):
    file = open('C:/Users/user/Desktop/FanoResult.txt', 'r')
    codeGet = file.readlines()[0].strip('\n')
    len = codeGet.__len__()
    pixelReturn = []
    global codeList

    i = 0
    current = ""
    current += codeGet[0]
    flag = 0
    while i < len:
        for key in codeList.keys():
            if current == codeList[key]:
                pixelReturn.append(key)
                flag = 1
                break
        if flag == 1:
            if i == len - 1:
                break
            else:
                i = i + 1
                current = codeGet[i]
                flag = 0
        else:
            i += 1
            if i < len:
                current += codeGet[i]
            else:
                break

    c = Image.new('L', (width, height))
    t = 0

    for i in range(width):
        for j in range(height):
            c.putpixel((i, j), pixelReturn[t])
            t = t + 1
    c.save('C:/Users/user/Desktop/Returnedfano.bmp')


def core():
    global E1
    global E2
    root = Tk(className='刘畅2017212184')
    root.geometry("600x600+100+0")  # 800宽度，800高度，x,y坐标，左上角
    label = Label(root)
    label['text'] = '二元Fano编码'
    label.pack()
    L1 = Label(root, text="图像文件的位置:")
    L1.place(x=130, y=100, width=100, height=50)
    E1 = Entry(root, bd=5)
    E1.place(x=270, y=100, width=300, height=40)

    L2 = Label(root, text="编码效率为:")
    L2.place(x=130, y=200, width=100, height=50)
    E2 = Text(root)
    E2.place(x=270, y=200, width=150, height=40)

    button = Button(root, text='开始编码', command=main)
    # 收到消息执行go函数
    button.place(x=250, y=400, width=70, height=50)
    root.mainloop()



def main():
    global E1
    global E2
    string = E1.get()
    image = toGray(string)
    Fanocoder(image)
    decode(image.size[0], image.size[1])
    R = efficient(image)
    E2.insert(INSERT, str(R))
core() 

如果需要实验报告，进行详细的算法解释，以及获取完整的工程，到这里下载

本文地址：http://www.51sjk.com/Upload/Articles/1/0/254/254632_20210628001156428.jpg