信息論 哈夫曼編碼 與 菲諾編碼的實現（對一幅BMP格式的灰度圖像（個人 證件照片）進行二元霍夫曼編碼和譯碼。并進行編碼效率的計算，對一幅BMP格式的灰度圖像進行二 元Fano編碼、譯碼 ）

原始圖片

灰度處理

編碼生成的碼表：noldList:

解碼后圖片

編碼結果

fano編碼實現

源碼：

哈夫曼編碼實現

#Writen by james ruslinimport json from math import log from tkinter import * from PIL import Image pixelFrequen = {} #全局 字典 nodeList = [] codeList = {} E1 = NONE E2 = NONEclass node:def __init__(self, leftChild=None, rightChild=None, father=None, value=0, count=None):self.leftChild = leftChildself.rightChild = rightChildself.father = fatherself.value = valueself.count = countdef calculater(p):return -log(p, 2)*pdef efficient(image):row = image.size[0]col = image.size[1]allnumber = row*colh = 0for key in pixelFrequen.keys():h += calculater(pixelFrequen[key] / allnumber)L = 0for key in pixelFrequen.keys():L += len(codeList[str(key)]) * pixelFrequen[key] / allnumberR = h/Lreturn Rdef toGray(string):im = Image.open(string)im = im.convert('L')im.save('C:/Users/user/Desktop/newGray.bmp')return im #返回圖片‘對象’def counter(list):global pixelFrequenfor i in list:if i in pixelFrequen.keys():pixelFrequen[i] += 1else:pixelFrequen[i] = 1def leafNodes(pixelValue): #通過組合數組，構造葉子for i in range(len(pixelValue)):nodeList.append(node(value=pixelValue[i][1], count=str(pixelValue[i][0])))return nodeListdef sortNodes(nodeList):nodeList = sorted(nodeList, key=lambda node: node.value) #按照node.value對node排序return nodeListdef huffmanTree(nodeList):nodeList = sortNodes(nodeList)while len(nodeList) != 1:left = nodeList[0]right = nodeList[1]new = node()new.leftChild = leftnew.rightChild = rightleft.father = newright.father = newnew.value = left.value + right.valuenodeList.remove(left)nodeList.remove(right)nodeList.append(new)nodeList = sortNodes(nodeList)return nodeListdef 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 pixelFrequenpixel = pixelFrequenpixel = sorted(pixel.items(), key=lambda item: item[1]) #以列表返回可遍歷的(鍵, 值) 元組數組。leafList = leafNodes(pixel)head = huffmanTree(leafList)[0] #leafList里的結點相互連接，形成樹global codeListfor i in leafList:codingNode = icodeList.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.fatherresult = ''for i in range(width):for j in range(height):for key, value in codeList.items():if str(imMatrix[i, j]) == key:result = result + valuefile = 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("編碼結果已寫入文件")def decode(width, height):file = open('C:/Users/user/Desktop/result.txt', 'r')codeGet = file.readlines()[0].strip('\n')len = codeGet.__len__()pixelReturn = []global codeListi = 0current = ""current += codeGet[0]flag = 0while i < len:for key in codeList.keys():if current == codeList[key]:pixelReturn.append(key)flag = 1breakif flag == 1:if i == len - 1:breakelse:i = i + 1current = codeGet[i]flag = 0else:i += 1if i < len:current += codeGet[i]else:breakc = Image.new('L', (width, height))t = 0for i in range(width):for j in range(height):c.putpixel((i, j), (int(pixelReturn[t])))t = t + 1c.save('C:/Users/user/Desktop/ReturnedHuffman.bmp')def core():global E1global E2root = Tk(className='劉暢2017212184')root.geometry("600x600+100+0") # 800寬度，800高度，x,y坐標，左上角label = Label(root)label['text'] = '二元huffman編碼'label.pack()L1 = Label(root, text="圖像文件的位置:")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="編碼效率為:")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='開始編碼', command=main)# 收到消息執行go函數button.place(x=250, y=400, width=70, height=50)root.mainloop()def main():global E1global E2string = 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編碼實現

# Writen by Liu import copy from math import log from tkinter import * from PIL import Image import jsonpixelFrequent = {}#鍵為像素值，鍵值為數量 nodeList = [] #存放結點 codeList = {} #鍵為像素值，鍵值為碼字 E1 = NONE E2 = NONEclass Node:def __init__(self, leftChild = None, rightChild = None, father = None, value = 0, count = None):self.leftChild = leftChildself.rightChild = rightChildself.father = fatherself.value = valueself.count = countdef calculater(p):return -log(p, 2)*pdef efficient(image):row = image.size[0]col = image.size[1]allnumber = row * colh = 0for key in pixelFrequent.keys():h += calculater(pixelFrequent[key]/allnumber)L = 0for key in pixelFrequent.keys():L += len(codeList[key])*pixelFrequent[key]/allnumberR = h/Lreturn Rdef toGray(string):im = Image.open(string)im = im.convert('L')im.save('C:/Users/user/Desktop/newGray.bmp')return im # 返回圖片‘對象’def counter(list): # 對像素字典初始化，鍵為像素，鍵值為其對應的數量global pixelFrequentfor i in list:if i in pixelFrequent.keys():pixelFrequent[i] += 1else:pixelFrequent[i] = 1def leafNode(pixelValueList):for i in range(len(pixelValueList)):nodeList.append(Node(value = pixelValueList[i][1], count = pixelValueList[i][0]))return nodeListdef sortNode(codeList):codeList = sorted(codeList, key=lambda Node: Node.value)return codeListdef initcodeList(list): # list = pixelFrequent(keys()) #初始化編碼表，鍵值為空串global codeListlength = len(list)for i in range(length):codeList.setdefault(list[i], "")def sortList(list): # 通過字典的鍵值進行字典的訪問排序global pixelFrequentTemplist = sorted(pixelFrequent.items(), key=lambda item: item[1])length = len(Templist)for i in range(length):list.append(Templist[i][0])return listdef FanoProgress(paralist): # list = pixelFrequent(keys())，對list排序 ，對編碼表進行更新，遞歸list = copy.copy(paralist)global pixelFrequentglobal codeListvalue_all = 0length = len(list)if length == 1:return 0for i in range(length):value_all += pixelFrequent[list[i]]count1 = 0count2 = 0for i in range(int((length*2)/3)):count1 += pixelFrequent[list[i]]distance = 0distance2 = 0if value_all - 2 * count1 > 0:while True:count1 = count1 + pixelFrequent[list[int((length*2)/3)+distance]]distance += 1if value_all - 2 * count1 <= 0:count2 = count1 - pixelFrequent[list[int((length*2)/3)+distance - 1]]breakif abs(value_all - 2 * count1) > abs(value_all - 2 * count2):distance -= 1else:distance -= 0listlower = 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 += 1if value_all - 2 * count1 >= 0:count2 = count1 + pixelFrequent[list[int((length*2)/3) - distance2]]breakif abs(value_all - 2 * count1) > abs(value_all - 2 * count2):distance2 -= 1else:distance2 -= 0listlower = 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): # 讀取像素列表，對應編碼表進行編碼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 = "" # 編碼結果，對每個像素點進行Fano編碼for i in range(width):for j in range(height):for key, values in codeList.items():if imMatrix[i, j] == key:result = result + valuesfile = 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("編碼結果已寫入文件")def decode(width, height):file = open('C:/Users/user/Desktop/FanoResult.txt', 'r')codeGet = file.readlines()[0].strip('\n')len = codeGet.__len__()pixelReturn = []global codeListi = 0current = ""current += codeGet[0]flag = 0while i < len:for key in codeList.keys():if current == codeList[key]:pixelReturn.append(key)flag = 1breakif flag == 1:if i == len - 1:breakelse:i = i + 1current = codeGet[i]flag = 0else:i += 1if i < len:current += codeGet[i]else:breakc = Image.new('L', (width, height))t = 0for i in range(width):for j in range(height):c.putpixel((i, j), pixelReturn[t])t = t + 1c.save('C:/Users/user/Desktop/Returnedfano.bmp')def core():global E1global E2root = Tk(className='劉暢2017212184')root.geometry("600x600+100+0") # 800寬度，800高度，x,y坐標，左上角label = Label(root)label['text'] = '二元Fano編碼'label.pack()L1 = Label(root, text="圖像文件的位置:")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="編碼效率為:")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='開始編碼', command=main)# 收到消息執行go函數button.place(x=250, y=400, width=70, height=50)root.mainloop()def main():global E1global E2string = E1.get()image = toGray(string)Fanocoder(image)decode(image.size[0], image.size[1])R = efficient(image)E2.insert(INSERT, str(R)) core()

如果需要實驗報告，進行詳細的算法解釋，以及獲取完整的工程，到這里下載

總結

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