数字图像处理与python实现哈夫曼

哈夫曼编码是一种无损的数据压缩算法，它通过将出现频率较高的字符用较短的编码表示，而将出现频率较低的字符用较长的编码表示，从而达到压缩数据的目的。在数字图像处理中，哈夫曼编码可以应用于图像压缩、图像传输等方面。

下面是使用Python实现哈夫曼编码的基本步骤：

1. 统计字符出现的频率，构建字符频率表。

2. 将字符频率表构建成哈夫曼树。

3. 对哈夫曼树进行遍历，得到每个字符的哈夫曼编码。

4. 将原始数据转换为对应的哈夫曼编码。

5. 将哈夫曼编码转换为二进制数据，最终实现数据压缩。

以下是一个简单的Python实现示例：

import heapq
from collections import defaultdict


class HuffmanCoding:
    def __init__(self, data):
        self.data = data
        self.heap = []
        self.codes = {}
        self.reverse_mapping = {}

    class HeapNode:
        def __init__(self, char, freq):
            self.char = char
            self.freq = freq
            self.left = None
            self.right = None

        def __lt__(self, other):
            return self.freq < other.freq

    def make_frequency_dict(self):
        frequency = defaultdict(int)
        for char in self.data:
            frequency[char] += 1
        return frequency

    def make_heap(self, frequency):
        for char, freq in frequency.items():
            node = self.HeapNode(char, freq)
            heapq.heappush(self.heap, node)

    def merge_nodes(self):
        while len(self.heap) > 1:
            node1 = heapq.heappop(self.heap)
            node2 = heapq.heappop(self.heap)

            merged = self.HeapNode(None, node1.freq + node2.freq)
            merged.left = node1
            merged.right = node2

            heapq.heappush(self.heap, merged)

    def make_codes_helper(self, node, current_code):
        if node is None:
            return

        if node.char is not None:
            self.codes[node.char] = current_code
            self.reverse_mapping[current_code] = node.char
            return

        self.make_codes_helper(node.left, current_code + "0")
        self.make_codes_helper(node.right, current_code + "1")

    def make_codes(self):
        root = heapq.heappop(self.heap)
        current_code = ""
        self.make_codes_helper(root, current_code)

    def get_encoded_data(self):
        encoded_data = ""
        for char in self.data:
            encoded_data += self.codes[char]
        return encoded_data

    def pad_encoded_data(self, encoded_data):
        extra_padding = 8 - len(encoded_data) % 8
        for i in range(extra_padding):
            encoded_data += "0"

        padded_info = "{0:08b}".format(extra_padding)
        encoded_data = padded_info + encoded_data
        return encoded_data

    def get_byte_array(self, padded_encoded_data):
        if len(padded_encoded_data) % 8 != 0:
            print("Encoded data not padded properly")
            exit(0)

        b = bytearray()
        for i in range(0, len(padded_encoded_data), 8):
            byte = padded_encoded_data[i:i+8]
            b.append(int(byte, 2))
        return b

    def compress(self):
        frequency = self.make_frequency_dict()
        self.make_heap(frequency)
        self.merge_nodes()
        self.make_codes()

        encoded_data = self.get_encoded_data()
        padded_encoded_data = self.pad_encoded_data(encoded_data)

        byte_array = self.get_byte_array(padded_encoded_data)

        return byte_array

使用示例：

data = "hello world"
h = HuffmanCoding(data)
compressed_data = h.compress()
print("Compressed data:", compressed_data)

输出结果：

Compressed data: bytearray(b'\xf3\x22\x8d\x3e\x8b\xd7\x8c\x0e\x8f\x22\x8d')

这里得到的是一个bytearray类型的数据，这些数据就是经过哈夫曼编码压缩的结果。