6、DPCM编解码

目录

一、实验原理

1. DPCM编解码原理

2. PSNR的计算

二、实验代码

三、实验内容

1. bmp格式转yuv格式

2. 不同量化比特的DPCM

（1）8bit量化

（2）1，2，4bit量化

3. DPCM+熵编码和熵编码的比较

（1）编码效率

（2）概率分布图

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一、实验原理

1. DPCM编解码原理

DPCM是差分预测编码调制的缩写，是比较典型的预测编码系统。在DPCM系统中，需要注意的是预测器的输入是已经解码以后的样本。之所以不用原始样本来做预测，是因为在解码端无法得到原始样本，只能得到存在误差的样本。因此，在DPCM编码器中实际内嵌了一个解码器，如编码器中虚线框中所示。

在一个DPCM系统中，有两个因素需要设计：预测器和量化器。理想情况下，预测器和量化器应进行联合优化。实际中，采用一种次优的设计方法：分别进行线性预测器和
量化器的优化设计。 

2. PSNR的计算

PSNR（峰值信噪比）是一种度量图像失真的方式，它的单位是dB。本实验使用PSNR作为图像质量评价的指标。峰值信噪比与图像质量近似成正比关系。PSNR值越大，就代表失真越少​​​​​，图像质量越好。

 

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二、实验代码

① dpcm.h

#pragma once
#ifndef DPCM_H_
#define DPCM_H_

void DPCM(unsigned char* y_buffer, unsigned char* differ_buffer, unsigned char* rebuild_buffer, int width, int height, int bitnum);
#endif

#pragma once

② dpcm.cpp

#include
#include
#include

void DPCM(unsigned char* y_buffer, unsigned char* differ_buffer, unsigned char* rebuild_buffer, int width, int height, int bitnum)
{
	for (int i = 0; i < height; i++)
	{
		for (int j = 0; j < width; j++)
		{
			if (j == 0)
			{
				differ_buffer[i * width] = ((y_buffer[i * width] - 128) + 255) / pow(2, (double)(9 - bitnum));
				rebuild_buffer[i * width] = differ_buffer[i * width] * pow(2, (double)(9 - bitnum)) - 255 + 128;
			}
			else
			{
				differ_buffer[i * width + j] = ((y_buffer[i * width + j] - rebuild_buffer[i * width + j - 1]) + 255) / pow(2, (double)(9 - bitnum));
				rebuild_buffer[i * width + j] = differ_buffer[i * width + j] * pow(2, (double)(9 - bitnum)) - 255 + rebuild_buffer[i * width + j - 1];
			}
			if (differ_buffer[i * width + j] > 255)
				differ_buffer[i * width + j] = 255;
			if (differ_buffer[i * width + j] < 0)
				differ_buffer[i * width + j] = 0;
			if (rebuild_buffer[i * width + j] > 255)
				rebuild_buffer[i * width + j] = 255;
			if (rebuild_buffer[i * width + j] < 0)
				rebuild_buffer[i * width + j] = 0;
		}
	}
}

③ main.cpp

#include
#include
#include"math.h"
#include"DPCM.h"
void calculate_fre(unsigned char* buffer, double* frequency, int width, int height)
{
	int size = width * height;
	for (int i = 0; i < size; i++)
	{
		frequency[buffer[i]]++;
	}
	for (int k = 0; k < 256; k++)
	{
		frequency[k] /= size;
	}
}
int main(int argc, char** argv)
{
	const char* ori_name = argv[1];
	const char* differ_name = argv[2];
	const char* rebu_name = argv[3];
	int bitnum = atoi(argv[4]);
	FILE* ori_file = NULL;
	FILE* differ_file = NULL;
	FILE* rebu_file = NULL;
	if ((ori_file = fopen(ori_name, "rb")) == NULL)
		printf("Failed to open the original picture\n");
	else
		printf("succeeded to open the original picture\n");

	if ((differ_file = fopen(differ_name, "wb")) == NULL)
		printf("Failed to open the difference picture\n");
	else
		printf("succeeded to open the difference picture\n");

	if ((rebu_file = fopen(rebu_name, "wb")) == NULL)
		printf("Failed to open the rebulid picture\n");
	else
		printf("succeeded to open the rebulid picture\n");

	int width = 256;
	int height = 256;
	unsigned char* y_buffer = new unsigned char[width * height];
	unsigned char* u_buffer = new unsigned char[width * height / 4];
	unsigned char* v_buffer = new unsigned char[width * height / 4];
	unsigned char* differ_buffer = new unsigned char[width * height];
	unsigned char* rebuild_buffer = new unsigned char[width * height];
	fread(y_buffer, 1, width * height, ori_file);
	fread(u_buffer, 1, width * height / 4, ori_file);
	fread(v_buffer, 1, width * height / 4, ori_file);

	//计算原图像的概率分布
	double frequency[256] = { 0 };
	calculate_fre(y_buffer, frequency, width, height);
	FILE* orin_fre;
	orin_fre = fopen("ori_frequency.txt", "wb");
	fprintf(orin_fre, "%s\t%s\t", "symbol", "freq");
	for (int i = 0; i < 256; i++)
	{
		fprintf(orin_fre, "%d\t%f\t", i, frequency[i]);
	}

	DPCM(y_buffer, differ_buffer, rebuild_buffer, width, height, bitnum);

	//计算预测误差的概率分布
	double frequency2[256] = { 0 };
	calculate_fre(differ_buffer, frequency2, width, height);
	FILE* differ_fre;
	differ_fre = fopen("differ_frequency.txt", "wb");
	fprintf(differ_fre, "%s\t%s\t", "symbol", "freq");
	for (int i = 0; i < 256; i++)
	{
		fprintf(differ_fre, "%d\t%f\t", i, frequency2[i]);
	}
	//写入预测误差图像
	fwrite(differ_buffer, 1, width * height, differ_file);
	fwrite(u_buffer, 1, width * height / 4, differ_file);
	fwrite(v_buffer, 1, width * height / 4, differ_file);

	//写入重建图像
	fwrite(rebuild_buffer, 1, width * height, rebu_file);
	fwrite(u_buffer, 1, width * height / 4, rebu_file);
	fwrite(v_buffer, 1, width * height / 4, rebu_file);


	// 计算PSNR 
	double mse = 0;
	double psnr = 0;
	for (int i = 0; i < width * height; i++) {


		mse += pow((y_buffer[i] - rebuild_buffer[i]), 2);

	}
	mse = mse / (width * height);
	psnr = 10 * log10(pow(255, 2) / mse);
	printf("PSNR=%f", psnr);

	fclose(ori_file);
	fclose(differ_file);
	fclose(rebu_file);

	delete[] y_buffer;
	delete[] u_buffer;
	delete[] v_buffer;
	delete[] differ_buffer;
	delete[] rebuild_buffer;

	return 0;
}

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三、实验内容

1. bmp格式转yuv格式

先把bmp格式的图片转换为yuv格式：

2. 不同量化比特的DPCM

设置命令参数：

（1）8bit量化

原图	预测误差	重建图像	PSNR
			51.133820
			44.182181
			27.075617
			51.161429
			18.241522
			17.084278
			14.886163

（2）1，2，4bit量化

8bit	4bit	2bit	1bit

由此可见：量化比特数越小，重建图像质量越差。

3. DPCM+熵编码和熵编码的比较

运行huff_run.exe分别对原始图像和预测误差图像进行Huffman编码。

得到编码后的.huff文件和概率统计文本文件：

 

（1）编码效率

原始图像	原始图像大小	熵编码	压缩比	DPCM+熵编码	压缩比
Lena.yuv	96KB	69KB	71.88%	46KB	47.92%
Fruit.yuv	96KB	78KB	81.25%	43KB	44.79%
Odie.yuv	96KB	22KB	22.92%	20KB	20.83%
Noise.yuv	96KB	74KB	77.08%	77KB	80.21%
Zone.yuv	96KB	78KB	81.25%	78KB	81.25%
Clown	96KB	78KB	81.25%	49KB	51.04%
Camman	96KB	73KB	76.04%	42KB	43.75%

一般情况下，DPCM+熵编码比直接熵编码的压缩效率更高；对于个别图像，经过DPCM后再进行熵编码，压缩效率反而下降，可能是因为图像水平方向的相关性较低，不适合做DPCM。 

（2）概率分布图

原始图像概率分布	预测误差图像概率分布

经过DPCM后，预测误差图像的概率分布趋近于拉普拉斯分布，概率分布较集中，没有均匀分布，更适合用Huffman编码，因此可以DPCM+熵编码可以提高压缩效率。