流媒体之色彩转换——RGB(X)与YUV之间转换

最新推荐文章于 2025-06-04 13:21:58 发布

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#色彩转换 #RGB转YUV #YUV转RGB #查表转换

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本文详细介绍了RGB32到RGB24的转换方法，以及RGB与YUV格式相互转换的多种算法，包括常规转换、去浮点转换、去浮点去乘法转换和查表转换，并提供了C++代码实现。

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文章目录

一：RGB32转RGB24

RGB32与RGB24相比多个Alpha分量，因此在转化的时候可以选择直接丢弃Alpha分量，也可以选择将r、g和b分别乘以归一化的Alpha因子。例如RGBA转RGB：

void rgba_to_rgb(const uint8_t *src, uint8_t *dst, uint32_t width, uint32_t height, bool alpha)
{
	uint8_t *src_ptr = const_cast<uint8_t *>(src);
	uint8_t *dst_ptr = dst;

	float a = 1.f;
	int src_pos = 0;
	int dst_pos = 0;
	if (alpha) {
		for (int i = 0; i < width; i++) {
			for (int j = 0; j < height; j++) {
				src_pos = i * 4 + j;
				dst_pos = i * 3 + j;
				a = (*(src_ptr + src_pos + 3)) / 255.f;
				*(dst_ptr + dst_pos) = *(src_ptr + src_pos) * a;
				*(dst_ptr + dst_pos + 1) = *(src_ptr + src_pos + 1) * a;
				*(dst_ptr + dst_pos + 2) = *(src_ptr + src_pos + 2) * a;
			}
		}
	}
	else {
		for (int i = 0; i < width; i++) {
			for (int j = 0; j < height; j++) {
				src_pos = i * 4 + j;
				dst_pos = i * 3 + j;
				*(dst_ptr + dst_pos) = *(src_ptr + src_pos);
				*(dst_ptr + dst_pos + 1) = *(src_ptr + src_pos + 1);
				*(dst_ptr + dst_pos + 2) = *(src_ptr + src_pos + 2);
			}
		}
	}
}

二：YUV与RGB相互转换

Keith Jack’s的书《Video Demystified》(ISBN 1-878707-09-4) 给出的转换公式：

RGB->YUV：

$Y=0.257R+0.504G+0.098B+16\\ Cr=V=0.439R-0.368G-0.071B+128\\ Cb=U=-0.148R-0.291G+0.439B+128$

YUV->RGB：

$B=1.164(Y-16)+2.018(U-128)\\ G=1.164(Y-16)-0.813(V-128)-0.391(U-128)\\ R=1.164(Y-16)+1.596(V-128)$

上述式子RGB范围为 $[0, 255]$ ；Y范围为 $[16, 235]$ ；UV范围为 $[16, 239]$ 。计算超出范围后需要截断处理。

CCIR 601定义的转换公式为：

RGB->YUV：

$Y=0.299R+0.587G+0.114B\\ Cr=V=0.713(R-Y)=0.500R-0.419G-0.081B\\ Cb=U=0.564(B-Y)=-0.169R-0.331G+0.500B$

YUV->RGB：

$R=Y+1.403V\\ G=Y-0.344U-0.714V\\ B=Y+1.770U$

上述式子RGB范围为 $[0, 1]$ ；Y范围为 $[0, 1]$ ；Cr和Cb范围为 $[- 0.5, 0.5]$ 。

如果把RGB和YUV的范围都缩放到 $[0, 255]$ ，常用的转换公式为：

RGB->YUV：

$Y=0.299R+0.587G+0.114B\\ Cr=V=0.500R-0.419G-0.081B+128\\ Cb=U=-0.169R-0.331G+0.500B+128$

YUV->RGB：

$R=Y+1.403*(V-128)\\ G=Y-0.343*(U-128)-0.714*(V-128)\\ B=Y+1.770*(U-128)$

2.1 YUV->RGB

2.1.1 常规转换

按照公式进行常规运算，包含浮点运算和乘法运算。

void yuv_to_rgb(uint8_t y, uint8_t u, uint8_t v, uint8_t *r, uint8_t *g, uint8_t *b)
{
	int _r = y + 1.403 * (v - 128);
	int _g = y - 0.343 * (u - 128) - 0.714 * (v - 128);
	int _b = y + 1.770 * (u - 128);

	*r = _r > 255 ? 255 : (_r < 0 ? 0 : (uint8_t)_r);
	*g = _g > 255 ? 255 : (_g < 0 ? 0 : (uint8_t)_g);
	*b = _b > 255 ? 255 : (_b < 0 ? 0 : (uint8_t)_b);
}

2.1.2 去浮点转换

去除转换公式中的浮点运算，但会有精度损失：
$R=Y+1.403*(V-128)\\ G=Y-0.343*(U-128)-0.714*(V-128)\\ B=Y+1.770*(U-128)$
转换为：
$V'=V-128\\ U'=U-128\\ R=Y+1.403*V'=Y+V'+0.403*V'≈Y+V'+((V'*103)>>8)\\ G=Y-0.343*U'-0.714*V'≈Y-((U'*88)>>8)-((V'*183)>>8)\\ B=Y+1.770*U'≈Y+U'+((U'*198)>>8)$

void yuv_to_rgb_faster(uint8_t y, uint8_t u, uint8_t v,
                       uint8_t *r, uint8_t *g, uint8_t *b)
{
	int _u = u - 128;
	int _v = v - 128;

	int _r = y + _v + ((_v * 103) >> 8);
	int _g = y - ((_u * 88) >> 8) - ((_v * 183) >> 8);
	int _b = y + _u + ((_u * 198) >> 8);

	*r = _r > 255 ? 255 : (_r < 0 ? 0 : (uint8_t)_r);
	*g = _g > 255 ? 255 : (_g < 0 ? 0 : (uint8_t)_g);
	*b = _b > 255 ? 255 : (_b < 0 ? 0 : (uint8_t)_b);
}

2.1.3 去浮点去乘法转换

接上面优化，去除乘法操作（改乘法为右移操作）：
$1))>>8)\\ =Y+V'+(((V'<<6)+(V'<<5)+(V'<<2)+(V'<<1)+V')>>8)\\ G≈Y-((U'*(64 + 16 + 8))>>8)-((V'*(128+32+16+4+2+1))>>8)\\ =Y-(((U'<<6)+(U'<<4)+(U'<<3)>>8)-(((V'<<7)+(V'<<5)+(V'<<4)+(V'<<2)+(V'<<1)+V')>>8)\\ B≈Y+U'+((U'*(128+64+4+2))>>8)\\ =Y+U'+(((U'<<7)+(U'<<6)+(U'<<2)+(U'<<1))>>8)$

void yuv_to_rgb_speed(uint8_t y, uint8_t u, uint8_t v,
                      uint8_t *r, uint8_t *g, uint8_t *b)
{
	int _u = u - 128;
	int _v = v - 128;

	int _r = y + _v + (((_v << 6) + (_v << 5) + (_v << 2) + (_v << 1) + _v) >> 8);
	int _g = y - (((_u << 6) + (_u << 4) + (_u << 3)) >> 8) - (((_v << 7) + (_v << 5)
		+ (_v << 4) + (_v << 2) + (_v << 1) + _v) >> 8);
	int _b = y + _u + (((_u << 7) + (_u << 6) + (_u << 2) + (_u << 1)) >> 8);

	*r = _r > 255 ? 255 : (_r < 0 ? 0 : (uint8_t)_r);
	*g = _g > 255 ? 255 : (_g < 0 ? 0 : (uint8_t)_g);
	*b = _b > 255 ? 255 : (_b < 0 ? 0 : (uint8_t)_b);
}

2.1.4 查表转换

查表法为事先将计算结果存储在表中，之后在表中查找。由于Y、U和V分量为 $[0, 255]$ 之间的离散值，所以可以采用查表法：

uint8_t g_r[256][256];
uint8_t g_g[256][256][256];
uint8_t g_b[256][256];
void setup_yuv_to_rgb_table()
{
	// R = Y + 1.403 * (V - 128);
	// g_r[Y][V]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			int r = i + 1.403 * (j - 128);
			g_r[i][j] = r > 255 ? 255 : (r < 0 ? 0 : (uint8_t)r);
		}
	}

	// G = Y - 0.343 * (U - 128) - 0.714 * (V - 128);
	// g_g[Y][U][V]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			for (int k = 0; k < 256; k++) {
				int g = i - 0.343 * (j - 128) - 0.714 * (k - 128);
				g_g[i][j][k] = g > 255 ? 255 : (g < 0 ? 0 : (uint8_t)g);
			}
		}
	}
	
	// B = Y + 1.770 * (U - 128);
	// g_b[Y][U]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			int b = i + 1.770 * (j - 128);
			g_b[i][j] = b > 255 ? 255 : (b < 0 ? 0 : (uint8_t)b);
		}
	}
}

void yuv_to_rgb_table(uint8_t y, uint8_t u, uint8_t v,
                      uint8_t *r, uint8_t *g, uint8_t *b)
{
	*r = g_r[y][v];
	*g = g_g[y][u][v];
	*b = g_b[y][u];
}

2.1.5 测试

void test_yuv_to_rgb()
{
	uint8_t y = 100, u = 100, v = 100;
	uint8_t r = 0, g = 0, b = 0;
	uint64_t loop = 1000000000;

	// Normal
	auto time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		yuv_to_rgb(y, u, v, &r, &g, &b);
	}
	std::cout << std::to_string(r) << ", " << std::to_string(g) << " ," << std::to_string(b) << std::endl;
	std::chrono::duration<double> time_spend = std::chrono::system_clock::now() - time_start;
	double time_cost = time_spend.count() * 1000;
	std::cout << "Normal Time: " << time_cost << " ms" << std::endl;

	// Faster
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		yuv_to_rgb_faster(y, u, v, &r, &g, &b);
	}
	std::cout << std::to_string(r) << ", " << std::to_string(g) << " ," << std::to_string(b) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Faster Time: " << time_cost << " ms" << std::endl;

	// Speed
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		yuv_to_rgb_speed(y, u, v, &r, &g, &b);
	}
	std::cout << std::to_string(r) << ", " << std::to_string(g) << " ," << std::to_string(b) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Speed Time: " << time_cost << " ms" << std::endl;

	// Table
	setup_yuv_to_rgb_table();
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		yuv_to_rgb_table(y, u, v, &r, &g, &b);
	}
	std::cout << std::to_string(r) << ", " << std::to_string(g) << " ," << std::to_string(b) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Table Time: " << time_cost << " ms" << std::endl;
}

测试结果：
在这里插入图片描述
移位操作替代乘法操作的优化实际运行结果并不一定好于乘法算法，另外Release模式下要去除全程序优化，否则时间测量无效。

2.2 RGB->YUV

2.2.1 常规转换

按照公式进行常规运算，包含浮点运算和乘法运算。

void rgb_to_yuv(uint8_t r, uint8_t g, uint8_t b, uint8_t *y, uint8_t *u, uint8_t *v)
{
	int _y = 0.299 * r + 0.587 * g + 0.114 * b;
	int _u = -0.169 * r - 0.331 * g + 0.500 * b + 128;
	int _v = 0.500 * r - 0.419 * g - 0.081 * b + 128;

	*y = _y > 255 ? 255 : (_y < 0 ? 0 : (uint8_t)_y);
	*u = _u > 255 ? 255 : (_u < 0 ? 0 : (uint8_t)_u);
	*v = _v > 255 ? 255 : (_v < 0 ? 0 : (uint8_t)_v);
}

2.2.2 去浮点转换

$Y=0.299R+0.587G+0.114B\\ Cr=V=0.500R-0.419G-0.081B+128\\ Cb=U=-0.169R-0.331G+0.500B+128$
转化为：
$Y=0.299R+0.587G+0.114B=(77R+150G+29B)>>8\\ Cr=V=0.500R-0.419G-0.081B+128=(128R-107G-21B+32768)>>8\\ Cb=U=-0.169R-0.331G+0.500B+128=(-43R-85G+128B+32768)>>8$

void rgb_to_yuv_faster(uint8_t r, uint8_t g, uint8_t b, uint8_t *y, uint8_t *u, uint8_t *v)
{
	int _y = ((77 * r + 150 * g + 29 * b) >> 8);
	int _u = ((128 * r - 107 * g - 21 * b + 32768) >> 8);
	int _v = ((-43 * r - 85 * g + 128 * b + 32768) >> 8);

	*y = _y > 255 ? 255 : (_y < 0 ? 0 : (uint8_t)_y);
	*u = _u > 255 ? 255 : (_u < 0 ? 0 : (uint8_t)_u);
	*v = _v > 255 ? 255 : (_v < 0 ? 0 : (uint8_t)_v);
}

2.2.3 去浮点去乘法转换

$Y=(R<<6+R<<3+R<<2+R+G<<7+G<<4+G<<2+G<<1+B<<4+B<<3+B<<2+B)>>8\\ U=(R<<7-G<<6-G<<5-G<<3-G<<1-G-B<<4-B<<2-B+32768)>>8\\ V=(-R<<5-R<<3-R<<1-R-G<<6-G<<4-G<<2-G+B<<7+32768)>>8$

void rgb_to_yuv_speed(uint8_t r, uint8_t g, uint8_t b, uint8_t *y, uint8_t *u, uint8_t *v)
{
	int _y = (((r << 6) + (r << 3) + (r << 2) + r + (g << 7) + (g << 4) + (g << 2) + (g << 1)
		+ (b << 4) + (b << 3) + (b << 2) + b) >> 8);
	int _u = (((r << 7) - (g << 6) - (g << 5) - (g << 3) - (g << 1) - g
		- (b << 4) - (b << 2) - b + 32768) >> 8);
	int _v = ((-(r << 5) - (r << 3) - (r << 1) - r - (g << 6) - (g << 4) - (g << 2) - g
		+ (b << 7) + 32768) >> 8);

	*y = _y > 255 ? 255 : (_y < 0 ? 0 : (uint8_t)_y);
	*u = _u > 255 ? 255 : (_u < 0 ? 0 : (uint8_t)_u);
	*v = _v > 255 ? 255 : (_v < 0 ? 0 : (uint8_t)_v);
}

2.2.4 查表转换

事先存储计算结果，转换时直接查表：

uint8_t g_y[256][256][256];
uint8_t g_u[256][256][256];
uint8_t g_v[256][256][256];
void setup_rgb_to_yuv_table()
{
	// Y = 0.299 * R + 0.587 * G + 0.114 * B;
	// g_y[r][g][b]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			for (int k = 0; k < 256; k++) {
				int y = 0.299 * i + 0.587 * j + 0.114 * k;
				g_y[i][j][k] = y > 255 ? 255 : (y < 0 ? 0 : (uint8_t)y);
			}
		}
	}

	// U = -0.169 * R - 0.331 * G + 0.500 * B + 128;
	// g_u[r][g][b]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			for (int k = 0; k < 256; k++) {
				int u = -0.169 * i - 0.331 * j + 0.500 * k + 128;
				g_u[i][j][k] = u > 255 ? 255 : (u < 0 ? 0 : (uint8_t)u);
			}
		}
	}

	// V = 0.500 * R - 0.419 * G - 0.081 * B + 128;
	// g_v[r][g][b]
	for (int i = 0; i < 256; i++) {
		for (int j = 0; j < 256; j++) {
			for (int k = 0; k < 256; k++) {
				int v = 0.500 * i - 0.419 * j - 0.081 * k + 128;
				g_v[i][j][k] = v > 255 ? 255 : (v < 0 ? 0 : (uint8_t)v);
			}
		}
	}
}

void rgb_to_yuv_table(uint8_t r, uint8_t g, uint8_t b, uint8_t *y, uint8_t *u, uint8_t *v)
{
	*y = g_y[r][g][b];
	*u = g_u[r][g][b];
	*v = g_v[r][g][b];
}

2.2.5 测试

void test_rgb_to_yuv()
{
	uint8_t r = 100, g = 100, b = 100;
	uint8_t y = 0, u = 0, v = 0;
	uint64_t loop = 1000000000;

	// Normal
	auto time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		rgb_to_yuv(r, g, b, &y, &u, &v);
	}
	std::cout << std::to_string(y) << ", " << std::to_string(u) << " ," << std::to_string(v) << std::endl;
	std::chrono::duration<double> time_spend = std::chrono::system_clock::now() - time_start;
	double time_cost = time_spend.count() * 1000;
	std::cout << "Normal Time: " << time_cost << " ms" << std::endl;

	// Faster
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		rgb_to_yuv_faster(r, g, b, &y, &u, &v);
	}
	std::cout << std::to_string(y) << ", " << std::to_string(u) << " ," << std::to_string(v) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Faster Time: " << time_cost << " ms" << std::endl;

	// Speed
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		rgb_to_yuv_speed(r, g, b, &y, &u, &v);
	}
	std::cout << std::to_string(y) << ", " << std::to_string(u) << " ," << std::to_string(v) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Speed Time: " << time_cost << " ms" << std::endl;

	// Table
	setup_rgb_to_yuv_table();
	time_start = std::chrono::system_clock::now();
	for (uint64_t i = 0; i < loop; i++) {
		rgb_to_yuv_table(r, g, b, &y, &u, &v);
	}
	std::cout << std::to_string(y) << ", " << std::to_string(u) << " ," << std::to_string(v) << std::endl;
	time_spend = std::chrono::system_clock::now() - time_start;
	time_cost = time_spend.count() * 1000;
	std::cout << "Table Time: " << time_cost << " ms" << std::endl;
}