x265中除了传统的RD Cost外，还有Psy-RdCost和SSIM-RdCost，这三种RD Cost的使用是通过命令行参数控制的，如果不设置，则默认使用的是Psy-RDCost,相关命令行参数如下：
- –[no-]psy-rd <0…5.0> Strength of psycho-visual rate distortion optimization, 0 to disable. Default 2.0
- –[no-]psy-rdoq <0…50.0> Strength of psycho-visual optimization in RDO quantization, 0 to disable. Default 0.0
- –[no-]ssim-rd Enable ssim rate distortion optimization, 0 to disable. Default disabled
- –dynamic-rd <0…4.0> Strength of dynamic RD, 0 to disable. Default 0.00
一、Psycho-visual Rate Distortion
x265中计算Psy-RD Cost的公式如下：
其中D指的是重建块的失真，psyRD表示的是psy-RDCost的强度，psyCost是指的是重建块和原始块AC能量的差，Rate指的是编码当前块所需的码率，x265中计算PsyRDCost的代码如下：
inline uint64_t calcPsyRdCost(sse_t distortion, uint32_t bits, uint32_t psycost) const
{
#if X265_DEPTH < 10
X265_CHECK((bits <= (UINT64_MAX / m_lambda2)) && (psycost <= UINT64_MAX / (m_lambda * m_psyRd)),
"calcPsyRdCost wrap detected dist: %u, bits: %u, lambda: " X265_LL ", lambda2: " X265_LL "\n",
distortion, bits, m_lambda, m_lambda2);
#else
X265_CHECK((bits <= (UINT64_MAX / m_lambda2)) && (psycost <= UINT64_MAX / (m_lambda * m_psyRd)),
"calcPsyRdCost wrap detected dist: " X265_LL ", bits: %u, lambda: " X265_LL ", lambda2: " X265_LL "\n",
distortion, bits, m_lambda, m_lambda2);
#endif
return distortion + ((m_lambda * m_psyRd * psycost) >> 24) + ((bits * m_lambda2) >> 8);
}即psy-RD Cost比传统的RD Cost计算多了一项m_lambda * m_psyRd * psycost，其中m_lambda和QP有关，m_psyRd由命令行参数psy-rd控制，表示Psy-RD Cost的强度
/* Scale PSY RD factor by a slice type factor */
static const uint32_t psyScaleFix8[3] = { 300, 256, 96 }; /* B, P, I */
m_psyRd = (m_psyRdBase * psyScaleFix8[slice.m_sliceType]) >> 8;m_rdCost.setPsyRdScale(param.psyRd);
void setPsyRdScale(double scale) { m_psyRdBase = (uint32_t)floor(65536.0 * scale * 0.33); }psyRDCost的计算代码如下：
这里的psyRD表示重建块的AC energy和原始块的AC energy之差，即（这里不理解为什么像素块和0的SATD减去下其和0的SAD表示AC能量）
template<int size>
int psyCost_pp(const pixel* source, intptr_t sstride, const pixel* recon, intptr_t rstride)
{
static pixel zeroBuf[8] /* = { 0 } */;
if (size)
{
int dim = 1 << (size + 2);
uint32_t totEnergy = 0;
for (int i = 0; i < dim; i += 8)
{
for (int j = 0; j < dim; j+= 8)
{
/* AC energy, measured by sa8d (AC + DC) minus SAD (DC) */
int sourceEnergy = sa8d_8x8(source + i * sstride + j, sstride, zeroBuf, 0) -
(sad<8, 8>(source + i * sstride + j, sstride, zeroBuf, 0) >> 2);
int reconEnergy = sa8d_8x8(recon + i * rstride + j, rstride, zeroBuf, 0) -
(sad<8, 8>(recon + i * rstride + j, rstride, zeroBuf, 0) >> 2);
totEnergy += abs(sourceEnergy - reconEnergy);
}
}
return totEnergy;
}
else
{
/* 4x4 is too small for sa8d */
int sourceEnergy = satd_4x4(source, sstride, zeroBuf, 0) - (sad<4, 4>(source, sstride, zeroBuf, 0) >> 2);
int reconEnergy = satd_4x4(recon, rstride, zeroBuf, 0) - (sad<4, 4>(recon, rstride, zeroBuf, 0) >> 2);
return abs(sourceEnergy - reconEnergy);
}
}二、SSIM Rate Distortion
x265中计算SSIM RD Cost的公式如下：
x265中的计算代码如下：
inline uint64_t calcSsimRdCost(uint64_t distortion, uint32_t bits, uint32_t ssimCost) const
{
#if X265_DEPTH < 10
X265_CHECK((bits <= (UINT64_MAX / m_lambda2)) && (ssimCost <= UINT64_MAX / m_lambda),
"calcPsyRdCost wrap detected dist: " X265_LL " bits: %u, lambda: " X265_LL ", lambda2: " X265_LL "\n",
distortion, bits, m_lambda, m_lambda2);
#else
X265_CHECK((bits <= (UINT64_MAX / m_lambda2)) && (ssimCost <= UINT64_MAX / m_lambda),
"calcPsyRdCost wrap detected dist: " X265_LL ", bits: %u, lambda: " X265_LL ", lambda2: " X265_LL "\n",
distortion, bits, m_lambda, m_lambda2);
#endif
return distortion + ((m_lambda * ssimCost) >> 14) + ((bits * m_lambda2) >> 8);
}其中SSIMCost为SSIM指标下的失真，SSIMCost的计算公式推导参考论文
x265中的计算如下
uint64_t Quant::ssimDistortion(const CUData& cu, const pixel* fenc, uint32_t fStride, const pixel* recon, intptr_t rstride, uint32_t log2TrSize, TextType ttype, uint32_t absPartIdx)
{
static const int ssim_c1 = (int)(.01 * .01 * PIXEL_MAX * PIXEL_MAX * 64 + .5); // 416
static const int ssim_c2 = (int)(.03 * .03 * PIXEL_MAX * PIXEL_MAX * 64 * 63 + .5); // 235963
int shift = (X265_DEPTH - 8);
int trSize = 1 << log2TrSize;
uint64_t ssDc = 0, ssBlock = 0, ssAc = 0;
// Calculation of (X(0) - Y(0)) * (X(0) - Y(0)), DC
ssDc = 0; //ssDc 表示整个块内所有4x4为块的左上角像素差值的平方和
for (int y = 0; y < trSize; y += 4)
{
for (int x = 0; x < trSize; x += 4)
{
int temp = fenc[y * fStride + x] - recon[y * rstride + x]; // copy of residual coeff
ssDc += temp * temp;
}
}
// Calculation of (X(k) - Y(k)) * (X(k) - Y(k)), AC
ssBlock = 0; //ssBlock 表示整个块内的原始像素-重建像素的差值的平方和
uint64_t ac_k = 0; //ac_k表示整个块内原始像素的平方和
primitives.cu[log2TrSize - 2].ssimDist(fenc, fStride, recon, rstride, &ssBlock, shift, &ac_k);
ssAc = ssBlock - ssDc;
// 1. Calculation of fdc'
// Calculate numerator of dc normalization factor 计算dc归一化因子的分子
uint64_t fDc_num = 0;
// 2. Calculate dc component
uint64_t dc_k = 0; //表示整个块内所有4x4为块的左上角像素平方和
for (int block_yy = 0; block_yy < trSize; block_yy += 4)
{
for (int block_xx = 0; block_xx < trSize; block_xx += 4)
{
uint32_t temp = fenc[block_yy * fStride + block_xx] >> shift;
dc_k += temp * temp;
}
}
fDc_num = (2 * dc_k) + (trSize * trSize * ssim_c1); // 16 pixels -> for each 4x4 block
fDc_num /= ((trSize >> 2) * (trSize >> 2));
// 1. Calculation of fac'
// Calculate numerator of ac normalization factor
uint64_t fAc_num = 0;
// 2. Calculate ac component
ac_k -= dc_k;
double s = 1 + 0.005 * cu.m_qp[absPartIdx];
fAc_num = ac_k + uint64_t(s * ac_k) + ssim_c2;
fAc_num /= ((trSize >> 2) * (trSize >> 2));
// Calculate dc and ac normalization factor
uint64_t ssim_distortion = ((ssDc * cu.m_fDc_den[ttype]) / fDc_num) + ((ssAc * cu.m_fAc_den[ttype]) / fAc_num);
return ssim_distortion;
}三、Rd SATD Cost
RD SATD Cost主要是用于帧内预测模式粗选的时候，为了降低复杂度，使用残差的哈达玛变换近似代替失真，这种方法省去了变换、量化、反量化、反变换等过程，可以大大降低复杂度。其计算公式如下：
其中，SATD表示原始块和预测块残差的SATD，Rmdoe仅为编码当前模式所需的比特数。
inline uint64_t calcRdSADCost(uint32_t sadCost, uint32_t bits) const
{
X265_CHECK(bits <= (UINT64_MAX - 128) / m_lambda,
"calcRdSADCost wrap detected dist: %u, bits %u, lambda: " X265_LL "\n", sadCost, bits, m_lambda);
return sadCost + ((bits * m_lambda + 128) >> 8);
}