hm inter prediction 111022 r3

HEVC Inter prediction

광운대학교 영상처리시스템연구실

2011-10-22 (SAT)

Contents

• Overview of inter prediction

• Inter prediction in HEVC

– GOP coding structure

– Adaptive motion vector prediction(AMVP)

– Merge

– Asymmetric motion partition(AMP)

– Interpolation filter

OVERVIEW OF INTER PREDICTION

Overview of inter prediction

• The encoder forms a model of the current frame based on the samples of a previously transmitted frame

• Motion-compensated predicted frame is subtracted from the current frame to reduce a residual ‘error’ frame

• Transform coding of the residual frame

Current frame

Residual frame

Motion-compensated

frame

Motion estimation

Previous frame

_

Overview of inter prediction

• The goals of inter prediction

– ME creates a model of the current frame based on available data in one or more previously encoded frames to match the current frame as closely as possible

n-1 frame n frame

Overview of inter prediction

• Transmitted data

– Motion vector (PMV, MVD)

– Reference index (LIST_0/LIST_1)

– Prediction mode

– Residual data (quantized coefficients)

… …

… …

How?

GOP CODING STRUCTURE

GOP coding structure

• Temporal prediction structure

– All Intra (No temporal prediction is allowed)

– Low Delay (LD)

• The first picture shall be coded as IDR picture

• GPB (Generalized P and B) picture (on/off)

– Random access (RA)

• Hierarchical B structure shall be used for coding

• IDR Intra picture or CDR(clean random access) picture shall be inserted cyclically per about one second in random access point

GOP coding structure – Low delay

IDR or

Intra picture GPB(Generalized P and B) picture

0

1

2

4

5 3

6

7

8

time

QPI

QPBL3=QPI+3

QPBL2=QPI+2

QPBL3 QPBL3 QPBL3

QPBL2

QPBL1=QPI+1 QPBL1

GOP coding structure – Random access

IDR or

Intra picture GPB(Generalized P and B) picture

0

5

3

2

7 6

4

8

1

time

Referenced B Picture

Non-referenced B Picture

8

4

1

2

3 5

6

7

0

QPI

QPBL4=QPI+4 QPBL4 QPBL4 QPBL4

QPBL3=QPI+3 QPBL3

QPBL2=QPI+2

QPBL1=QPI+1

POC

Coding

order

GOP coding structure – Random access

Variables: m_iHrchDepth = log2GOP_size + 1; iTimeOffset = (1<<m_iHrchDepth-1-iDepth); iStep = iTimeOffset<<1; iNumPicRcvd = GOP_size;

for( iDpeth=0; iDepth<m_iHrchDepth; iDepth++ ) { iTimeOffset = (1<<m_iHrchDepth-1-iDepth); iStep = iTimeOffset<<1; for(;iTimeOffset<=iNumPicRcvd; ) { compressSlice(); iTimeOffset += iStep; } }

IDR or

Intra picture

GPB(Generalized

P and B) picture

0

5

3

2

7 6

4

8

1

time

Referenced B

Picture

Non-

referenced B

Picture

8

4

1

2

3 5

6

7

0

: Depth == 0

: Depth == 1 : Depth == 2

: Depth == 3

*uiPOCCurr = iPOCLast – (iNumPicRcvd – iTimeOffset);

AMVP (ADAPTIVE MOTION VECTOR PREDICTION)

MV prediction of H.264/AVC

• Median of each component of MV

– No transmission overhead

• Slice-based use of temporal MV predictor

C B

A

Current Block 𝑀𝑉𝑥 = 𝑀𝐸𝐷𝐼𝐴𝑁(𝐴𝑥, 𝐵𝑥, 𝐶𝑥)

𝑀𝑉𝑦 = 𝑀𝐸𝐷𝐼𝐴𝑁(𝐴𝑦 , 𝐵𝑦 , 𝐶𝑦)

Fig. Spatial neighboring block

MV prediction of HEVC

• Explicit signaling of MV predictor index

– Transmission overhead

• PU-based use of temporal MV predictor

B1

A1

B2 B0

A0

Current Block

Fig. Spatial AMVP candidates

Co-located PU

Center

Right-bottom

Fig. Temporal AMVP candidates

AMVP

• Decoder receives

– ref_idx

– mvd

– mvp_idx

B1

A1

B2 B0

A0

Current Block

Fig. Spatial AMVP candidates

Co-located PU

Center

Right-bottom

Fig. Temporal AMVP candidates

AMVP – Decoder side AMVP syntax

prediction_unit( x0, y0 , log2CUSize ) { Descriptor if( skip_flag[ x0 ][ y0 ] ) { merge_idx[ x0 ][ y0 ] ue(v) | ae(v) } else if( PredMode = = MODE_INTRA ) {

… } else { /* MODE_INTER */ if( entropy_coding_mode_flag || PartMode != PART_2Nx2N ) merge_flag[ x0 ][ y0 ] u(1) | ae(v) if( merge_flag[ x0 ][ y0 ] ) { merge_idx[ x0 ][ y0 ] ue(v) | ae(v) } else { if( slice_type = = B ) { if( !entropy_coding_mode_flag ) { combined_inter_pred_ref_idx ue(v) if( combined_inter_pred_ref_idx == MaxPredRef ) inter_pred_flag[ x0 ][ y0 ] ue(v) } else inter_pred_flag[ x0 ][ y0 ] ue(v) | ae(v) } if( inter_pred_flag[ x0 ][ y0 ] = = Pred_LC ) { if( num_ref_idx_lc_active_minus1 > 0 ) { if( !entropy_coding_mode_flag ) { if( combined_inter_pred_ref_idx == MaxPredRef ) ref_idx_lc_minus4[ x0 ][ y0 ] ue(v) } else ref_idx_lc[ x0 ][ y0 ] ae(v) } mvd_lc[ x0 ][ y0 ][ 0 ] se(v) | ae(v) mvd_lc[ x0 ][ y0 ][ 1 ] se(v) | ae(v) mvp_idx_lc[ x0 ][ y0 ] ue(v) | ae(v) }

AMVP – Decoder side AMVP syntax

else { /* Pred_L0 or Pred_BI */ if( num_ref_idx_l0_active_minus1 > 0 ) { if( !entropy_coding_mode_flag ) { if( combined_inter_pred_ref_idx == MaxPredRef ) ref_idx_l0_minusX[ x0 ][ y0 ] ue(v) } else ref_idx_l0_minusX[ x0 ][ y0 ] ue(v) | ae(v) } mvd_l0[ x0 ][ y0 ][ 0 ] se(v) | ae(v) mvd_l0[ x0 ][ y0 ][ 1 ] se(v) | ae(v) mvp_idx_l0[ x0 ][ y0 ] ue(v) | ae(v) } if( inter_pred_flag[ x0 ][ y0 ] = = Pred_BI ) { if( num_ref_idx_l1_active_minus1 > 0 ) { if( !entropy_coding_mode_flag ) { if( combined_inter_pred_ref_idx == MaxPredRef ) ref_idx_l1_minusX[ x0 ][ y0 ] ue(v) } else ref_idx_l1[ x0 ][ y0 ] ue(v) | ae(v) } mvd_l1[ x0 ][ y0 ][ 0 ] se(v) | ae(v) mvd_l1[ x0 ][ y0 ][ 1 ] se(v) | ae(v) mvp_idx_l1[ x0 ][ y0 ] ue(v) | ae(v) } } } }

AMVP – Encoder side processing

1. Search for three candidates (spatial:2, temporal:1)

2. Remove redundant MVPs

3. Additional candidate list – Zero vector candidates are created by combining zero vector and

refIdx

4. Decision of best MVP before motion estimation – Distortion : SAD

– Rate: Truncated unary code (MVP index)

– RDCost = Distortion + (Bits*λ + 0.5)>>16;

5. Decision of the best MVP candidate after motion estimation – Best MVP index: smallest mvd = Best_MV – MV of mvp_idx[i]

mvp_idx bin

0 0

1 10

2 110

Starting point for ME

AMVP – Spatial AMVP candidates

• Spatial AMVP candidates

– mvLxA: Left spatial candidates

• Derivation order: A0 ⇒ A1

• First available MV

– 1st: scan without scaling (vec1, vec2)

– 2nd: scan with scaling (vec3, vec4)

– mvLxB: Above spatial candidates

• Derivation order: B0 ⇒ B1 ⇒ B2

• First available MV

– 1st: scan without scaling (vec1, vec2)

– 2nd: scan with scaling, if scaling wasn’t used before (vec3, vec4)

Fig. Spatial AMVP candidates

B1

A1

B2 B0

A0

Current Block

AMVP – Spatial AMVP candidates

• Spatial AMVP candidates

– Four candidates can be derived at each neighboring PU

• vec1: same reference index, same list

• vec2: same reference index, different list

• vec3: different reference index, same list

• vec4: different reference index, different list

time

k l mji picture id

current

block

neighboring

block b

jL0mv

mL1mv

jmvL1

imvL0 1

2

3

4

AMVP – Temporal AMVP candidate

• Temporal AMVP candidate

– Derivation order:

1. Right-bottom position of co-located PU

2. Center position of co-located PU

Co-located PU

Center

Right-bottom

Fig. Temporal AMVP candidates

mvL1

mvL0

current picture

co-located picture

reference picture

Co-located partition

mvL1Col

AMVP - MV Scaling

• Scaling of MV predictor has been modified (JCTVC-F142)

– HM3 rounds half towards plus infinity

– Proposed scheme rounds half towards zero

HM version Modification

HM3 𝐷𝑖𝑠𝑡𝑆𝑐𝑎𝑙𝑒𝐹𝑎𝑐𝑡𝑜𝑟 × 𝑚𝑣 + 128 ≫ 8

HM4 𝑆𝑖𝑔𝑛(𝐷𝑖𝑠𝑡𝑆𝑐𝑎𝑙𝑒𝐹𝑎𝑐𝑡𝑜𝑟 × 𝑚𝑣)

× 𝐷𝑖𝑠𝑡𝑆𝑐𝑎𝑙𝑒𝐹𝑎𝑐𝑡𝑜𝑟 × 𝑚𝑣 + 127 ≫ 8

𝐷𝑖𝑠𝑡𝑆𝑐𝑎𝑙𝑒𝐹𝑎𝑐𝑡𝑜𝑟: 𝑠𝑐𝑎𝑙𝑖𝑛𝑔 𝑓𝑎𝑐𝑡𝑜𝑟

MERGE

Merge

• Decoder receives

– ref_idx

– mvd

– mvp_idx

– merge_flag

– merge_index

Fig. Merge candidates

D

C B

A

E

Current Block

Co-located PU

Center

Right-bottom

Merge – Decoder side Merge skip syntax

coding_unit( x0, y0, log2CUSize ) { Descriptor if( entropy_coding_mode_flag && slice_type != I ) skip_flag[ x0 ][ y0 ] u(1) |ae(v) if( skip_flag[ x0 ][ y0 ] ) prediction_unit( x0, y0, log2CUSize, log2CUSize, 0 , 0 ) else {

… } }

prediction_unit( x0, y0 , log2CUSize ) { Descriptor if( skip_flag[ x0 ][ y0 ] ) { merge_idx[ x0 ][ y0 ] ue(v)|ae(v) } else if( PredMode = = MODE_INTRA ) {

… } else { /* MODE_INTER */

… } }

• Merge skip

Merge – Decoder side Merge syntax

prediction_unit( x0, y0 , log2CUSize ) { Descriptor if( skip_flag[ x0 ][ y0 ] ) { merge_idx[ x0 ][ y0 ] ue(v)|ae(v) } else if( PredMode = = MODE_INTRA ) {

… } else { /* MODE_INTER */ if( entropy_coding_mode_flag || PartMode != PART_2Nx2N ) merge_flag[ x0 ][ y0 ] u(1) |ae(v) if( merge_flag[ x0 ][ y0 ] ) { merge_idx[ x0 ][ y0 ] ue(v)|ae(v) } else {

… } }

• General case - merge

Merge – Encoder side processing

1. Search for five candidates

– Output: Mv, RefIdx, Predflag for LIST_0/LIST_1

– S0, S1, S2, S3: Spatial candidates

– Col: Temporal candidate

2. Remove redundant candidates

3. Additional candidate list (JCTVC-F470)

– Combined bi-directional merge candidate (5 times)

– Scaled bi-directional merge candidate (1 time)

– Zero vector merge candidate

4. Decision of the best MRG candidate

S0 S1 S2 S3 Col merge_idx bin

0 0

1 10

2 110

3 1110

4 1111

Merge – Spatial merge candidates

• Spatial merge candidates (4 candidates)

– Derivation Order: A, B, C, D, E

Fig. Spatial merge candidates

D

C B

A

E

Current Block

Merge – Temporal merge candidate

• refIdx derivation for merge TMVP (JCTVC-E481)

– Decide three refIdx

• refIdxLeft: A

• refIdxAbove: B

• refIdxCorner: C or D or E

– Decide majority of them

– If three of them are not available

• refIdx = 0

– Otherwise

• Set minimum of available refIdx

• Derivation of temporal merge candidate

– Same process with TMVP

D

C B

A

E

Current Block

Merge – Temporal merge candidate

• Example) Decision of reference frame

D

C B

A

E

Current Block

Curr PU

B

A

E

ex) second 4x8 PU in 8x8 CU

Neighbor LIST RefIdx

A LIST_0 0

LIST_1 1

B LIST_0 -1

LIST_1 1

C NULL

D NULL

E LIST_0 -1

LIST_1 1

LIST_0

refIdxLeft 0

refIdxAbove -1

refIdxCorner -1

LIST_1

refIdxLeft 1

refIdxAbove 1

refIdxCorner 1

LIST_0 0

LIST_1 1

Merge – Additional cand. list

1. Combined bi-directional merge candidate (5 times)

mvL0_A(uni) mvL1_B(uni)

mvL1_B(bi)

mvL0_A(bi)

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_B, ref 0

2

3

4

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_B, ref 0

2 mvL0_A, ref 0 mvL1_B, ref 0

3

4

Cur List 0 Ref 0

List 1 Ref 0

Merge – Additional cand. list

2. Scaled bi-directional merge candidate (1 time)

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_A, ref 1

2

3

4

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_A, ref 1

2 mvL0_A, ref 0 mvL0’_A, ref 0

3

4

mvL0_A(ref 0)

Cur

mvL0’_A(ref 0)

mvL1_A(ref 1)

List 0 Ref 0

List 0 Ref 1

List 1 Ref 0

List 1 Ref 1

Merge – Additional cand. list

3. Zero vector merge

– Zero vector merge candidates are created by combining zero vector and refIdx

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_A, ref 1

2 mvL0_A, ref 0 mvL1_A, ref 1

3

4

Merge L0 L1

0 mvL0_A, ref 0 -

1 - mvL1_A, ref 1

2 mvL0_A, ref 0 mvL1_A, ref 1

3 (0,0), ref 0 (0,0), ref 0

4

AMP (ASYMMETRIC MOTION PARTITION)

Asymmetric motion partition (AMP)

• Rectangular shape PU splitting of a block for inter prediction

• AMP is used from the size of 64x64 to 16x16 CU

• AMP improves the coding efficiency, since irregular image patterns

2NxnU 2NxnD nLx2N nRx2N

Asymmetric motion partition (AMP)

Random access HE Random access LC

Y U V Y U V

Class A -0.9 -1.2 -0.9 -0.7 -0.7 -0.5

Class B -0.9 -1.0 -1.0 -0.7 -0.7 -0.6

Class C -0.9 -1.0 -1.1 -0.7 -0.9 -0.9

Class D -0.8 -1.0 -0.9 -0.5 -0.7 -0.6

Class E

Overall -0.9 -1.0 -1.0 -0.7 -0.7 -0.7

Enc Time[%] 144% 151%

Dec Time[%] 99% 99%

Low delay (B) HE Low delay (B) LC

Y U V Y U V

Class A

Class B -1.1 -1.5 -1.5 -0.9 -0.8 -0.6

Class C -1.0 -1.2 -1.3 -0.7 -0.6 -0.7

Class D -1.1 -1.3 -1.5 -0.6 -0.5 -0.9

Class E -2.3 -2.2 -2.4 -1.7 -1.1 -1.3

Overall -1.3 -1.5 -1.6 -0.9 -0.7 -0.8

Enc Time[%] 144% 150%

Dec Time[%] 99% 99%

Table. Experimental result of AMP without encoding speed-up

Random Access HE Random Access LC

Y U V Y U V

Class A -0.5 -0.8 -0.5 -0.4 -0.6 -0.2

Class B -0.5 -0.8 -0.7 -0.4 -0.5 -0.5

Class C -0.6 -0.8 -0.8 -0.5 -0.6 -0.7

Class D -0.5 -0.9 -0.8 -0.4 -0.5 -0.6

Class E

Overall -0.5 -0.8 -0.7 -0.4 -0.6 -0.5

Enc Time[%] 112% 112%

Dec Time[%] 99% 98%

Low delay B HE Low delay B LC

Y U V Y U V

Class A

Class B -0.7 -1.1 -1.2 -0.5 -0.4 -0.3

Class C -0.7 -1.0 -0.9 -0.4 -0.4 -0.7

Class D -0.7 -1.2 -0.8 -0.5 -0.7 -0.2

Class E -1.5 -1.9 -1.7 -1.0 -1.0 -0.9

Overall -0.8 -1.2 -1.1 -0.6 -0.6 -0.5

Enc Time[%] 111% 111%

Dec Time[%] 100% 99%

Table. Experimental result of AMP with encoding speed-up

INTERPOLATION FILTER

Interpolation filter of H.264/AVC

• 1/4th accuracy motion vector

– Cascaded filtering: 6-tap half-pel + bi-linear for luma

– Bi-linear for chroma (1/8th)

Integer-pel – no interpolation

Half-pel – 6-tap

Quarter-pel – 6-tap + bi-linear

Interpolation filter of HEVC

• 1/4th accuracy motion vector

– 1-pass filter: 8-tap for both 1/2nd and 1/4th pel

– 4-tap filter for chroma (1/8th)

Integer-pel – no interpolation

Half-pel – 8-tap

Quarter-pel – 8-tap

Interpolation filter

• Two modifications in HM4.0 and WD4.0

– The motion compensation process to simplify the process by removing rounding operations

– Ensure that all data after each of the vertical and horizontal filtering passes holds in 16-bit memory

– Advantage

• Software simpler

• Text simpler

• No difference in performance

Interpolation filter

• Integer samples

– Upper-case letters

• Fractional sample positions

– Lower-case letters

– For quarter sample luma interpolation

A-1,-1 A0,-1 a0,-1 b0,-1 c0,-1 A1,-1 A2,-1

A-1,0 A0,0 a0,0 b0,0 c0,0 A1,0 A2,0

d-1,0 d0,0 e0,0 f0,0 g0,0 d1,0

h-1,0 h0,0 i0,0 j0,0 k0,0 h1,0

n-1,0 n0,0 p0,0 q0,0 r0,0 n1,0

A-1,1 A0,1 A0,1 b0,1 c0,1 A1,1 A2,1

A-1,2 A0,2 A1,2 A2,2

Interpolation filter

• Interpolation filter coefficients

– Luma

– Chroma

α Filter(α)

1/4 { -1, 4, -10, 57, 19, -7, 3, -1 }

1/2 { -1, 4, -11, 40, 40, -11, 4, -1 }

α Filter(α)

1/8 { -3, 60, 8, -1 }

1/4 { -4, 54, 16, -2 }

3/8 { -5, 46, 27, -4 }

1/2 { -4, 36, 36, -4 }

Interpolation filter

• Luma interpolation process (1D interpolation filter)

– For fractional positions a0,0, b0,0 and c0,0, horizontal 1D filter is used.

– For fractional positions d0,0, h0,0 and n0,0, vertical 1D filter is used.

– The input of 1D interpolation function is integer position values.

– The output is interpolated value X, which has fractional position α.

A-1,-1 A0,-1 a0,-1 b0,-1 c0,-1 A1,-1 A2,-1

A-1,0 A0,0 a0,0 b0,0 c0,0 A1,0 A2,0

d-1,0 d0,0 e0,0 f0,0 g0,0 d1,0

h-1,0 h0,0 i0,0 j0,0 k0,0 h1,0

n-1,0 n0,0 p0,0 q0,0 r0,0 n1,0

A-1,1 A0,1 A0,1 b0,1 c0,1 A1,1 A2,1

A-1,2 A0,2 A1,2 A2,2

Interpolation filter

• Example) 1/2 position b0,0

– 8-tap separable DCTIF coefficient of 1/2 position

{ -1, 4, -11, 40, 40, -11, 4, -1 }

A-1,-1 A0,-1 a0,-1 b0,-1 c0,-1 A1,-1 A2,-1

A-1,0 A0,0 a0,0 b0,0 c0,0 A1,0 A2,0

d-1,0 d0,0 e0,0 f0,0 g0,0 d1,0

h-1,0 h0,0 i0,0 j0,0 k0,0 h1,0

n-1,0 n0,0 p0,0 q0,0 r0,0 n1,0

A-1,1 A0,1 A0,1 b0,1 c0,1 A1,1 A2,1

A-1,2 A0,2 A1,2 A2,2

𝑏0,0 = −1 ∗ 𝐴−3,0 + 4 ∗ 𝐴−2,0 − 11 ∗ 𝐴−1,0 + 40 ∗ 𝐴0,0 + 40 ∗ 𝐴1,0 − 11 ∗ 𝐴2,0 + 4 ∗ 𝐴3,0 − 1 ∗ 𝐴4,0 + 32 /64

Interpolation filter

• Luma interpolation process (2D separable interpolation filter)

– For remaining positions first horizontal 1D filter is applied for extended block, and then vertical 1D filter is used.

A-1,-1 A0,-1 a0,-1 b0,-1 c0,-1 A1,-1 A2,-1

A-1,0 A0,0 a0,0 b0,0 c0,0 A1,0 A2,0

d-1,0 d0,0 e0,0 f0,0 g0,0 d1,0

h-1,0 h0,0 i0,0 j0,0 k0,0 h1,0

n-1,0 n0,0 p0,0 q0,0 r0,0 n1,0

A-1,1 A0,1 A0,1 b0,1 c0,1 A1,1 A2,1

A-1,2 A0,2 A1,2 A2,2

Interpolation filter

• Example) 1/4 position e0,0

– 2D separable Interpolation

– 8×horizontal 1D filter + 1×vertical 1D filter

A-1,-1 A0,-1 a0,-1 b0,-1 c0,-1 A1,-1 A2,-1

A-1,0 A0,0 a0,0 b0,0 c0,0 A1,0 A2,0

d-1,0 d0,0 e0,0 f0,0 g0,0 d1,0

h-1,0 h0,0 i0,0 j0,0 k0,0 h1,0

n-1,0 n0,0 p0,0 q0,0 r0,0 n1,0

A-1,1 A0,1 A0,1 b0,1 c0,1 A1,1 A2,1

A-1,2 A0,2 A1,2 A2,2

Interpolation filter

• 1D filtering

• 2D filtering

– Intermediate value should be saved and processed

𝑎0,0 = −1 × 𝐴−3,0 + 4 × 𝐴−2,0 − 10 × 𝐴−1,0 + 57 × 𝐴0,0 + 19 × 𝐴1,0 − 7 × 𝐴2,0 + 4 × 𝐴3,0 − 1 × 𝐴4,0 + 𝑜𝑓𝑓𝑠𝑒𝑡1 ≫ 𝑠𝑕𝑖𝑓𝑡1

𝑎0,0 = −1 × 𝐴−3,0 + 4 × 𝐴−2,0 − 10 × 𝐴−1,0 + 57 × 𝐴0,0 + 19 × 𝐴1,0 − 7 × 𝐴2,0 + 4 × 𝐴3,0 − 1 × 𝐴4,0 ≫ 𝑠𝑕𝑖𝑓𝑡1

𝑑1𝑖,0 = −1 × 𝐴𝑖,−3 + 4 × 𝐴𝑖,−2 − 10 × 𝐴𝑖,−1 + 57 × 𝐴𝑖,0 + 19 × 𝐴𝑖,1 − 7 × 𝐴𝑖,2 + 4 × 𝐴𝑖,3 − 1 × 𝐴𝑖,4

𝑒0,0 = −1 × 𝑑1−3,0 + 4 × 𝑑1−2,0 − 10 × 𝑑1−1,0 + 57 × 𝑑10,0 + 19 × 𝑑11,0 − 7 × 𝑑12,0 + 4 × 𝑑13,0 − 1 × 𝑑14,0 + 𝑜𝑓𝑓𝑠𝑒𝑡2 ≫ 𝑠𝑕𝑖𝑓𝑡2

𝑒0,0 = −1 × 𝑎−3,0 + 4 × 𝑎−2,0 − 10 × 𝑎−1,0 + 57 × 𝑎0,0 + 19 × 𝑎1,0 − 7 × 𝑎2,0 + 4 × 𝑎3,0 − 1 × 𝑑14,0 ≫ 𝑠𝑕𝑖𝑓𝑡2

Interpolation filter – Example template<int N, bool isVertical, bool isFirst, bool isLast> Void TComInterpolationFilter::filter(Short const *src, Int srcStride, Short *dst, Int dstStride, Int width, Int height, Short const *coeff) { Int row, col; Int cStride = ( isVertical ) ? srcStride : 1; // isVertical: 1(vertical filtering), 0(horizontal filtering) src -= ( N/2 - 1 ) * cStride; // N: 8(Luma), 4(Chroma) Int offset; Short maxVal; Int headRoom = IF_INTERNAL_PREC - (g_uiBitDepth + g_uiBitIncrement); // IF_INTERNAL_PREC: 14, guiBitdepth+g_uiBitIncrement: 10(HE),8(LC) Int shift = IF_FILTER_PREC; // IF_FILTER_PREC: 6 // isFirst: whether first filtering or not if ( isLast ) { // last filtering shift += (isFirst) ? 0 : headRoom; // isFirst: shift = 6, other case: shift = 6+4(HE), 6+6(LC) offset = 1 << (shift - 1); // isFirst: offset = 1<<6 = 32, other case: offset = 1<<10(HE), 1<<12(LC) offset += (isFirst) ? 0 : IF_INTERNAL_OFFS << IF_FILTER_PREC; // !isFirst: offset = 1<<10 + 1<<11(HE), 1<<12 + 1<<11(LC) maxVal = g_uiIBDI_MAX; // maxVal: 1023(HE), 255(LC) } else { // other case shift -= (isFirst) ? headRoom : 0; // isFirst: shift = 2(HE), 0(LC) offset = (isFirst) ? -IF_INTERNAL_OFFS << shift : 0; // isFirst: -((1<<IF_FILTER_PREC-1)<<2)=-(1<<7)(HE), -(1<<5)(LC) maxVal = 0; } for (row = 0; row < height; row++) { for (col = 0; col < width; col++) { Int sum; sum = src[ col + 0 * cStride] * coeff[0]; sum += src[ col + 1 * cStride] * coeff[1]; sum += src[ col + 2 * cStride] * coeff[2]; sum += src[ col + 3 * cStride] * coeff[3]; sum += src[ col + 4 * cStride] * coeff[4]; sum += src[ col + 5 * cStride] * coeff[5]; sum += src[ col + 6 * cStride] * coeff[6]; sum += src[ col + 7 * cStride] * coeff[7]; Short val = ( sum + offset ) >> shift; if ( isLast ) { // clipping in last filtering val = ( val < 0 ) ? 0 : val; val = ( val > maxVal ) ? maxVal : val; } dst[col] = val; // store filtering output pixel } src += srcStride; dst += dstStride; } } modified version for seminar

Interpolation filter – Example. Half-pel template<int N, bool isVertical, bool isFirst, bool isLast> Void TComInterpolationFilter::filter(Short const *src, Int srcStride, Short *dst, Int dstStride, Int width, Int height, Short const *coeff) { Int row, col; Int cStride = ( isVertical ) ? srcStride : 1; // isVertical: 1(vertical filtering), 0(horizontal filtering) src -= ( N/2 - 1 ) * cStride; // N: 8(Luma), 4(Chroma) Int offset; Short maxVal; Int headRoom = IF_INTERNAL_PREC - (g_uiBitDepth + g_uiBitIncrement); // IF_INTERNAL_PREC: 14, guiBitdepth+g_uiBitIncrement: 10(HE),8(LC) Int shift = IF_FILTER_PREC; // IF_FILTER_PREC: 6 // isFirst: whether first filtering or not if ( isLast ) { // last filtering shift += (isFirst) ? 0 : headRoom; // isFirst: shift = 6, other case: shift = 6+4(HE), 6+6(LC) offset = 1 << (shift - 1); // isFirst: offset = 1<<6 = 32, other case: offset = 1<<10(HE), 1<<12(LC) offset += (isFirst) ? 0 : IF_INTERNAL_OFFS << IF_FILTER_PREC; // !isFirst: offset = 1<<10 + 1<<11(HE), 1<<12 + 1<<11(LC) maxVal = g_uiIBDI_MAX; // maxVal: 1023(HE), 255(LC) } else { // other case shift -= (isFirst) ? headRoom : 0; // isFirst: shift = 2(HE), 0(LC) offset = (isFirst) ? -IF_INTERNAL_OFFS << shift : 0; // isFirst: -((1<<IF_FILTER_PREC-1)<<2)=-(1<<7)(HE), -(1<<5)(LC) maxVal = 0; } for (row = 0; row < height; row++) { for (col = 0; col < width; col++) { Int sum; sum = src[ col + 0 * cStride] * coeff[0]; sum += src[ col + 1 * cStride] * coeff[1]; sum += src[ col + 2 * cStride] * coeff[2]; sum += src[ col + 3 * cStride] * coeff[3]; sum += src[ col + 4 * cStride] * coeff[4]; sum += src[ col + 5 * cStride] * coeff[5]; sum += src[ col + 6 * cStride] * coeff[6]; sum += src[ col + 7 * cStride] * coeff[7]; Short val = ( sum + offset ) >> shift; if ( isLast ) { // clipping in last filtering val = ( val < 0 ) ? 0 : val; val = ( val > maxVal ) ? maxVal : val; } dst[col] = val; // store filtering output pixel } src += srcStride; dst += dstStride; } } modified version for seminar

-1 4 -11 40 40 -11 4 -1

Example) 1/2 position b0,0

8-tap separable DCTIF coefficient of 1/2 position isFrist = true; isLast = true; (uni-direction case) shift = 6; offset = 1<<(6-1) = 32; maxVal = 1023(HE), 255(LC); cStirde = 1; (horizontal filtering)

A0,0 a0,0 b0,0 c0,0 A1,0

d0,0 e0,0 f0,0 g0,0 d1,0

h0,0 i0,0 j0,0 k0,0 h1,0

n0,0 p0,0 q0,0 r0,0 n1,0

A0,1 A0,1 b0,1 c0,1 A1,1

Interpolation filter – Example. Quarter pel template<int N, bool isVertical, bool isFirst, bool isLast> Void TComInterpolationFilter::filter(Short const *src, Int srcStride, Short *dst, Int dstStride, Int width, Int height, Short const *coeff) { Int row, col; Int cStride = ( isVertical ) ? srcStride : 1; // isVertical: 1(vertical filtering), 0(horizontal filtering) src -= ( N/2 - 1 ) * cStride; // N: 8(Luma), 4(Chroma) Int offset; Short maxVal; Int headRoom = IF_INTERNAL_PREC - (g_uiBitDepth + g_uiBitIncrement); // IF_INTERNAL_PREC: 14, guiBitdepth+g_uiBitIncrement: 10(HE),8(LC) Int shift = IF_FILTER_PREC; // IF_FILTER_PREC: 6 // isFirst: whether first filtering or not if ( isLast ) { // last filtering shift += (isFirst) ? 0 : headRoom; // isFirst: shift = 6, other case: shift = 6+4(HE), 6+6(LC) offset = 1 << (shift - 1); // isFirst: offset = 1<<6 = 32, other case: offset = 1<<10(HE), 1<<12(LC) offset += (isFirst) ? 0 : IF_INTERNAL_OFFS << IF_FILTER_PREC; // !isFirst: offset = 1<<10 + 1<<11(HE), 1<<12 + 1<<11(LC) maxVal = g_uiIBDI_MAX; // maxVal: 1023(HE), 255(LC) } else { // other case shift -= (isFirst) ? headRoom : 0; // isFirst: shift = 2(HE), 0(LC) offset = (isFirst) ? -IF_INTERNAL_OFFS << shift : 0; // isFirst: -((1<<IF_FILTER_PREC-1)<<2)=-(1<<7)(HE), -(1<<5)(LC) maxVal = 0; } for (row = 0; row < height; row++) { for (col = 0; col < width; col++) { Int sum; sum = src[ col + 0 * cStride] * coeff[0]; sum += src[ col + 1 * cStride] * coeff[1]; sum += src[ col + 2 * cStride] * coeff[2]; sum += src[ col + 3 * cStride] * coeff[3]; sum += src[ col + 4 * cStride] * coeff[4]; sum += src[ col + 5 * cStride] * coeff[5]; sum += src[ col + 6 * cStride] * coeff[6]; sum += src[ col + 7 * cStride] * coeff[7]; Short val = ( sum + offset ) >> shift; if ( isLast ) { // clipping in last filtering val = ( val < 0 ) ? 0 : val; val = ( val > maxVal ) ? maxVal : val; } dst[col] = val; // store filtering output pixel } src += srcStride; dst += dstStride; } } modified version for seminar

-1 4 -10 57 19 -7 3 -1

Example) 1/4 position e0,0

2D separable interpolation (1) Horizontal filtering isFrist = true; isLast = false; shift = 2(HE), 0(LC); offset = -(1<<7); maxVal = 0; cStirde = 1; (horizontal filtering)

A0,0 a0,0 b0,0 c0,0 A1,0

d0,0 e0,0 f0,0 g0,0 d1,0

h0,0 i0,0 j0,0 k0,0 h1,0

n0,0 p0,0 q0,0 r0,0 n1,0

A0,1 A0,1 b0,1 c0,1 A1,1

Interpolation filter – Example. Quarter pel template<int N, bool isVertical, bool isFirst, bool isLast> Void TComInterpolationFilter::filter(Short const *src, Int srcStride, Short *dst, Int dstStride, Int width, Int height, Short const *coeff) { Int row, col; Int cStride = ( isVertical ) ? srcStride : 1; // isVertical: 1(vertical filtering), 0(horizontal filtering) src -= ( N/2 - 1 ) * cStride; // N: 8(Luma), 4(Chroma) Int offset; Short maxVal; Int headRoom = IF_INTERNAL_PREC - (g_uiBitDepth + g_uiBitIncrement); // IF_INTERNAL_PREC: 14, guiBitdepth+g_uiBitIncrement: 10(HE),8(LC) Int shift = IF_FILTER_PREC; // IF_FILTER_PREC: 6 // isFirst: whether first filtering or not if ( isLast ) { // last filtering shift += (isFirst) ? 0 : headRoom; // isFirst: shift = 6, other case: shift = 6+4(HE), 6+6(LC) offset = 1 << (shift - 1); // isFirst: offset = 1<<6 = 32, other case: offset = 1<<10(HE), 1<<12(LC) offset += (isFirst) ? 0 : IF_INTERNAL_OFFS << IF_FILTER_PREC; // !isFirst: offset = 1<<9 + 1<<11(HE), 1<<11 + 1<<11(LC) maxVal = g_uiIBDI_MAX; // maxVal: 1023(HE), 255(LC) } else { // other case shift -= (isFirst) ? headRoom : 0; // isFirst: shift = 2(HE), 0(LC) offset = (isFirst) ? -IF_INTERNAL_OFFS << shift : 0; // isFirst: -((1<<IF_FILTER_PREC-1)<<2)=-(1<<7)(HE), -(1<<5)(LC) maxVal = 0; } for (row = 0; row < height; row++) { for (col = 0; col < width; col++) { Int sum; sum = src[ col + 0 * cStride] * coeff[0]; sum += src[ col + 1 * cStride] * coeff[1]; sum += src[ col + 2 * cStride] * coeff[2]; sum += src[ col + 3 * cStride] * coeff[3]; sum += src[ col + 4 * cStride] * coeff[4]; sum += src[ col + 5 * cStride] * coeff[5]; sum += src[ col + 6 * cStride] * coeff[6]; sum += src[ col + 7 * cStride] * coeff[7]; Short val = ( sum + offset ) >> shift; if ( isLast ) { // clipping in last filtering val = ( val < 0 ) ? 0 : val; val = ( val > maxVal ) ? maxVal : val; } dst[col] = val; // store filtering output pixel } src += srcStride; dst += dstStride; } } modified version for seminar

-1 4 -10 57 19 -7 3 -1

Example) 1/4 position e0,0

2D separable interpolation (2) Vertical filtering isFrist = false; isLast = true; shift = 10(HE), 12(LC); offset = 1<<9 + 1<<11(HE), 1<<11 + 1<<11(LC); maxVal = 1023(HE), 255(LC); cStirde = srcStride; (vertical filtering)

A0,0 a0,0 b0,0 c0,0 A1,0

d0,0 e0,0 f0,0 g0,0 d1,0

h0,0 i0,0 j0,0 k0,0 h1,0

n0,0 p0,0 q0,0 r0,0 n1,0

A0,1 A0,1 b0,1 c0,1 A1,1

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