Prediction Coding - Advanced Video Coding Systems - page 72

Fig. 4.15 Illustration of
chroma sub-pixel
interpolation

a 0 , i = ( − A − 3 , i + 4 × A − 2 , i − 10 × A − 1 , i + 57 × A 0 , i + 19 × A 1 , i − 7 × A 2 , i

+ ×

A 3 , i − A 4 , i + ((

<< − )>> )) >> ( −

3 1 BitDepth 8 1 BitDepth )

(4.42a)

8

b 0 , i = ( − A + 4 × A − 11 × A + 40 × A 0 , i + 40 × A 1 , i − 11 × A 2 , i

− 3 , i − 2 , i − 1 , i

+ 4 × A 3 , i − A 4 , i + (( 1 << BitDepth − 8 )>> 1 )) >> ( BitDepth )

(4.42b)

− 8

c 0 , i

= ( − A + 3 × A − 7 × A + 19 × A 0 , i + 57 × A 1 , i − 10 × A 2 , i

− 3 , i − 2 , i − 1 , i

+ 4 × A 3 , i − A 4 , i + (( 1 << BitDepth − 8 )>> 1 )) >> ( BitDepth )

(4.42c)

− 8

For chroma interpolation, Fig. 4.15 gives an example of the chroma sub-pixel.
The capital letters indicate the chroma integer pixel point. Let a x , y ( d x , d y ) indicates

63 sub-pixels in the square of four integer pixels. indicates the sub-pixel

position. A x , y indicates the chroma pixel point at the picture coordinate

( d x , d y )

( x , y ) .The

sub-pixel a x , y ( d x , d y ) is calculated as follows,

C [d y ][0] × A x , y − 1 + C [d y ][1] × A x , y +
C [d y ][2] × A x , y + 1 + C [d y ][3] × A x , y + 2 + 32

⊨
⊩

>> 6 , if d x = 0 ;

C [d x ][0] × A x − 1 , y + C [d x ][1] × A x , y
+ C [d x ][2] × A x + 1 , y + C [d x ][3] × A x + 2 , y + 32

>> 6 , else if d y = 0 ;

a x , y ( d x , d y ) =

⊛
⊝

⊞
⊠

C [d y ][0] × a x , y − 1 ( d x , 0 ) + C [d y ][1]

× a x , y ( d x , 0 ) + C [d y ][2] × a x , y + 1 ( d x , 0 )

>> ( 20 − BitDepth ) , otherwise .

+ C [d y ][3] × a x , y + 2 ( d x , 0 )

+ ( 1 << ( 19 − BitDepth ))

(4.43)