Inter-Picture Prediction in HEVC - High Efficiency Video Coding (HEVC) - page 131

Tabl e 5. 4 Filter coefficients
for luma interpolation in
MCP

Phase Luma filter coefficients

1/4 Π1; 4; 10; 58; 17; 5; 1=64

1/2 Π1; 4; 11; 40; 40; 11; 4; 1=64

Tabl e 5. 5 Filter coefficients
for chroma interpolation in
MCP

Phase Chroma filter coefficients

1/8 Π2; 58; 10; 2=64

1/4 Π4; 54; 16; 2=64

3/8 Π6; 46; 28; 4=64

1/2 Π4; 36; 36; 4=64

the DCT coefficients to the spatial domain using DCT basis sampled at desired
fractional positions instead of integer positions. Fortunately, these operations can
be combined into a single FIR filtering step. Let the available samples at integer
positions be denoted as a column vector s and the forward transform as a matrix B .
The DCT coefficients c can be computed as c D B s . Since DCT basis is
composed of cosine functions (which are continuous in nature), they can be sampled
at fractional positions. Let the DCT basis sampled at desired fractional positions be
denoted by a row vector r . This is used to transform back the DCT coefficients
to the spatial domain, which results in the interpolated value s D r B s .These
stages can be combined into a single filter f D r B . In addition to the above
steps, the reference samples are smoothed in the actual HEVC design to combat
noise in the reference samples. Therefore the final interpolation filter can be written
in the form f D r B W ,where W is a diagonal matrix with weights for
smoothing. The resulting filter coefficients are rounded to 6-bit precision (for a
simple fixed-point implementation) and an integer optimization is carried out under
the normalization constraint to ensure that the filter coefficients provide close to
desired frequency response even after rounding. For the chroma interpolation filters,
a slightly different smoothing of reference samples is performed during the filter
design. The filter coefficients' bit-depth of 6 also makes it possible to realize the
entire MCP process for 8-bit videos using 16-bit intermediate buffers. The filter
coefficients resulting from the design described above for luma and chroma MCP
are given in Tables 5.4 and 5.5 , respectively. The magnitude responses of half-pel
luma interpolation filters of H.264/AVC and HEVC are depicted in Fig. 5.8 . It can
be seen that the half-pel interpolation filter of HEVC comes closer to the desired
response than the H.264/AVC filter.

5.3.1.2 High Precision Filtering Operations

In H.264/AVC, some of the intermediate values used within interpolation are
shifted to lower accuracy, which introduces rounding error and reduces coding
efficiency. This loss of accuracy is due to several reasons. Firstly, the half-pixel