Since each subband represents a filtered and subsampled
version of the frame component, coefficients within
each subband
correspond to specific areas of the underlying picture and hence those
that relate to the same area can be related. It is most
productive to relate coefficients that also have the same
orientation (in terms of combination of high- and low-pass
filters). The relationship is illustrated below,
showing the situation for HL bands i.e. those that have been
high-pass filtered horizontally and low-pass filtered
vertically.
Figure: Parent-child relationship between subband
coefficients
In the diagram it's easy to see that the subsampling
structure means that a coefficient (the
parent) in the lowest HL band corresponds spatially to a 2x2
block of coefficients (the children) in the next HL band, each
coefficient of which itself has a 2x2 block of child coefficients in
the next band, and so on. This relationship relates closely to
spectral harmonics: when coding image features (edges,
especially) significant coefficients are found distributed
across subbands, in positions related by the parent-child
structure, and corresponding to the original position of the
feature. In particular, a coefficient is more likely to be
significant if its parent is, and children with zero or small
parents or ancestors may have different statistics from
children with large parents or ancestors.
These factors suggest that when entropy coding coefficients,
it will be helpful to take their parents into account in
predicting how likely, say, a zero value is.
By coding from low-frequency subbands to high-frequency
ones, and hence by coding parent before child subbands,
parent-child dependencies can be exploited in these ways
without additional signalling to the decoder.
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