background image
ISO/IEC 10918-1 : 1993(E)
TISO1780-93/d116
DCT path
DCT (dif)
Lossless (dif)
+
Point transform
Bounded error on
reconstructed image
DCT (dif)
Lossless path
Predicted (dif)
No error on
reconstructed image
Predicted (dif)
Predicted (dif)
Figure K.6 Sketch of the basic operations of the hierarchical mode
Figure K.6 [D116] = 14 cm = 547 %
K.7.2.1
DCT Hierarchical progression
If a DCT hierarchical progression uses reduced spatial resolution, the early stages of the progression can have better image
quality for a given bit rate than the early stages of non-hierarchical progressive coding of the DCT coefficients. However,
at the point where the distortion between source and output becomes indistinguishable, the coding efficiency achieved
with a DCT hierarchical progression is typically significantly lower than the coding efficiency achieved with a non-
hierarchical progressive coding of the DCT coefficients.
While the hierarchical DCT progression is intended for lossy progressive coding, a final spatial differential coding stage
can be used. When this final stage is used, the output can be almost lossless, limited only by the difference between the
encoder and decoder IDCT implementations. Since IDCT implementations can differ significantly, truly lossless coding
after a DCT hierarchical progression cannot be guaranteed. An important alternative, therefore, is to use the input point
transform of the final lossless differential coding stage to reduce the precision of the differential input. This allows a
bounding of the difference between source and output at a significantly lower cost in coded bits than coding of the full
precision spatial difference would require.
K.7.2.2
Spatial hierarchical progression
If lossless progression is required, a very simple hierarchical progression may be used in which the spatial lossless coder
with point transformed input is used as a first stage. This first stage is followed by one or more spatial differential coding
stages. The first stage should be nearly lossless, such that the low order bits which are truncated by the point transform are
essentially random otherwise the compression efficiency will be degraded relative to non-progressive lossless coding.
CCITT Rec. T.81 (1992 E)
175
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