 ISO/IEC 10918-1 : 1993(E)
Referring to the final scan (Al
=
0), the points marked with "t" are the threshold values, while the points marked with "r"
are the reconstruction values. The unquantized output is obtained by multiplying the horizontal scale in Figure K.8 by the
quantization value.
The quantization interval for a coefficient value of zero is indicated by the depressed interval of the line. As the bit
position Al is increased, a "fat zero" quantization interval develops around the zero DCT coefficient value. In the limit
where the scaling factor is very large, the zero interval is twice as large as the rest of the quantization intervals.
Two different reconstruction strategies are shown. The points marked "r" are the reconstruction obtained using the normal
rounding rules for the DCT for the complete full precision output. This rule seems to give better image quality when high
bandwidth displays are used. The points marked "x" are an alternative reconstruction which tends to give better images on
lower bandwidth displays. "x" and "r" are the same for slice 0. The system designer must determine which strategy is best
for the display system being used.
K.10
Example of point transform
The difference between the arithmetic-shift-right by Pt and divide by 2
Pt
can be seen from the following:
After the level shift the DC has values from
+
127 to ­128. Consider values near zero (after the level shift), and the case
where Pt
=
1:
Before
Before
After
After
level shift
point transform
divide by 2
shift-right-arithmetic 1
131
+
3
+
1
+
1
130
+
2
+
1
+
1
129
+
1
+
0
+
0
128
+
0
+
0
+
0
127
­1
+
0
­1
126
­2
­1
­1
125
­3
­1
­2
124
­4
­2
­2
123
­5
­2
­3
The key difference is in the truncation of precision. The divide truncates the magnitude; the arithmetic shift truncates the
LSB. With a divide by 2 we would get non-uniform quantization of the DC values; therefore we use the shift-right-
arithmetic operation.
For positive values, the divide by 2 and the shift-right-arithmetic by 1 operations are the same. Therefore, the shift-right-
arithmetic by 1 operation effectively is a divide by 2 when the point transform is done before the level shift.
178
CCITT Rec. T.81 (1992 E)