**ISO/IEC 10918-1 : 1993(E)**

**K.8**

**Suppression of block-to-block discontinuities in decoded images**

A simple technique is available for suppressing the block-to-block discontinuities which can occur in images compressed

by DCT techniques.

The first few (five in this example) low frequency DCT coefficients are predicted from the nine DC values of the block

and the eight nearest-neighbour blocks, and the predicted values are used to suppress blocking artifacts in smooth areas of

the image.

The prediction equations for the first five AC coefficients in the zig-zag sequence are obtained as follows:

**K.8.1**

**AC prediction**

The sample field in a 3 by 3 array of blocks (each block containing an 8

×

8 array of samples) is modeled by a

two-dimensional second degree polynomial of the form:

P(x,y)

=

A1(x

2

y

2

)

+

A2(x

2

y)

+

A3(xy

2

)

+

A4(x

2

)

+

A5(xy)

+

A6(y

2

)

+

A7(x)

+

A8(y)

+

A9

The nine coefficients A1 through A9 are uniquely determined by imposing the constraint that the mean of P(x,y) over

each of the nine blocks must yield the correct DC-values.

Applying the DCT to the quadratic field predicting the samples in the central block gives a prediction of the low

frequency AC coefficients depicted in Figure K.7.

TISO1790-93/d117

x

x

x

x

x

DC

**Figure K.7 DCT array positions of predicted AC coefficients**

Figure K.7 [D.117] = 8 cm = 313 %

The prediction equations derived in this manner are as follows:

For the two dimensional array of DC values shown

DC

1

DC

2

DC

3

DC

4

DC

5

DC

6

DC

7

DC

8

DC

9

The unquantized prediction equations are

AC

01

=

1,13885 (DC

4

DC

6

)

AC

10

=

1,13885 (DC

2

DC

8

)

AC

20

=

0,27881 (DC

2

+

DC

8

2

×

DC

5

)

AC

11

=

0,16213 ((DC

1

DC

3

) (DC

7

DC

9

))

AC

02

=

0,27881 (DC

4

+

DC

6

2

×

DC

5

)

The scaling of the predicted AC coefficients is consistent with the DCT normalization defined in A.3.3.

**176**

**CCITT Rec. T.81 (1992 E)**