FAST LEG CODEBOOK GENERATOR FOR ETC IMAGE COMPRESSION

Image Lena Rank

Table 3 Bit-rate reduction performance in HVQ

Original Proposed Gain

[‘%#I

0.3199 0.2670 16.5 0.3424 0.2672 21.9 Original Proposed b,,, h, h,

1

h,,, h, h, Image . Lena 0.0839 0.3350 0.4189~0.0515 0.2713 0.3229 Gain [‘YO] 22.9

Conclu.sitm We proposed a simple dynamic index mapping which considerably reduces the index entropy by expoiting interhlock correlation. It was shown that it provides a considerable amount of hit-rate reduction not only in ordinary VQ but also in many hybrid VQ systems. Since the proposed index encoding scheme requires only a small amount of additional computation and does not change the quantiser structure. it is expected to he easily applied to other VQ systems.

Bank

0 IEE 1995

E1ecironic.s Lefters Online Nu: 19951030

Seung Jun Lee. Kyeong Ha Yang. Chul Woo Kim and Choong Woong Lee ( D e p a r i m r n i of El?cfronics Engineering. Smul Narronul U n l w r s i t j . Koreu)

12 June l Y Y j

0.0877 0.3525 0.4402 0.0554 0.2735 0.3290 25.3

References

I CCRSHO A . and G R A Y R M : ‘Vector quantisalion and signal compression’ (Kluwer Academic Publisher. 1992)

N A S R A B A D I . N M

.

and FEI*G. Y . ‘Image compression using address-

vector quantization‘. IEEE T r a m , 1990. COM-38. (12). pp. 2166 2173

2

3 FIORAVANTI. R

.

F l O R 4 V A N T L S , and GIUSTO. D D : ‘An efficient neural prediction for vector quantization’. Proc. ICASSP. Adelaide. Australia, 1994, pp. 613-616

4 KIM.T: ‘Side match and overlap match vector quantizers for images’, IEEE Trans., 1992, IP-I. (2). pp. 170-185

Fast

LBG codebook generator for BTC image

Kuang-Shyr Wu and Ja-Chen Lin

compression

Indeuing 1erm.s /muye processing Duru compresiion, Vccror quunfi.sufiun, Bluck codes

When the high-mean and low-mean generated hy the BTC image cornpression technique are to be quantised using VQ, the computalion lime required to search for the nearest centroid can

be reduced significantly using the proposed method. Experiments comparing the full-search and EHPM algorilhms demonstrate this.

fnrroducfion: The image compression technique BTC uses two val- ues U and h, called the high-mean and low-mean. to replace all val- ues in a block. T o increase the compression ratio, the high/low mean pairs are often quantised further through VQ [ I , 21. We con- centrate here on the task of LBG [3] codebook generation for the (high/low) mean pairs. A typical LBG cycle contains the steps: (i) for each data point q. assign q to the ,jth cluster if l ~ c , q ~ ~ = minis,<, llcrqlI

(ii) replace { c , ) , ~ i ’ by the new centroids of the ,V clusters just formed.

Here, C = {c, = (,rc,. jc,)),=,“ is the codebook in question. We present the new method for reducing the time needed in step (ij. First, evaluate to obtain C = ( C , = (.rc,

+

vc,)/2},=,” and C = ( c , = ( Y C ,

+

jr,)/2},-i,v, which are the sum-projection and subtraction-

projection of the codebook to the straight lines .I= .x and ,I = -x, respectively. Assume that the { F , } , = , v has been sorted. For each data point q we proceed as follows, to obtain the nearest code- word

(11-11

always denotes a 2-D Euclidean norm

\i[()?+()3,

whereas

denotes the I-D absolute value):

A / g o r i t h r i ~

Step 1: Calculate ij = (xq+jy)i2 and

9

= (uq- dimensional binary searching to search for the

lC,-yl

= m i n l ~ , c .

lC,-yl.

The corresponding c,, an initial guess for the current nearest codeword (CNC) of q. Step 2 : Calculate d,,,,, = IIcIqIl. Construct the remaining set (RS) by collecting those c, t C whose C , satisfy

(1) Step 3: Delete ck from RS, because E , has been checked Step 4: If RS is empty. then return CNC as the nearest codeword of q and exit.

Step 5: In the RS, obtain the ck whose

E,

satisfies

I?,,

~

41

= miri

I?,

~

41

( 2 ) c, ER S

(Unlike in step I, there is no need to perform a binary search here. Since { C , ) , 7 1 ” ha.s been sorted, {

4)

U { Cr),-i’ has been sorted after step I ;

(4)

U {

F,l

E, E RS} has been sorted after step 2. There- fore, one of the two neighbours of the previous C L must be the candidate.)

Step 6: If c,, violates any of the followmg three inequalities:

li

- FkI

<

( d m m / d a Irq - XCkl

<

n.,,,,,

Iyq - yo.

I

<

d,,,,,, (3) (4) ( 5 ) then go to step 3, else calculate d = !lc,qIl.

Step 7: If d < d,,,,,, then update d,,,,,, and CNC with d and ci, respec- tively. (Also use this new d,,, to delete from the RS the e, whose

E

violates eqn. I .)

Step % GO to S t e p 3.

Qe c, obtained in step 1 is deleted in step 3, and hence the c, obtained in step 5 is different. Furthermore, after the deletion of the codewords c, in step 7, the C l of every codeword cI remaining in the RS must satisfy

14

- < (d,JdZ). Since the next c, obtained in the next execution of step 5 is also chosen from the RS, then c, must also satisfy

14 -

GI <

( & z n / J z ) (6)

Lena 45’1indsum -projection axis)

/

Baboon Couple Crowd

\t

x q t d m l n

-45’111~ (su bt rmtion -pro]ectlon OXIS)

b

Mg.

1 Searching area for nearest codeword and detail of shadedportion a Searchin area for nearest codeword

b Detail ofshaded portion in a

Eqns. 3 - 6 together imply that the c, that could be a CNC must fall in the shaded area enclosed by the e;ght-sided regular polygon shown in Fig. la. The reason there is a 2 term in eqns. 3 and 6 is shown in Fig. lb, which is an enlarged picture of the shaded region sketched in Fig. la. The circle has a radius d,,, and touches the upright eight-sided regular polygon eight times. The sum-projection of the two touching points

( I Q + & , Y Q +

”>

and ( I Q

-

-,yq -

-

Jz

Jz

Jz

are

and

respectively. In the above algorithm, d,, becomes smaller and smaller, and only those c,s satisfying eqns. 3 4 simultaneously will need to evaluate the 2-D distance

l/Ck+ll

(the only exception is the ck found in step 1 where eqns. 3 - 6 are not checked at all because d,. is not yet defmed). The idea

used

in the algorithm is quite obvious. First, if the current nearest codeword is c, and d,, = ~ ~ c k - q ~ [ , then only those c, with the property ~ ~S d,, c are pos- , ~ ~ ~ sible to be the nearest codeword of q. In other words, only those E, interior to the circle centred at q and with a radius d,, (see Fig. Ib) are possible. Secondly, the circular disc is interior to the eight- sided-polygon constrained by eqns. 3 - 6 (see Fig. 1). Hence, only those c, interior to the polygon are possible. The circular disc is a more accurate estimation (of the codeword) than the polygon. However,

use

of the circular disc is very time-consuming (many vectordistances are evaluated).

Experimental results: We compared the proposed algorithm w t h the full-search and an elegant algorithm EHPM [4] which also reduces the number of vector-distance

(11.11)

computations. Table 1

shows the total number of vector-distance computations (tnovdc) required to make the

L E

converge.

Since

there is some overhead (eqns.

1

-

5)

for

reducing

the number of

11.1/

computations in OUT

method, to be fair t o the other two methods we also list in Table 1 the total

CPU

time needed in

LBG

(including both steps

1

and

2).

Regardless which of the two criteria is used t o compare the per- formance, the proposed method shows better results than the full- search and

EHPM

algorithms.

Au three

methods obtain the same

(fmal)

codebook

and require the same number of LBG cycles. The only difference is the CPU time.

Table 1: Comparison of total number of vector-distance computa- tions (tnovdc) and CPU time

Codehook

M2p

I

sues _uerformance

time@)

c

time@)

I

time(s)

Machine used is SUN-SPAR( IO. FS: ‘full search’

Conclwwm: The proposed fast nearest codeword searching algo-

rithm

accelerated

the vector quantisation of the highilow means generated in

BTC

compression. The method condensed the search- ing area, and reduced the total CPU time required for the LBG.

Acknowledgmmt; This study was supported by the National Sci-

ence

Council,

Republic of China, under contract NSC83-0404 E009-08 1.

0 IEE 1995

Electronics Letters Online No: 19950978

Kuang-Shyr

Wu

and Ja-Chen Lin (Deportment of Computer and Information Science, National Chiao Tung University. Hsinchu, Taiwan 30050. Republic of China)

Ja-Chen Lin: corresponding author

25 May 1995

References

1 UDPIKAR,V.R., and RAINA,J.P.: ‘BTC image coding using vector quantization’, IEEE Trans., 1987, COM-35, (3), pp. 352-356 2 WEITZMAN. A., and MITCHELL, H.B.: ‘An adaptive BTC-VQ image

compression algorithm operating at a fixed bit-rate’, Signal Process. Image Commun., 1993, 5, pp. 287-294

3 L I N D E , Y , BUZO,A., and GRAY,R.M.: ‘An algorithm for vector quantizer design’, IEEE Trans., 1980, COM-28, (I), pp. 8495 4 GUAN, L., and KAMEL, M.: ‘Equal-average hyperplane partitioning

method for vector quantization of image data’, Pattern Recognit. Lett., 1592, 13, pp. 693499

Multicomponent heterodyne laser Doppler

anemometer using chirp-modulated

Nd:YAG ring laser and fibre delay lines

J.W. Czarske and H. Mtiller

Zndexing terms: Doppler velocimerry, Anenometers, Ring lasers, Solid lasers, Optical delay lines

A two-dimensional directional laser Doppler anemometer using a frequency modulated NdYAG laser is presented for the first time. The magnitude and sign of the fluid velocity were

determined by employing the heterodyne technique without having to use an external frequency shifter.