BSTJ 60: 3. March 1981: A New Code for Transmission of Ordered Dithered Pictures. (Johnsen, O.)

7.5 MB·English

Com 8 Ana tg gh Coen

A New Code for Transmission of Ordered
Dithered Pictures

By 0. JOHNSEN
Ctanuscrt receive Saptunber 22, 1980)

This paper presents a new predictor for coding dithered pictures.
A dithered picture, a two-tone picture which gives the usion of @
‘ieture with many shades of rey, 8 obtained by comparing the gre
Tevet picture nith a postion-dependen! threshold. When the intensity
ofa picture element (pe) exconds the threshold, itis classified af
tonite; othereiae it black In the new prediction scheme, the color
(of peli proce from pels having nearly the same threshold level,
"Therefore, the position ofthe pes use for prediction vartes according
to the threshold level. Computer simulations shew that prediction
terrors ave reduced by 60 percent for certain classes of arigmae, and
le entropy is reduced by 20 percent eampared tn the rest obtadned
with a preaious predictor. An advantage of this new prediclion
scheme is that it appears ta be lees vents lo piture content

1. INTRODUCTION

Dithering van image processing technique thal eran two-level
cur that givea the lusion of a multilevel piccore by appropriately
"ranging the spatial density ofthe two love (usually lack and whice)
fon the picture’ The dithering lechnigque consis of comparing a
‘malslevel image with a position-dependent threshold and eetting pols
to white when the input signal exceeds che threshold. Othor pels are
set to black, The matrix of chresholdvaluos (called tho dither mais)
is repeated over the entive picture lo provide the threshold pattern for
the whole image

"The merit of @ either matrix is judyed from Une quality of its
rendition of the orginal piture. A elas of dither matrices of special
interest i the orlered dither matices. which use a simple recursion
algorithm lo create dither matrices of sire "52" eo nile + 1
Urightness level,
In the case ofthe 4 4 mates, Une 16 threshold eves are put the
following positions:

oe aw
Baw 6
sua 8 a
wT th 6

The ordered dither matrices have the advantage of rendering ere
level pictur with as gond a subjective quality a with empires Wither
matrices” Moreover, we thovr that ondeeed dither matrices are espe
‘ally convonicn: for the propose new predictor. Figure {shows three
dithered picwres. “Karen,” “Engineer drawing," and “House” that
tre itd for corspular simulations. The orginal for these petures sre
Dem hy 10 em and were scanned (o generate an array of S12 by 812
pele The pels were digitized with a uniform bit rom ende (256 level).
‘Matrix 1 then becomer

8 18 40108
200 72232 104
36 18 24 160| a
2s 120 21688

[Note that Fis. Ln, b, and ¢ were made from digitising the same
originale at wsed in Rafe. 4 and 6 but not from the aatne digitized

"Efficiently cuting the bite of the dithered image reduces the data,
‘ate I the pela of che dicheredpictore are sampled in a typieal raster
can fashion, the frequent alternations between black and white pela
provent the dizcet use of rurlengsh coding, which is an efficient
‘evlundaney roluction acheme.* Others have proposed a modification
ta the atraightorward raster scan sampling oF to the dire use of the
Picture pela, Juice proposed a ciffrent sernpling onler abit inter:
leaving code Necraval et al? devised a predictive coding technique
that isan extension of their two-level facsimile ceding achwane.” To
both cares, the binary picture containing the interleaved bits or the
prodiction erroor ean be olin ran-iength cee, Im Netravalls
Coding technique, the predition of the value of «pel (1 whi,
black) is made dependent on the values of four neighbor pels as well,
4 to the threshold level. Figure 2 shove the ordered dither matrix of
42) and the prediction that he used. With a dither mate of 16
threshold levels, and « prediction from 4 neighboring pela the prec
tion table has 256 possible states. This prediction scheme takes advan-
lage ofthe correlation between adjacent pes, but it can only partially
‘exploit the much slonger corrlation dh exists beioreen neighboring
pele with the same or ilar thee level

"The scheme proposed in this paper predicts « pel according to the

380. THE TLL SYSTEM TECHNICAL JOURNAL, MARCH 1991
‘elue of nearly pals ofthe same of similar threshold level. ‘The new
predictor gives for two of the three test pictures 50 percent fower
predictinn evots compared to fhe previous one, and 10 pereent fower
fedictnn erote for the vind cnt picture

I PREDICTION PRINCIPLES AND ALGORITHMS.
2.4 Predition piel

‘Apel can bos he predicted from the fllowing information

{ed the threshold level af the pel ef

(6) the values of the nearest lelzady coded) pels with similar
threshold levels

‘We use four revs pels fr prediction and consider piriunes which
hhave ton slithered using the 4 4 ordered dither matrix of (2). There
tre then 16 threshold levels and sinew ch pel used for prediction hee
nly tao passile valvos, 2 slates are defined by all the posible

NEW CODE FOR ORDERED CITHERED PICTURES 981
‘combinntios ofthe predictor nnd ofthe ehreahold level, The predic
‘ode Book concaine 254 bits, each indicating whether the pels pre~
Gictad to be black or white. "The coe book in simply olkained by
ntistieal measurement. From these predictions, we generate a nes?
pieture where the pes correctly predicted ave pu co “0” while the pels
Incorrectly predicted are pu lo." The new picture, called the “error
piecure,” can easily be rur-length coded and transmitted efficiently
Knowledge of the predicior cole book allows the receiver to recom
ternee the original dithored pierure. "The four pele used for prediction

(a) the ewo nearest pels with the same threshold level,

(©) the nearest pel with tho noxt higher threehold lev,

{e) the nearest pel withthe nea lower Unresod level
For eater) and (e), when we pels satiety the role at the same time,
‘the pel with the emallast correlation withthe other predietion pels
chosen. se, for caso (), i there are no pele with s higher threshold
level, a sooond pel with the next lower threshold level ie used for
prediction. A similar siturtion ean appear in eae (6),
2.2 Predition algortv

Lot thi pl to be predicted Sy, ave potion (ij), where # isthe
line number, ji tae position on Ove line, and i and j are increasing
flows and tothe right, respectively. The to noureal pels with the
‘ame threshold level naturally have coordinaves (¢— 4;/} sod (&j ~
4) since a4 4 dither mix i ued

‘To flud che tee other pels ured for prediction, we must look ac the
suture ofthe 4 > 4 ordered dither matzx The procedure iscsi
in the appendix. We give lere only che result, showing that the
‘hopdinatee ofthe four pela ued forthe prediction nee

Pas,
faye
avin

‘The position of the prediction ye with variable postion is given
according to the positon of Si within the dither matrix by

NEW CODE FOR ORDERED OIIHERED PICTURES 265
pulad and WS aot ar pice Samer isa assy.” ere

|icasce iene doay nay
foSy41 feay-1 iaay i 2y
foupar gaugar foay tay
a reer

Figure 3 shows the postin ofthe four pole used for the prediction

"Nate that forthe wight ple in he ewe ght rows of the mate The
prediction el ich varie potion i These

"This new predictar can be called a position-dependent predicror
since one ofthe pels used for the prediction is variable. Inthe case
‘where using a postion dependent predictor i undesirable, the predic-
lor nee ran be reduced nnd only Tre pels oun he eo Une foe
te used in che prediction can be Ged tothe enostsel postion (F—
25). Both cased lead co slight increase in the numberof prediction

"Tho came prediction principle can be applied to different dither
rmalries nr different sives of mace, bul wth care. For example,
‘oe appling the aame rule tan ordered § x 8 dither matrix, cree
ofthe four pels of che predictor are fixed and their locations, compared
ta the pel to be predicted, are inthe ame direction but twice aa fer a8

Bat ae ine tr! Reig a the Bae Se ee

384 THE BELL SYSTEM TECHNICAL, JOURNAL, MARCH 1811
for 4X 4 mattis, heir enti ae

Lins,
2 im,
ah inasea

“The prediction pel with vaviahle position agsin has the same relative
position for the right half of the mattis, che coerdinates boing (i — 4
Ji). Por the other bal, the position is variable, bat often the seme
‘within egch 2x2 submatex. The postion macrx of the prediction pel
‘rth variable position ean be constructed by looking atthe structire
fof the 2>¢2 and 4 x 4 aubmnsteies.

Tes questionable whether such a predictor xives quod prediction
“The pretction is owe made eovording to the wulve of te pels vice a8
fay way, asin the cave of « 1% 4 dither matrix. The error rate i
therefore likely to ierease. ‘The beet solution ie to use the sme
prediction algortn a for the 4% 4 dither matrin, since the 8 8
[thor muirin composed of four 4 4ither matrices whose threshold
levels ans ony ver lightly diferent. The number of prediction error
would then be only slightly higher thi i che picture was dithered
wrth «4 % A matrix A alight decrosse in prediction errors can be
Dbtained by considering all Ureshold levela instead of 16 for
fomstracting the predition table. The predierion table would then
ontain 1024 states instead of 256

the caso of eshersliller matrices (nonordered) the prediction
principle is the ane but, he algorithm ia diferent, since the position
Df the nearee pela with similar threshold level changes tn mast cass,
‘ea of the four pels need for prediction would have a variable pecition,
thus showing the advantage of wing the ordered dither matrices with
this prediction sehume

"This prediction scheme can be extended by adding more pela to the
predictor, for example, using pls einer to the pel to be prediced,
Morlyseereaing the nmber of prediction errors lang aaharp edge

1, SIMULATION RESULTS.

‘Computer simulations ate performed sing the three dither pie
tures of Fig. 3.'The results exe compared ta thuve obtained uring the
technive proposed by Netravai et Two meaaure of performances
fre made: counting the numer of prediction errors and measuring. the
fencopy of the minlength staciaion of che picture containinx the
prediction errors The entropy is convert in. bis per pel. The un
Temgth entropy measured i the classes! runclength entenpy, given for
‘example in Ret 6.

‘able gives the mumber of prediction errors with th: now prsicor.
or camyursou, the numberof prediction errors wih The technique i
Tet isso given, Compared withthe predictor of Ref 6, the number

New CODE FOR ORDTRCD OHTHERED PICTURES 385
of podiion eros i edce hy 5 erent for Karen and “House”
thu prcent or "Baphcrng dang”

"Table ves the eatropy comport Four entopes ae given
‘The Be is he entopy of he ruben sate tbe prediion
civ when sng asa prion ible foreach ple. The
Site heats etropy cae where aig petition cable
ued for al ue pears he pedicin table Is ptnized othe
fm of he tre pice

"Pe hr eto he eopy of he rung sain of he
prediction aco when he prion err ane deed acorn
{Ea otal of er goes ordering) nego ener
4h relton ers ofthe pel of eso filed the ihe i
"line fh ear robbs ae high wie they ar put nce ee
‘ie shon their evr robbie we The goes tel
wed

“Toe fre encopy Se che ane at he later but with a singe
prison ale re tre caren

Sth entopy remem show tho great improvements ciined
ty thine petition cig compare to oe cn on ea
orion “Hows” he retin in the eng xoy
2 to 00 pert, ut Hi nit to peront for agieting
Sawing” When sings prediction table woe th rection
trust i 8 pect for “Kien and “Hone but reaches 10
ferent fr "ngierigtnewing” inthe eae fgnd-had odeing,
the decene in entopy wi he nw pedcton thi cope
tall ie 7s porn fr laren and“Houn whl saceane
Of poren!epear fr Hngaering dang.” Wken a ge pede
ton table or ll pare tbe docete Bu pereoot end 17
Percent for “Kes” and “Tous” and 3 percent for “Engineering
inna”

"Ta ain obltned with de nee pred for “Kare” an Hou
se vor ifleent for "gineeing awn can be oxpaned by fhe
picareeharsveraice The "Raver ant" leurs eel
Ettne pre wth ly esa changas bec he

“Engin crowing rapa plese Sncinng mony ne

Table |Compariaon of the number of
prediction erore

Ec HG

386 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1961
Table tI—Camparison of entropies (in bits/p6)

T Rex Per,
RiLtieing wibsepnte re 0am 85a

‘Ripteahcigth p-bed of. am am a8
lois

(Etsudedoy wise we 0th 8

“Geman ce prin ae "

changes in grey level. These steep changes aro well predicted with
NNotravali's predictor and therefore practically no improvemonts are
buat with the new predictor,

‘An advantage of ehia new technique is that the predictor it awite
independent ofthe cbnractrinies of individual pictures. The entropy
swith the predicvr aptzized for the um of Ue thrw pelures less
than 2 percent higher than with inividua peeditoes fr each picture.
‘With Netravals predictor the entropy is sometime 10 percent higher
‘when the preietor ia optimized fr the sum ofthe three pictures

"The nelvantage of using a good-bad ordering is smaller with the new
prediczy, the decreaae in entropy’ being aout 10 pereen. We empha
ce bun, thatthe good:-bad ordering lends ta nearly eaonoton-
‘ally decreasing runlenath distribution and therefore the Tuna are
fazy to onde, while without ordering. the rur-length diribution
‘ery irre, Straightforward ran-length codes can be devised which
‘ode the pictures obtained afer prediction and renmdering with an
‘eMficiensy of about 90 percent,

Iv, SUMMARY AND CONCLUSION

We have decribed » new predictive coding scheme fr dithered
pictures where the pels wed for prediction have variable positions
“The proletion it made according tothe value of nearby pls that have
ncarly the sire dheeshold level and according to the valuo of the
threshold of the pel to be coded. We obtain decrome of 20 0 0
pent fn the rundengeh entropy compared to an warlier prediction
feheme in the case of dithered pictures of natural wenes. The bit rate

NEW CODE FOR ORDERED DITHERED PIcTUNES 387
is reduced to 0.18 to 0.25 bite/pel. Wo obtain a alightly isher entropy
‘shen w fx the eiton ofthe pele used fr peedition. Tn the ease of
_raphical picuues, the entropy is about the same as before. The new
prodictor has the advantage of being nearly independent ofthe char
felaistirs of Untiidual petures, In tse case af & ending type, the
zur length distibutiore ae be used tn propor a ore whe perfor
‘ances should be near those given by the entropy measures. This
prediction schame was conceived for images dichered with a 4X 4
fered dithered atts, but can be eaaly applied ta other dither
‘matrices We envision extensions that would improve the performance
in region chat have sharp changes in brightness.

APPENDIX
"The to nearest pels with the same threshold level naturally have
coordinates (1~ tj} and (i,j ~ 4 since 04 %4 dither mats is used.
‘To find the two other pels used for prediction, we examine the
structure ofthe 4 *'4 ordered dither matrix, Let us aumber the four
2 2 matrices oomtained sn the 4 % 4 dither matrix ns Qs 2 and 3
according 60 he increase in Vir average Uhrsholdl valu, Figure 4
‘howe Ue relative pou, We must alae semetuber thal Ue 44
‘matrix is eurounded by identical matrices whose pela can aso be used
prediction pos
ora pel in submstrix 1, the neighboring pel with the nexL-higher
threchol level wil bo in tho seme relative position in submaeie2 with
coordinates (i ~ 2: ) "The neighbor with the nexclosrer threshold
level willbe in the seme relative position in eubmacri 0 Thet neighbor
cn be ether in submatrix 0 of the same 4 <4 matrix or in submacrix
(ot the matrix ndjucen: to the right. Both cazes lead to ehe same
<dacance from the neighbor to the pel co be predicted, bur the later
‘nse lends to the smallest correlation with che other prediction pela
and is therefore chosen, ‘That prediction pel has potion (2 ~ 25/42)
‘Simulany, i the pol to be predieced ia im submatrix 2, the two pels

980 THE BELL SYSTEM TECHNICAL JOURNAL, MARCH 1981