INTERACTIVE FOCUS AND CONTEXT DISPLAY OF LARGERASTER IMAGES

Uwe Rauschenbach1

Tino WeinkaufHeidrun Schumann

Universityof Rostock,ComputerScienceDepartment

D-18051RostockGERMANY

{urausche,weinkauf,schumann}@informatik.uni-rostock.dehttp://wwwicg.informatik.uni-rostock.de/

ABSTRACT

This paperpresentsthe RECTANGULAR FISHEYE V IEW, an interactive focus–and–context presentationtechniquefor largerasterimageson mobilecomputerswith smalldisplaysandlimited processingpower.Boththeviewing of locally availableimagesandthedemand–drivendisplayandtransmissionof remotely–storedimagesaresupportedby the technique.The underlyinggeometrycalculationsareexplained,andthedesigndecisionsfor supportingrapidinteractivefeedbackarediscussed.A scenariois describedwhichdemonstratestheperformanceof themethod.

Keywords: Fish Eye View, RasterImages,Interactive Display, Focus–and–Context Techniques,MobileComputers

1 INTRODUCTION

Graphicalpresentationof large amountsof informa-tion on computerdisplayshasto copewith theprob-lem of limited screenspace. The viewer of suchapresentationhastwo conflictinggoalsin mind: Here-questsahighdegreeof detailbut alsowantsto haveanoverview over the whole presentationfor orientationpurposes.Visualizationresearchersproposedfocus–and–context techniquesto solve this conflict for thedisplayof largelayoutson desktopworkstations.

Usingmobilecomputers,bothprocessingpower anddisplay spaceare more limited than in a worksta-tion scenario. Additionally, mobile devices oftenfetch graphicaldataas raster images from a remoteserver usinga low–bandwidthdatalink. A presenta-tion techniquefor thosemobilesettingsmustbeableto display a large raster image in a screen–space–saving manner, tradingoff thetwo requirements“de-tail” and “overview” againsteach other. Further-more, its computingrequirementsshouldbe moder-

1This work wassupportedby TheGermanScienceFoundationundercontractno. Schu-887/3-3.

ate in order to work on the targetedhardware andto allow rapid interactive control. Last but not least,theschemeshouldwork with ademand–driventrans-missionmethodlike the onepresentedin [Rausc99],transmittingonly thoseimagedatawhich areneededfor display.

After reviewing relatedwork, we will proposetheRECTANGULAR FISHEYE V IEW asa new techniquemeetingtheserequirements.In contrastto [Rausc99],wherewe discussedthe transmissionimplicationsofour technique,thispaperfocusesonthenecessaryge-ometrycalculationsandthe interactivity of the tech-nique.

2 RELATED WORK

In the researchfield of visualization, focus–and–context techniqueshave beenproposedto solve theproblem of displaying very large layouts on desk-top workstationsequippedwith powerful processors.These techniquescombine a focus display, whichshows a part of the layout at a high degreeof detail,

anda context display, which presentsthe whole pic-ture in lower detail to provide theoverview. Thepo-sition of thefocusis determinedby thecurrentpointof interestof theuser.

Thereareseveralpossibilitiesfor focus–and–contextdisplays:focusandcontext canbedisplayedseparateovertime(thiscorrespondsto zooming) or in two sep-aratepresentationssideby side.Thisapproachavoidsintroducingdistortion,but theuseris requiredto makethelink betweenfocusandcontext mentally. Anotherapproachis thefisheyeview, wherefocusandcontextare integratedin one presentation.Dependingon ameasureof distancefrom thefocus,thecontext is dis-tortedsuchthatits spacerequirementsdecrease.Thisapproachoffers a detailedview nearthe point of in-terestandmaintainslarge–scalefeaturesof thewholelayout at the costof introducingdistortion far awayfrom thepointof interest.

Let us now discusssomeof the many works in thefield of fisheyeviewsrelatedto ourtechnique.An ex-cellent,comprehensivebibliographyaboutnon–linearmagnificationtechniquesand fish eye views can befound on the Nonlinear Magnification Home Page[Keahe98].

Fisheye techniqueshave first beenusedin computerscienceby Furnas[Furna82] for the presentationofstructureddata,achieving context reductionby hid-ing nodesin thestructurebasedon thedistancefromthefocusandaninterestmeasure.Otherworks(e.g.,[Keahe96]) proposemethodsfor non–linearmagni-fication, where the scaling factor (magnificationorminification) is definedas a two–dimensionalfunc-tion of the locationin the picture. Thesetechniquesmay use a different scaling factor for every pixel,which introducessmooth,concentricdistortionsandrequiresahigh computingeffort.

Sincethe focusshows only a part of the whole pic-ture in high detail, the useroften wishesto move itto anotherpositionto revealdetail thereashis pointof interestchanges.This interactiveexploration re-quiresrecomputation,which needsa powerful pro-cessorfor fastresponseusingthetechniquedescribedabove. Sarkaret al. [Sarka93] proposedfor graphi-cal layoutsamethodcalled“rubbersheets”whichdi-videstheimageinto stripesandstretchesall pixelsofa stripeby thesamefactor. Thus,computingrequire-mentsaredecreased.

3 THE RECTANGULAR FISHEYE VIEW

3.1 Requirements

The basicrequirementsto a focus–and–context dis-play techniquefor mobileenvironmentshave already

beenstatedin section1. Additionally, flexible tai-lorability of focusregion andcontext areasis highlydesirable.Especially, theusershouldbesupportedinexactlyspecifyingtheareaandthedegreeof detailofthe focus. Sincenot all partsof the presentationof-fer the samedegreeof detail, interactiontechniqueswith shortresponsetime have to be provided for re-vealinghiddendetailsby re–positioningthefocus.Inordernotto destroy basicpropertiesof theimage(likeangles,proportionalityor parallelity),no distortionisacceptablein thefocusarea.In thecontext area,dis-tortion is thefoundationfor saving displayspaceandcannot beavoided. Interactive controlover themag-nitudeof this distortionmustbe provided to supportthe user in adaptingthe tradeoff betweendistortionandspacerequirementsto hiscurrenttask.

3.2 Description of the technique

We will now proposethe RECTANGULAR FISHEYE

V IEW asa new focus–and–context techniquefor theinteractive display of large rasterimagesin mobileenvironments. This techniquehasbeendesignedtomeettherequirementsstatedabove.

To keepthecomputingeffort low andallow the inte-grationwith a region–of–interest–basedimagetrans-mission technique,the image is divided into non–overlappingrectangularparts in eachof which thedistortion is chosenthe samefor all pixels. As dis-tortion parameters,we areusingdownscalingfactorswhich arepowersof two in orderto speedupcompu-tationsandto allow theintegrationwith thetransmis-sionmethod.

Thefigures1 and7 illustratetheidea.A focus regionR0 in the centerof the image is not downscaledatall. It is surroundedby context belts, which displaytheremainingimagepartsin a downscaledversiontosave screenspace.EachbeltCj

�j � 0� is definedas

a pixel setdifferencebasedon thecontext rectanglesRj (seefigure1) asfollows:

Cj � Rj � Rj � 1 � (1)

The j–thbelt is assignedacontext downscaling factorsj : � 2 j which controlsthedistortionof the belt andthe amountof screenspacesaved. Sincethe degreeof interestof theuserin imagedetailsdecreaseswithincreasingdistancefrom the focus, the downscalingfactor of a belt is the higher the further that belt isaway from the focus. In order to attacheachcon-text belt to its neighbourwithout discontinuities,thebelt Cj is split into 8 � j partial rectangles. Eachofthesepartial rectanglesis assignedonescalingfactorfor theX– andanotheronefor theY–direction.Someof thefactorsarepre–determinedby thecontext beltsinsidethe belt Cj , andthe remainingonesaresetto

2� j . The grid of partial rectanglesis calledthe down-scaling grid. Figure7 showssuchagrid with two con-text belts,denotingthepairof downscalingfactorsforeachgrid rectangleasdownscaling pair sX sY � . Fig-ures3 to 6 show the resultof performingthe down-scaling.

Tailorability of thefocusdoesnot only meanto spec-ify its sizeandpositionbut alsoto definethe degreeof detailneeded.Thiscanbedoneby zooming, whichassignsa zoom factor z to the focus. To fit into ourscheme,we choseto supportzoomfactorswhich arepowersof two. In order to maintainthe assumptionthat the focusoffers the highestdegreeof detail,wemultiply all downscalingfactorby thezoomfactor2.

Thecontext beltscanbedisplayedin differentratiosto eachother(e.g., the first belt with s1 � 2 may bechosentwice aswide asthesecondonewith s2 � 4).Theseratio parameters allow the user to tailor thecontext beltswith respectto distortionandspacere-quirementsto his needs.An automaticchoiceof theratio parametersusinglinearoptimisationtechniquescanbe usedto force the sizeof the RECTANGULAR

FISHEYE V IEW to fit into the available display orwindow size.Furtherflexibility canbegainedby theopportunity to selectwhich context belts shouldbevisible.

4 GEOMETRY CALCULATIONS

After having describedthe basic structure of theRECTANGULAR FISHEYE V IEW, this sectionwillexplainhow to computethecornercoordinatesof thecontext rectangles. The computationis basedon thesizeof theimage, thepositionandsizeof thefocusre-gionandthecontext belt ratio andvisibility. Modify-ing theseparametersthroughdirectmanipulation(seesection5) supportsthetailorability of theview andre-quiresrapidrecomputationof thecoordinatemappingto updatethedownscalinggrid.

Theseinputparametersareneeded:

PicWid width of original image

PicHgt heightof original image

nBelt numberof beltsplusfocus

Scli downscalingparameterof belt i

Ratioi ratioparameterof belt i

i � 0 � � � nBelt � 1

Poslef t � 0Postop� 0

Posright � 0Posbot � 0 coordinatesof thefocus

2Thezoomfactoris interpretedasdownscalingfactor, too– thehigherthis factor, thesmallerthedisplayedimage.

ThearrayScli containsfor the focusthezoomfactorz andfor eachvisible context belt the productof itscontext downscalingsj and z. Analogously, Ratioi

containsanundefinedvaluefor thefocusandtheratioparameterfor eachvisiblebelt.

Focus

Belt 1

Belt i

Belt nBelt � 1

� � � � � � � � � � � � � � � � � � � � ��������������������� � � � � � � � � � � � � � � � � � � � ��������������������� � � � � � � � � � � � � � � � � � � � ��������������������� � � � � � � � � � � � � � � � � � � � ��������������������

��������������������

��������������������

��������������������

��������������������

��������������������

��������������������

��������������������

��������������������� � �

���

� �� �

� �� �

Figure1: Geometricstructure.

To describethe geometricstructureof the RECTAN-GULAR FISHEYE V IEW, only the coordinatesPosr � iof the belt rectangles areneeded(cf. figure 1). Forreasonsof consistency, the belt rectanglewith thenumberzerois formedby thefocus,andthebelt rect-angleswith a numbergreaterthanzerorepresentthecontext rectangles.Thus,thecomputationhasto cal-culatethefollowing coordinates:

Posr � i coordinateof belt i in directionr

in theoriginal image

wherer ��� lef t top right bot �The coordinatesPosr � nBelt � 1 are defined implicitlyby the point 0 0� and the size of the original im-age PicWid PicHgt � and correspondto its cornerpoints. The rectanglevertex coordinatesof the beltsi � 1 � � � nBelt � 2 remain to be computed. Todo that, the spacebetweenthe focus and the im-ageboundaryhasto bedistributedbetweenthebeltsi � 1 � � � nBelt � 1 accordingto theratio parametersspecifiedin Ratioi. Thewidth of abelt i in onedirec-tion r is computedasfollows:

Widr � i ���� Posr � nBelt � 1 � Posr � 0 ��� Ratioi

∑nBelt � 1k� 1 Ratiok

(2)

Thewidthof belt i in thefour directionsisnow usedtocomputethecoordinatesof its belt rectanglebasedonthe(alreadycomputed)coordinatesof thenext–innerbelt i � 1 asfollows:

Posr � i ��

Posr � i � 1 � Widr � i r ��� lef t top�Posr � i � 1 � Widr � i r ��� right bot � (3)

As� mentionedearlier, the partial rectanglesin theRECTANGULAR FISHEYE V IEW are createdfromrectangularregions in the original imageby down-scalingthemin both directionsby – possiblydiffer-ent– factors.After having computedequation(3), theproblemmayarisethat thedivision of thewidth andheightof theseresultingrectanglesdoesnot deliveran integerresult. Theconsequencewould bediscon-tinuity problemsat the boundarybetweentwo beltsarisingfrom skippedpixels.In orderto overcomethisproblem,weintroduceaboundaryconditionfor equa-tion (2) which variesWidr i for all belt rectanglesex-cludingthefocussuchthatadivisionwithoutremain-derby Scli is possible:

Widr i ! 0 " mod Scli # (4a)" Distr i $ Widr i #%! 0 " mod Scli & 1# (4b)

Distr i ' Widr i ' 0 (4c)

where

i ( 1 ) * * * ) nBelt $ 1

Distr i (�+Posr nBelt , 1 $ Posr i , 1 +This boundary condition assumesthat width andheightof thefocusrectanglearemultiplesof thezoomfactor. Furthermore,theremainingspacemustbedi-vidablewithout remainderby thedownscalingfactorScl1 of the first belt. If this conditionis not met, theimagemayhave to bepadded.

To satisfy the boundarycondition (4), the resultsWidr i from equation(2) are iteratively incrementedby oneuntil (4) is met. It canbeproventhatthis leadsalwaysto apartitioningwherewidth andheightof thebelt rectanglesaremultiplesof the respective down-scaling factorsScli . This boundarycondition maylead to small deviations from the belt size relationsspecifiedin Ratioi, but it ensuresthatnopixel rowsorcolumnsareskipped.

5 INTERACTION ISSUES

5.1 Manipulating the parameters

As statedin section3.1,theusermustbeofferedcon-trol overtheparametersof theRECTANGULAR FISH-EYE V IEW in order to supportrapid interactive ex-plorationof the presentedcontent. This is achievedby varioustechniquesof interactive directmanipula-tion. Especially, control of sizeandposition of thefocusmustbe achievablein a fastandintuitive way,such that the usercan explore various partsof thepresentedimage in detail driven by his special in-terest. To do this, the operationsMove, Resize andJump areprovided. This hasbeencombinedwith azoom–and–pan–approach(Zoom+Pan), which makes

it easyto obtainan overview over the whole image.Furtherparameterisationto control the context belts(ratio parameters,visibility of belts) is possibleforfine–tuning.

We will now discussthe direct manipulationtech-niques.

Move. This functionallows to changethefocusposi-tion in theoriginal imageby smallsteps.Moving thefocusdoesnot influencethespacerequirementsof theRECTANGULAR FISHEYE V IEW sincethesizeof thefocusregion andthecontext parametersremaincon-stant. Moving will usuallybe exploited if the pointof interestdrifts slowly into theneighbourhoodof thefocus.

Jump. Using this function, the focuscanbe set in-stantaneouslyto a new location possibly far awayfrom theold oneby specifyingthecentrepositionofthe new focus. This function is usuallyexploited tosetthepoint of interestinto thecontext areain orderto explore somefeaturestherein greaterdetail. Thetotal view sizeis not changed.

Define . If theuserrequiresa focusregionwith a newpositionanda differentsize,theDefine functionsup-portsthis goal. Thefunctiontakestheupperleft andthelower right cornerof thenew focusasparametersaffectsthesizeof theview.

Resize. The demandfor controlling the sizeof theareaof interestcanbemetusingthis function,whichallows theuserto adjustthesizeof thefocusregion.Changingthefocussizeinfluencesthespacerequire-mentsof thewholeRECTANGULAR FISHEYE V IEW.

Zoom+P an. The RECTANGULAR FISHEYE V IEW

savesscreenspaceby supportingfocus–and–context,but it is neverthelessnot always guaranteedthat thedisplayis largeenoughto show thewholeimage.Byspecifyinga zoomfactor, the total sizeof the RECT-ANGULAR FISHEYE V IEW canbe adjustedin stepsof powersof two. If not the whole imageis visible,panningoffers– comparedto scrolling– a fastalter-native to revealinvisibleparts.

5.2 Optimisations for fast response

The interactivity of the RECTANGULAR FISHEYE

V IEW enablesthe userto explore andto understandthe displayedimage. Thus, it is importantthat eachactionof theuserresultsin a fastresponseof thesys-tem. Only by interactive responsetimestheusercandevelopa feelingfor thedistortedpresentation.

This is especiallyimportantfor the techniquesMoveand Resize, which are only efficient for the user ifeachsmallpositionor sizechangeresultsin a rapidly

updateddisplay to reflect the changes. In order tomeetthis requirement,screenredrawing is donebelt–sequentiallyin aninterruptiblemanner. First, thenewfocus region is drawn, followed by the first contextbeltandsoon. Interruptibility ensuresthattheredrawsequenceis abortedbeforecompletionif during thedisplayupdateoneof thefunctionsMove or Resize isexecutedagain.

For generatingthe RECTANGULAR FISHEYE V IEW,large partsof the original image have to be scaledwhich is computationallyintensive. That’s why itis advantageousto storethe imagedataredundantlyat differentscalinglevelsandto reusethe correctly–scaledversionduringinteractionfeedbackin ordertodecreasethe responsetime. The generationof thepre–scaledversionscanbedonein apreprocesswhenloadingthe image,or imagepartsscaledfor displayin anearlierinteractionstepcanbereused.

When creatingredundancy it is necessaryto find atradeoff betweentheadditionalmemoryrequirementsand the savings in processingpower. Redundancyis very high if a copy of the imagescaledaccord-ing to eachpossibledownscalingpair is stored. Forinstance,storing all resolutioncombinationsin fig-ure7 resultsin 206- 25%redundancy. It canbeshownthattheredundancy divergesfor agrowing numberofcontext belts. However, the redundancy can be re-ducedto 33- 3% independentlyfrom the numberofbeltsif only imageversionsscaledusingpairs . sX / sX 0with sX 1 sY arestoredredundantlyandtheremainingscaledimagepartsaregeneratedonrequestby scalingtheaccordingpre–storedversion.For thelatter, therearetwo opportunities:scalingupa low resolutionim-age,whichresultsin highcomputingspeed,or scalingdown a high resolutionimage,which resultsin highquality. During interaction, speedis moreimportantthanquality. That’s why we areusingupscaling:If,for example,a partial rectanglewith a downscalingof . 2 / 40 is requested,it is generatedby scalingupthe X direction of the correspondingrectanglepre–storedwith downscaling . 4 / 40 . During periodswith-out interaction, we usedownscalingto re–computetheview at higherquality (seebelow).

If a transmittedimageis viewedonlineduring trans-mission (cf. [Rausc99]) using the RECTANGULAR

FISHEYE V IEW, only someimagepartsareavailableatacertainscalinglevel. Furthermore,recoveringtheimagefrom thewaveletcoefficient field of the trans-missiontechniqueis tooslow for interactiveresponsetimes. Thus,an efficient imagerepresentationmustbe exploited to storescaledversionsof thoseimagepartswhichareavailable.

We realiseda local image cache which is illustratedin figure2. To achieve efficient storage,eachscalinglevelof theimageisdividedinto tiles. Only thosetiles

Figure2: Redundantlocal imagecache.

requirestoragespacewhich contain imagedataal-readytransmitted.Sinceonly thefocusis availableatfull resolution,just this imagepartneedsto bestoredat level (1,1). Focusandfirst context belt areavail-ableat thenext downscalinglevel andsoon. Movingthefocusinitiatesnew transmissionswhichaddsomemoretiles to eachlevel. If a tile whichis notavailableat a certainscalinglevel is neededfor display, datafrom thecorrespondingtile at thenext lower level areupscaledandusedinstead.This ensuresfastdisplayrefreshandefficient storageby exploiting the sparsenatureof thetransmittedimagedata.

If theuserdoesnot interactwith theview, a socalledquality view is computedand replacesthe rapidlycomputed,but lower quality representationuseddur-ing interaction. This quality view is generatedbydownscalingthe full resolutionversionof the image(if a locally–available imageis displayed)or by di-rect recovery from the wavelet coefficient buffer (ifthe transmissiontechniquedescribedin [Rausc99] isused).

As a resultof exploiting the local imagecachewith33- 3% redundancy, even the computationallyinten-sive techniquesmove andresize canbeexecutedwithinteractiveresponsebehaviour.

6 EXAMPLE

To illustrate the possibleamountof bandwidthandscreenspacesaved, we will now describea scenariowherea scannedimageof the Rostockpublic trans-port map (seefigure 7) is transmittedvia GSM andviewed online during transmissionusing the RECT-ANGULAR FISHEYE V IEW. The bandwidthof the

simulatedtransmissionchannelis 7200bits per sec-ond,which approximatestheusablebandwidthwhenrunningHTTP via a GSM mobile phone. For moredetail on the transmissionmethod, pleaserefer to[Rausc99].

Figure7 shows thedownscalinggrid overlaidon theoriginal 1024x1024pixel image. The focus size ischosento be256x256pixels,andtherearetwo beltsbelt1 andbelt2 with downscalingScl1 2 2 andScl2 24. Both beltsareassignedthe sameratio parametervalueRatio1 2 Ratio2 2 1. That means,both beltswill havethesamewidth in theresultingfisheyeviewin thefigures3 to 6. Considerablesavings in displayspacecanbe achievedusingthis configuration– theRECTANGULAR FISHEYE V IEW requiresonly 25%of thescreenareaneededfor theoriginal image.

By combiningtheviewing methodwith thetransmis-sionschemeproposedin [Rausc99], substantialband-width savings can be achieved, too – in theory, thesameamountasfor thescreenspace.In practice,theresultsslightly deviate from thatsincethecompress-ibility of theimagevarieslocally.

Priorto startingtheimagetransmission,theinitial po-sition of the focus hasto be determined.This maybedoneby usingsomecontext information,e.g.,theposition of the viewer or a point of interest. Here,it is assumedthat the userplansto arrive in Rostockby train. That’s why the focusis positionedinto themainstationarea.Figure3 shows thetransmittedim-ageafter27 seconds.Althoughonly a small fractionof the imagedatahasbeentransmittedat this earlystage,theinformationin thefocusregion is recognis-able. Comparedto the27 secondstransmissiontimefor theRECTANGULAR FISHEYE V IEW, transmittingthe whole imageat the samedegreeof detail wouldhave taken 115 seconds.Thus, the RECTANGULAR

FISHEYE V IEW requiresonly 23.4%the bandwidthat this earlystage.Spendingthese27 secondstrans-missiontime on thewhole imagewould have leadtoan incomprehensibleresult. Figure8 illustratesthatby comparingthe quality of RECTANGULAR FISH-EYE V IEW andwholeimageafter27 seconds.

At this point, the usermovesthe focusdown andtothe left. The viewing softwareimmediatelychangesthelayoutbasedon thedataalreadyreceived;theleftandthelower partof thenew focusregion arerecon-structedfrom the available dataat lower resolution(seefigure 4). A requestspecifyingthe new grid issentto the server, instructingit to changethe trans-missionsettings. Given the new configuration,onlythosedatawhich have not yet beentransmittedarenow sentasdifferential refinementinformation. Sixsecondsaftermoving thefocus(pluslatency for send-ing therequestto theserver), thenew focusregion isavailableat the samedegreeof detail asthe old one

(seefigure5). Furtherprogressive refinementis car-ried out automatically, and88 secondsafter startingthetransmission,thereadabilityof thewholefish eyeview (seefigure 6) has reacheda stagewhich cannot be further improved by transmittingmore data(althoughthecompressionartefactscouldstill be re-duced). Note that transmittingthe whole imageatthe quality of the focusin figure6 would have taken321 seconds– the RECTANGULAR FISHEYE V IEW

needs27%of thattime resp.bandwidth.

7 CONCLUSION

In this paper, we have presentedthe RECTANGULAR

FISHEYE V IEW asa new techniquefor the interac-tivefocus–and–context displayof largerasterimages.Specialattentionhasbeenpaid to low computingre-quirements,low display spaceconsumptionand theopportunityto integrateredundancy–freeimagedatatransmission. This makes the techniqueespeciallysuitableto beusedin mobileenvironments.

Thesegoalsareachievedbyoverlayingadownscalinggrid of rectangleson theimageandto applythesamedownscalingfactorcombinationfor X andY directionto all pixels in the individual rectangles.Dependingontheexactconfigurationof thegrid, thescreenspaceandtransmissionbandwidthsavings canbe substan-tial asdescribedin section6.

Theinteractivity of thetechniqueoffersahighdegreeof control to theuser. This is necessarysincethedis-play techniquesavesspaceby usingdistortion.Rapiddirect–manipulative interactionallows theuserto ex-plore the displayedimageandto tradeoff spacere-quirementsanddistortion. To supportinteractive re-sponsetimes,wehaveintroducedaredundantstoragemechanismfor sparseimagedatarepresentations.

REFERENCES

[Furna82] G.W. Furnas. The fisheye view: a new look atstructuredfiles. Technicalmemorandum82-11221-22,Bell Labs,18 October1982.

[Keahe96]T.A. Keahey andE.L. Robertson. Techniquesfor non-linearmagnificationtransformations. InProc. IEEE Symposiumon Information Visualiza-tion, IEEE Visualization, pages38–45, October1996.

[Keahe98]T.A. Keahey. The nonlinear magnificationhomepage.http://www.cs.indiana.edu/hyplan/tkeahey/research/nlm/nlm.html,26 October1998.Version1.5.

[Rausc99] U. Rauschenbach. The rectangularfish eyeview as an efficient method for the transmissionanddisplayof large images. In Proc. IEEE Inter-national Conferenceon Image Processing(ICIP),Kobe,Japan,25–28October1999.

[Sarka93] M. Sarkar, S.S. Snibbe,O. Tversky, and S.P..Reiss. Stretchingthe rubbersheet. In Proc. ACMSymposiumon User InterfaceSoftware and Tech-nology, 1993.

Figure3: Initial RECTANGULAR FISHEYE V IEW,512x 512pixels,24562bytestransmitted.

Figure5: RECTANGULAR FISHEYE V IEW with thenew focus,30091bytestransmitted.

ACKNOWLEDGEMENT

The authorswish to thank the Warnow Regional PublicTransportBoardandthe Nitschke AdvertisingStudiosforkindly permittingto usetheir mapimagedata.

Figure 4: RECTANGULAR FISHEYE V IEW aftermoving thefocus,24562bytestransmitted.

Figure6: RECTANGULAR FISHEYE V IEW with thenew focus,79617bytestransmitted.

Figure7: Original imagewith downscalinggrid. 1024x 1024pixels.

Figure8: Qualitycomparisonaftertransmitting24562bytes:RECTANGU-LAR FISHEYE V IEW from figure3 (right) versuswholeimage(left).