Image Coding Using Data-dependent Triangulation - IEEE Xplore

IMAGE CODING USING DATA-DEPENDENT TRIANGULATION

D e p t . of' El(.lectuicaland E l e c t r o n i c Engineering, Imperial College, London S W 7 2BT, UK. E-nmil: 1.rilalQic.a.c.uk

Abstract: In this paper. ail image c-oding t,echniquc t,hat combines irregular subsampling and t.rinngiilat,ioii is proposed, First. a Delannay t,riangulal.ioiiis constructed over a set. of visually significant sampling as the t,riaIigulat,ioiiprogresses. Then R dat,a~clependent,t,riangulat,iori is genpoiiibs selerterl increiiieiit~t~lly erat,ed. starting from the Delauna): t,uiangulation. Iiy a series of edge swaps based on t,liP quality of blie approsiniat,ioii.Bilinear iiiterpolat,ion is used t80approsimat,e t,he t,riangular regions. T h e simulation resiiit,s show tlie superiorit,?: of tlie proposrd algorit,lirii over JPEG at, low bit, rat,es (0.206bpp and 0.113 bpp) as well as it,s robustness. angles depends on t,lie specific t,riangulat,ion of t,lie data point,s and t*liat a n arbit,rary triangulat,ioii rnay Recent,ly, many image coding algorilhms t8hat,exploit not, be an acceptable solnt,ion. t,he geometrical features of the image have been deIt, is widely accepted t,liat a good triangulat,ioii veloped. Image represeiit,at,ion using t8riangnlation, for int,erpolnt#ionpurposes should be as equiangular alt,lioiigh iiot widely used. lias been investmigatedwit81i as possible. This is Iiecanse error Iiounds for int.erpromising results. In tlir algorithm proposed by polation over t,rianglcs increase as t,lie t,riaiigles beKashimura et, al. [I]: a Delaunay t,riangulat,ion is come longer and t,hiiiner [2]. Ilo~vever.Rippa [3] has o l h i n e d using sampling point,s previously selected shown: using the same e,rror bounds in [>I. tmliatm long from the boundary lilies of tlie image. Then, biliiiand thiii t,riangles r a n lie good for int,erpolat,iiis a ear iiit,erpolatioii is applied t,o each briaiigular region function with n preferred direct8ion. using t,hc grey level values at, t,he sampling poiiits. Delcrrrnoy Tkzcrtiqtrlatzon: The \vell-ltnown Lklau~ c the e sampling points are chosen prior t,o t.he t,riangulation, t,he select,ioii is not, adapt,ive t,o tmheimage nay t,riangulation [4] is very popular because it, pro(lures t,riaiigles as equiangular as possible. It is 11 properties. oii prosiinit,y relationships Iiet,meeii the points and is an image coding algorit'hin nsually defined by its dual problem, t,he Voronoi diat,liat, also coiiibines irregiilar subsanipling with trigram, but, it, may also he defined by it,s own geoiiietL angulat,ion. T h e set of sampling poiiit.s is selertcd rical propert,ies. in a progressive iiianiier result,ing in a n effect,ive disfimdament,al propert.ies of t,he Delaut,ribiit,ioii of point,s. Start,iiig from R I)elaunay t#riaii011 are I~aseclon t.he following crit,rria: golat,ion. a clnta-dependent, triangrilat,ion which t,alies t,lie circle crit,erioii and thc iiiiii-mas aiigle criterion int,o account, t8heqiialit8yo l t,he approxiinat,ion is then (showii to be equivalent8by Lawsoa [SI). Tlir rirclr coiistxucted. Bilinear int,erpolat,ioiiis used t,o approscriterion ensiircs t,liat, 110 point, belorigiiig t,o tlie set iinat,e each t,riangular region. T h e results show t,hat, t,his t,echiiiclne achieves rirc-cpt,ablequalil,y at r;rt,es as of sampling poiiits lies witliiii t,he circumcircle of any triangle in t,lie Delaimay triangulation. The minlom as 0.1u bpp. angle crit,erion eiisures that8.if iii a Delaunay h giilatioii tlie diagonal of any quadrilateral roiisist,iiig 2 Triaiigiilatioii of pairs of ad,jacent,t,riniigles is replaced I q t,lie other. A t,riangulat,ioiiof a finitmeset, of points in t,lie plane t.lien t,he iniiiiininn of t,he int,ernal angles of the U is a subdivision of t,lie plane in which all it,s regions sult,ing t8riaiiglesdoes not. in(-rease. Converselj.. a t,riaiigulat,ion that. aat,isfies t,liese criteria is unique aiid are t8riaiigles. It, ( x i lie olit,ainrrl by ,joining Ipairs of that, is the Delaunag t8riaiigulation. point,s wit,li iion-iiit,ersect,ing st,raight lines. TrianguThe uniqueness of t h e Delannay Criaiigulation is a lat,ion as a inet,liod for approxiiiiat,ioii of surfaces is very at,t,ractiveprol3ert.y for coding purposes 11 used in inany areas snrh as coiiipiit,c~rgrapliirs. geographic dat>aprocessing. iiiedical iiiiagery. and i m n it, meaiis t,liat. only Ihe posit,ioii of t,he poiiit,s is iiwded puter aided design. t,o reconst,riict, t,lie t,riangulat,ioii at, the decoder entl. On t,he ot,her h a n d . t,liis technique complet,ely disrcIn gmeral. B giwii sei, of point,s iiiay give many different. t,riangulal.ioiis. It, is rlear t,hat. t,he garrls t,lir image contrnts. Dcrtcr-Delmclent 'li-zcritgrilatron: Dat,a-depeiitlenl, qnality of blie piecewise linear iiiterpolabion over tri1

Introduction

0-7803-41 37-6/97/$10.0001977 IEEE

DSP 97 - 531

t.riangulat.ions[a] take int,o account8not, only the posii,ioii of t,lie sampling poini,s Ibiit, also t,lirir ilat,a values. -_ 1liese t,riangnlat,ionsn i a l use ~ ol'dat,a-rlrpeiideiil cri(,?ria t,o i i i e a s ~ i rt,lir ~ qualily of a t,riangulat,ion. It, i s esprct,crl i h a t ai1 opi,imal i,riangulation. with rrsprct t,o a given dai.s-rlel,encleiit, crit,eriori. will provide a r approxiniatioii 6linii t,hr Drlaniioy t,riangulnt,iori. Dai,a-drpriidriit txiangulat,ioiis m a y produce long anti t,liiii i,rianglrs ivliicli coiitmriImtet30i,lie improvriiiriii of ilie .2l1l)ro"iiriat,ion. Since a n optimal t,riaiigulat,ion ma!. h e diflicult, to att,ain. t,he aim o f (,his inriliod is to find a locally opt,iiiial t,riaiigulat8iou.Tile iiiaiu tool Tor prodricirig a dat,a-drpcnrlrni t~riaiigulaiioiiis Lansori's lo