a low-pws tiltcrcd image rlh its lower layer, cxcep! for the ~r layer, all pmcessns of a layer execute the s:ime in- structions in panllel. This pyramid scheme can k ...
MvA'92
lAPRWorbhoponMachineV~sionAppl~cat~ms Dac.7-9,1992, Tokyo
AN EFFICIENT PARALLEI, IMPLEMENTATlON OF
THE LAPLACIAN PYRAMID ALGORITHM Mill X b t , AMelhmid Hachicha. and blain Mtrigot ESIGETEL. 1, rue du pjrt de Valvin~.772315 Avon Cdcx. France
IEE, UniversitC Paris-Sd, BAt. 220,91405 Orsay Ceden. France
ARSTRACT The Lnplnrion pyrontid ci?din~is a useful image prorexsitt~tool. !IS rrrnnine time widt o seq~~enrinf murhrnr is 0 ( n 2 ) H F ~ P n*n ~ P is the si:e ofrhr ori~inn/ i m a ~ rThis . pnper dfsrrihes a pc~rrwllclimp~~mrnrarinn of this ~lparithm on SIMD machinex like pymmidc and meshrs. In rhese mnrhinrs. rhr ronr~rnrddnta ond a ~ s o c i a t ~oprralions rl or@ ollocoted m e l e r n e n r u ~processors, a d a nlellorfanired scheduling is trsrd to ollou~an ~ v e n l vdisrrfbur1.d roatpurarion executed In pamllrl. Wirli a prqerly sizrd pymrnid nufrhin~the n m n i n ~rime is reduced to OtH) u h ~ r eH is the pvramid's hrighl. W h t n rhr nturhine is snrnller rhun rhr Lnplurirrn prmniid, fire rmnw rr divided into sqmenrr anci rhr compulurion B carried urlr sqrnen! hv se.cntmr, Hnn,r~ur,o prohl~nron ~ h e p e s i p h ~ r v of tach seRrnPnr I S ~ n c o l 4 n t ~ rTO ~ drrrnedv . rhis p r d ~ l e m , nun rn~rhodsare propos~d.The hcsr one a l l n w a running r i m n of fl(r?/m2 + log nt) nphrrc mLm is fhr sir* of rhc pvrari~idmi~chinr's Imsr. 1. INTRODUCTFON Our curren1 pmject. cnrried out jointly hy ESIGETEL and the Wnivessitt Patis-Sud. comrns the implcmcntation of imagc coding algoritt~nis[h]with SPHINX15I. a multiSlMD hin-pynmid machlnc dcsrgncd hy zhc Univcrsitfi hris-Sud in France. This papcr dcsvriks an clticient parallel imp~cmcnrdinnn l the Laptacim pyramid algorithm(21. This alpc)rithm. prescntetl hy P.J. Run and E.H. Adclson scveral years ago. is ured for image cumflression, pmgrcssivc image uansmcssinn, and other applications in irnagc processingdomain. The rcaon of using a rnnrlrivcly prdllel machine i s to seducc t k running timc n l compulsrion. In this paper. we arc pan~cularlyinrercffcd in using a p y m t d machine such a? SPHINX md PAPIAr31, m ~ din comparing thcm with rncshcs like W P I I].
In the FnlIwing scclions. after a hricf pmscntation of ~ h Laplacian c p y m i d coding, wc prcrcnt in dctail ils parallcl ~nlpIcmcntal~nn follnwed hy s p r f n m m c c evalualinn.
2. E.APLAClhN PYRAMID CODING
The Laplacim pymicl coding mnsim of rwn main steps: !he gcncntion or a Gauwiw pyramid and rha! of n Laplacian pyramitl. Each laycr of thc Gaussian p y m i d is a low-pws tiltcrcd image rlh its lower layer, cxcep! for the hasc which 17 the original imng of size n*n. Thc dlffcrcncc ktwccn one layer rif thc Gausdm pyramid and the
expanded imace obtained fmm the Iayer immediately ahnve gives rhecomspondine: layer o f rhi Laptac~anpyr& mld. Thc expanded images fnrrn a p y m i d called expand& Gaussian pyramid.
The Gaussian p y m i d is thc wqucnce of the rcduccd low-pass liltcrctf image? {gk]=(gn. g l . pH-, J ;enenred fmm (the original imagc) by a REDUCE funcrron:
....
whcre H i s thc hcigh a l LhC pyrmid and w 0 is the weighting function. Expanded Gaussian Pvrarnid The expandcd Gaussian p y m i d i s Ihc scqucnce (if the expanded i m a ~ c s { F ' ~ gcncmtcd } fmm I&l hy "EXPAND hnaic~n:
(2.3)
gWk=EXPAND(gk+,) ?
L
~ ' ~ (=i4jp-. I;??,w(p.q)g,,,l(i-p)~. ) (I-..
Ci-q)/2)
42.4)
where only the terms with (i-p) and ti-q) all cvcn an: considered.
hlacian m i d
The Laplacian p y m i d IL,] is just the ditfcrcncc OF E R ' ~ ~ : wimLH.]=&.1.
Isk]
h=gk-g'k,k
