A 3D Model Retrieval System Using The Derivative Elevation And 3D-ART

Transcription

1 3 Model Rereal Sysem Usng he erae leaon nd 3-R Jau-Lng Shh* ng-yen Huang Yu-hen Wang eparmen of ompuer Scence and Informaon ngneerng hung Hua Unersy Hsnchu awan RO -mal: bsrac In recen years he demand for a conen-based 3 model rereal sysem becomes an mporan ssue Hence we wll propose wo feaures ncluded eleaon descrpor () and derae eleaon descrpor () o exrac he exeror nformaon for 3 model rereal o dere beer rereal resuls we wll combne he exeror feaures wh an neror feaure 3-R by a noel releance feedbac approach he expermens are conduced on he Prnceon Shape Benchmar (PSB) daabase xpermen resuls show ha our proposed mehod s superor o ohers Inroducon Wh he deelopmen of compuer graphcs and compuer anmaons 3 models are becomng as ubquous as mages and deo hus s necessary o deelop an auomac and effcen rereal sysem for 3 models he prmary challenge o a conen-based 3 model rereal sysem s how o exrac he mos represenae feaures o dscrmnae he shapes of arous 3 models [] Vranc e al appled Fourer ransform o he sphere wh sphercal harmoncs o generae embedded mul-resoluon 3 shape feaures [] o be roaon naran pose normalzaon mus be conduced pror o feaure exracon herefore Funhouser e al proposed a modfed roaon naran shape descrpor based on he sphercal harmoncs n whch no pose normalzaon s needed [3] Some feaures o represen he 3 models are based on he hsograms of geomerc sascs ners e al red o search smlar 3 models usng shape hsograms whch characerze he area of nersecons of a 3 model wh a collecon of concenrc shells and secors [4] he MPG-7 shape specrum descrpor (SS) [5] calculaes he hsogram of he curaures of all pons on he 3 surface SS represens he dsrbuon of geomerc characerscs and s robus o essellaon of 3 polygonal models Osada e al [] proposed fe feaures 3 3 and 4 o represen 3 models by he probably dsrbuons of geomerc properes compued from a se of randomly seleced pons locaed on he surface of he model For nsance he bes feaure among hese fe feaures s he dsrbuon of dsances beween wo random pons Howeer hese feaures are naran o essellaon of 3 polygonal models hus Shh e al [7] proposed grd (G) o mproe 3 model s frs decomposed no a oxel grd he dsrbuon of dsances beween any wo randomly seleced ald grds s measured o represen a 3 model he 3 models also can be descrbed by s slhouees from dfferen ews Users can fnd smlar 3 models by shape feaures Super and Lu [8] explo slhouee conours for 3 objec recognon uraure and conour scale space are exraced o represen each slhouee hen e al [9] proposed he LghFeld descrpor (LF) o represen 3 models he LF s compued from 0 slhouees ach slhouee s represened by a bnary mage he Zerne momens and Fourer descrpors are employed o descrbe each bnary mage In fac slhouees represened by bnary mages can no descrbe he alude nformaon of he 3 model from dfferen ews Shh e al [0] proposed he eleaon descrpor () o represen he alude nformaon of a 3 model from sx ews Howeer LF and represen only he exeror shape of 3 model whou capurng he neror shape nformaon Kuo and heng [] proposed a 3 shape rereal sysem based on he prncpal plane analyss Frs by projecng he 3 model ono s prncpal plane a 3 model can be ransformed no a bnary mage he feaure ecors are hen exraced from he bnary shape mage Howeer usng only one bnary mage can no represen a complex 3 model well herefore Shh e al [] proposed he prncpal plane descrpor (PP) o descrbe a 3 model wh hree bnary mages by projecng on he prncpal second and

2 hrd planes he proper feaure ecors can be exraced from hree bnary mages o do 3 model rereal Noon and Klen proposed a 3 shape rereal mehod usng 3 Zerne momens whch s naurally an exenson of sphercal harmoncs based descrpors [3] Rcard e al [4] presened a 3 shape descrpor he 3 ngular Radal ransform (3-R) for 3 model rereal Frs he 3 models are represened n sphercal coordnaes Nex a Prncpal omponens nalyss (P) s appled o algn he 3 models along he z-axs hen he 3 exenson of MPG-7 s R [5] s appled o exrac feaure ecors In hs sudy we use he exeror and neror feaures for 3 model rereal he exeror feaures nclude he eleaon descrpor () and derae eleaon descrpor () hese wo exeror feaures can be combned o form a new feaure called In addon 3-R s used o exrac he neror nformaon of 3 models In summary many nds of feaures hae been commonly used for searchng smlar 3 objecs In fac no one can approprae for all nds of 3 models o rea hs problem and 3-R are combned for 3 model rereal Moreoer a new releance feedbac approach s proposed o selec he proper weghs beween and 3-R for beer rereal resuls he res of he paper s organzed as follows In Secon he proposed 3 model rereal mehod wll be descrbed In Secon 3 ges he expermenal resuls o show he effeceness of he proposed feaures Fnally conclusons are gen n Secon 4 Fg he boundng box of he 3 dog model s decomposed no a oxel grd leaon escrpor In hs secon we wll ge some reew of for 3 model rereal [0] Frs a 3 model s represened by sx gray-leel mages whch descrbe he alude nformaon of a 3 model from sx dfferen ews For each gray-leel mage he feaures ha descrbe he energes a dfferen rad are exraced o form he 3 he Proposed 3 Model Rereal Mehod In hs sudy hree descrpors ncludng eleaon descrpor () derae eleaon descrpor () and 3-R are used for 3 model rereal Before exracng he feaure ecors he 3 model s algned accordng o he prncpal plane [] leaon descrpor () wll be nroduced frs [0] Based on derae eleaon descrpor () whch s an mproed erson of wll be proposed In fac and can only represen he exeror nformaon of 3 model Moreoer 3-R [4] wll be adoped o exrac he neror nformaon of he 3 model he xeror Feaure he exeror feaures nclude eleaon descrpor () and derae eleaon descrpor () Boh are used o represen he exeror nformaon of 3 models 5 4 (a) (b) (c) Fg 3 dog model and s sx gray-leel eleaons (a) he fron eleaon and he rear eleaon 4 (b) he op eleaon and he boom eleaon 5 (c) he rgh eleaon 3 and he lef eleaon Fg 3 he dfferen radus of concenrc crcles for he eleaon he man seps for compung he eleaon descrpor of he 3 models are descrbed as follows: () 3 model s algned by s prncpal plane [] he prncpal plane s defned as he symmerc

3 plane on whch he sum of dsance of all pons projeced s mnmal () he polygonal surfaces are segmened no a oxel grd (see Fg ) he oxel s assgned f s whn one oxel wdh of a polygonal surface and 0 oherwse o normalze for ranslaon and scale he objec s mass cener s moed o he pon (3 3 3) and he aerage dsance from non-zero oxels o he mass cener s scaled o (3) Sx eleaons are hen dered o descrbe he alude nformaon of projecons from sx dfferen ews: fron op rgh rear boom and lef Le he fron op rgh rear boom and lef eleaons be successely noaed as = as shown n Fg he projecons of sx eleaons are gray-leel mages he gray-leel alue s hgher when he pxel s more close o ewer On he oher hand he gray-leel alue s lower when he pxel s far away from ewer (4) ach eleaon s decomposed no 3 concenrc crcles around he cener pon as shown n Fg 3 For he sum of gray alues of all pxels locaed whn he j-h concenrc crcle s defned as c (j) he normalzed dfference beween wo neghborng c (j) s hen dered: c c ( j ) c (3) for j 3 and se c 0 for all he eleaon descrpor s defned as: where [( ) ( ) ( ) [ () () (3)] for he eleaon descrpor s hen used as he feaure ecor for 3 model rereal erae leaon escrpor In hs secon erae leaon escrpor () s proposed o exrac he conour nformaon of 3 model he sx eleaons are frs dered hs process s dencal o ha proposed n Nex he dfference beween curren pxel and s neghbors s used o exrac he feaure ecor from each eleaon (see Fg 4) 4 P 3 P Fg 4 he pxel and s 8 neghbos ] 4 5 (a) (b) (c) Fg 5 3 dog model and s new sx gray-leel derae eleaons (a) he fron derae eleaon and he rear derae eleaon 4 (b) he op derae eleaon and he boom derae eleaon 5 (c) he rgh derae eleaon 3 and he lef derae eleaon he man seps for compung he derae eleaon descrpor of he 3 models are descrbed as follows: () Frs he sx eleaons are frs dered as () he sx derae eleaons are represened as (see Fg 5) For he -h derae eleaon he gray-leel alue of s defned as I : 8 j IP 8 P j P j where s a pxel on and P s he j-h neghbor of (see Fg 4) (3) ach eleaon s decomposed no 3 concenrc crcles around he cener pon by he sep (4) n hen he derae eleaon descrpor s defned as where [( ) ( ) ( [ () () (3)] for he derae eleaon descrpor s hen used as he feaure ecor for 3 model rereal o ge he beer rereal resuls and wll be combned o form a feaure ecor as: [ [ () () for () () (3) (3) 3 sance ompuaon () ) (33) ] () 3 (34) (3)] ach 3 model can be represened by sx eleaons Snce he relae posons of he eleaons are aen no accoun he machng operaons are 3! 3 =48 (4)]

4 [0] ach machng operaon corresponds o a permuaon of he sx eleaons Le and u denoed he query model q and he machng model of he dsance of beween q and s defned as follows: s ( ) u p ( ) 3 j u p ( ) where p () denoes he -h alue for he -h permuaon and 48 In he same way he dsance of and beween q and can be defned as: s ( ) u p ( ) and 3 j s ( ) u p ( ) 4 j u u p ( ) p ( ) where p () denoes he -h alue for he -h permuaon and 48 he Ineror Feaure In order o mproe he rereal effcency he neror feaure s used o combne wh he exeror feaure 3-R he 3-R [4] s an exenson of MPG-7 s regon-base shape descrpor ngular Radal ransform (R) he 3-R can express oxel dsrbuon whn 3 model he man seps for compung 3-R are descrbed as follows: () Frs 3 model s algned by he sep () n () 3 model s hen segmened no oxel grds and normalzed by he sep () n (3) ach grd s represened by he sphercal coordnae (4) he 3-R coeffcens of a 3 model are defned by : F nm m where F nm m V nm m ( ) f ( ) d d d s he R coeffcen of order n m θ and m ϕ f ( ) s a 3 model funcon n sphercal coordnaes and V ( ) s he nm m 3-R bass funcon ha are separable along he angular and he wo radal drecons: V ( ) ( ) ( ) R ( ) nm m m m n he angular bass funcons are defned by an exponenal funcon: m m ( ) exp( jm ) ( ) exp( jm ) and he radal bass funcons s defned by a cosne funcon: R n n 0 ( ) cos( n) n 0 he 3-R s formed by he magnudes of all complex R coeffcens he defaul 3-R consss of 74 coeffcens F for 0 n nm m 0 m θ 4 and 0 m ϕ 4 excludng n = 0 m θ = 0 and m ϕ = 0 In summary 3 R s defned as: [ () () 3 sance ompuaon (74)] Le and u denoed he 3-R of he query model q and he machng model he dsance of 3-R beween q and s defned as follows: s 74 4 Feaure ombnaon ( ) u ( ) In he radonal releance feedbac algorhm he relean models (smlar o query model n curren rereal resul) mus be manually seleced by user s response o deermne he wegh of feaures In hs sudy a new releance feedbac approach s proposed o auomacally selec relean 3 models s menoned aboe he exeror and neror feaure and 3-R wll be combned Based on he auomacally seleced relean models he weghs of and 3-R can be deermned he seps of auomac releance feedbac approach are as follows: () For gen a query model he dsances of q beween all of mach models = n (n s he oal number of models n he daabase) and s s are sored n an ncreasng order For he op g 3 models we defne her grades G_ and G_3R as g g- g- and respecely In hs sudy g s defned as 0 In addon G_ and G_3R of all oher objecs are defned as zero ha s he 3 models

5 wh hghes smlary measure wll hae he hghes grade () he relean models are auomacally seleced by grades If G_ and G_3R boh were no zero he model s aen as he relean model he grades of relean models are redefned as: G _ f G _ 0 and R G _ G _ 3R 0 G _ 3R R 0 G _ 3R 0 oherwse f G _ G _ 3R oherwse 0 and 0 (3) ccordng o he relean models he weghs of and can be auomacally deermned Based on he grades of hese relean objecs he feaure wegh s calculaed as: n G _ q n R R G _3R q for each machng objec he weghed dsance s defned as: IS IS IS he smlary measure beween q and s defned as: Sm IS q Noe ha he large Sm a machng model has he more smlar s o he query one Based on hs new releance feedbac algorhm we can fnd more smlar models o he query one 3 xpermenal resuls o demonsrae he effeceness of he proposed mehod for dfferen 3 models some expermens hae been conduced on he Prnceon Shape Benchmar (PSB) daabase [5] he PSB daabase conans 84 models ( classes) whch are dded no 907 ranng models (90 classes) and 907 es models (9 classes) Noe ha n hs daabase he number of models s dfferen for each class Fg shows some example models n he PSB daabase he performance s measured by he recall he recall s defned: recall N / where N s he number of relean models rereed and s he oal number of relean models n he daabase In our expermenal each model n daabase s presened as a query one able shows he recall alues for all query models usng he proposed descrpors and oher mehods In he exeror feaures we can see ha s beer han or In addon o he exeror feaure we also ae he neror feaure (3-R) no accoun By usng he new releance feedbac approach and 3-R are combned for a beer rereal resuls Noe ha he combnaon of and 3-R ges much beer effeceness han only usng he exeror or neror feaures (a) (b) Fg he Prnceon Shape Benchmar (PSB) daabase (a) Some classes n PSB daabase (b) ll models belong o he sedan class able he recall for he PSB es daabase Mehod Recall R R 040 PP [] 0343 SH [3] 070 SS [5] 0587 G [7] 0830

6 4 oncluson Wh he deelopmen of compuer graphcs and rual reales he demand for a conen-based 3 rereal sysem becomes urgen In hs sudy wo feaures eleaon descrpor () and derae eleaon descrpor () are used as he exeror feaures hese wo exeror feaures are combned wh he neror feaure 3-R by a new releance feedbac approach for 3 model rereal he expermens hae been conduced on he Prnceon Shape Benchmar (PSB) daabase xpermen resuls show ha he proposed mehods are superor o ohers Reference [] JWH angelder and R Velamp surey of conen based 3 shape rereal mehods Shape Modelng pplcaons pp [] V Vranc Saupe and J Rcher ools for 3-objec rereal: Karhunen- Loee ransform and sphercal harmoncs Proceedngs of I Worshop on Mulmeda Sgnal Processng pp [3] Funhouser P Mn M Kazhdan J hen Halderman obn and Jacobs search engne for 3 models M rans on Graphcs ol no pp [4] M ners G Kasenmuller HP Kregel and Sedl 3 shape hsograms for smlary search and classfcaon n spaal daabases Proceedngs of h Inernaonal Symposum on Spaal aabases (SS 99) pp [5] S Manjunah P Salember and Sora Inroducon o MPG-7 Mulmeda onen escrpor Inerface John Wley & Sons Ld 00 [] R Osada Funhouser B hazelle and obn Shape srbuons M rans on Graphcs ol no 4 pp [7] JL Shh H Lee and J Wang 3 Objec Rereal Sysem Based on Grd lecroncs Leers ol 4 no 4 pp [8] BJ Super and H Lu aluaon of a hypoheszer for slhouee-based 3- objec recognon Paern Recognon ol 3 pp [9] Y hen XP an Y Shen and M Ouhyoung On sual smlary based 3 model rereal ompuer Graphcs Forum ol no 3 pp [0] JL Shh H Lee and J Wang New 3 Model Rereal pproach Based on leaon escrpor Paern Recognon ol 40 no pp [] Kuo and S heng 3 model rereal usng prncpal plane analyss and dynamc programmng Paern Recognon ol 40 no pp [] JL Shh and W Wang 3 Model Rereal pproach based on he Prncpal Plane escrpor Proceedngs of he Second Inernaonal onference on Innoae ompung Informaon and onrol (III) pp [3] M Noon R Klen Shape rereal usng 3 Zerne descrpors ompuer-ded esgn ol 3 pp [4] J Rcard oeurjolly and Basur Generalzaons of angular radal ransform for and 3 shape rereal Paern Recognon Leers ol no 4 pp [5] P Shlane P Mn M Kazhdan Funhouser he Prnceon shape benchmar Proceedngs of Shape Modelng pplcaons pp