NeuralNetwork Based 3D Surface Reconstruction

Transcription

1 Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, NeuralNetwor Bae 3D Surface Recontruction Vincy Joeph Coputer Departent haoal Shahani Engineering College, Banra, Mubai, Inia. Shalini Bhatia Coputer Departent haoal Shahani Engineering College, Banra, Mubai, Inia. Abtract hi paper propoe a novel neural-networ-bae aaptive hybri-reflectance three-ienional (3-D urface recontruction oel. he neural networ cobine the iffue an pecular coponent into a hybri oel. he propoe oel conier the characteritic of each point an the variant albeo to prevent the recontructe urface fro being itorte. he neural networ input are the pixel value of the twoienional iage to be recontructe. he noral vector of the urface can then be obtaine fro the output of the neural networ after upervie learning, where the illuinant irection oe not have to be nown in avance. Finally, the obtaine noral vector can be applie to integration etho when recontructing 3-D obect. Facial iage were ue for training in the propoe approach Keywor-Labertian Moel;neural networ;refectance Moel; hape fro haing urface noral an integration I. INRODUCION Shape recovery i a claical coputer viion proble. he obective of hape recovery i to obtain a three-ienional (3-D cene ecription fro one or ore two-ienional (- D iage. Shape recovery fro haing (SFS i a coputer viion approach, which recontruct 3-D hape of an obect fro it haing variation in -D iage. When a point light ource illuinate an obect, they appear with ifferent brightne, ince the noral vector correponing to ifferent part of the obect urface are ifferent. he patial variation of brightne, referre to a haing, i ue to etiate the orientation of urface an then calculate the epth ap of the obect II. DIFFEREN APPROACHES FOR RECONSRUCION A. Labertain Moel A ucceful reflectance oel for urface recontruction of obect houl cobine both iffue an pecular coponent [1]. he Labertian oel ecribe the relationhip between urface noral an light ource irection by auing that the urface reflection i ue iffue reflection only. hi oel ignore pecular coponent. B. Hybri Reflectance Moel A novel hybri approach generalize the reflectance oel by coniering both iffue coponent an pecular coponent. hi oel oe not require the viewing irection an the light ource irection an yiel better hape recovery than previou approache. A hybri approach ue two elf-learning neural networ to generalize the reflectance oel by oeling the pure Labertian urface an the pecular coponent of the non- Labertian urface, repectively. However, the hybri approach till ha two rawbac: 1 he albeo of the urface i iregare or regare a contant, itorting the recovere hape. he cobination ratio between iffue an pecular coponent i regare a contant, which i eterine by trial an error. C. Neural Networ Bae Hybri Reflectance Moel hi oel intelligently integrate both reflection coponent. he pure iffue an pecular reflection coponent are both fore by iilar fee-forwar neural networ tructure. A upervie learning algorith i applie to prouce the noral vector of the urface for recontruction. he propoe approach etiate the illuinant irection, viewing irection, an noral vector of obect urface for recontruction after training. he 3-D urface can alo be recontructe uing integration etho. III. DESCRIPION Fig. 1 how the cheatic bloc iagra of the propoe aaptive hybri-reflectance oel, which conit of the iffue an pecular coponent. hi iagra i ue to ecribe the characteritic of iffue an pecular coponent of aaptive hybri-reflectance oel by two neural networ with iilar tructure. he copoite intenity R hybri i obtaine by cobining iffue intenity R an the pecular intenity R bae on the aaptive weight (x,y an (x,y. he yte input are the -D iage intenitie of each point, an the output are the learne reflectance ap. Fig. how the fraewor of the propoe yetric neural networ which iulate the iffue reflection oel. he input/output pair of the networ are arrange lie a irror in the center layer, where the nuber of input noe equal the nuber of output noe, aing it a yetric neural networ. 116

2 Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, Figure 1 Bloc iagra of the propoe aaptive hybri-reflectance oel Figure Fraewor of the propoe yetric neural networ for iffue reflection oel he light ource irection an the noral vector fro the input -D iage in the left ie of the yetric neural networ are eparate an then cobine inverely to generate the reflectance ap for iffue reflection in the right ie of the networ. he function of each layer i icue in etail below. A. Function of Layer Layer 1: hi layer noralize the intenity value of the input iage. Noe I i enote the i th pixel of the -D iage an enote the nuber of total pixel of the iage. hat i f i I i, i 1,..., (1 a, i 1,..., (1 i f i Layer : hi layer aut the intenity of the input -D iage with correponing albeo value. I i f i, i 1,..., α i Layer 3: he purpoe of Layer 3 i to eparate the light ource irection fro the -D iage. he light ource irection of thi layer are not noralize. f ˆ I i ω i,, i 1,..., 1,, 3 (3 i 1 ( 3 a f, 1,, 3 Layer 4: he noe of thi layer repreent the unit light ource. Equation (4 i ue to noralize the non-noralize light ource irection obtaine in Layer

3 1 f 1,, Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, (4 (4 a f. ( Layer 5: Layer 5 cobine the light ource irection an noral vector of the urface to generate the iffue reflection reflectance ap. 3 f, 1,..., 1 ˆ, (5 R a f, 1,..., (6 Layer 6: hi layer tranfer the non-noralize reflectance ap of iffue reflection obtaine in Layer 5 into the interval [0,1]. a f ˆ R, 1,..., (6 55 ax( ( f in ( 55 ax( in( ( in ( in ( 1,..., (7 where (,,..., 1 an the lin weight between Layer 5 an 6 are unity. Siilar to the iffue reflection oel, a yetric neural networ i ue to iulate the pecular coponent in the hybri-reflectance oel. he aor ifference between thee two networ are the noe repreentation in Layer 3 an 4 an the active function of Layer 5. hrough the upervie learning algorith erive in the following ection, the noral urface vector can be obtaine autoatically.[3] hen, integration etho can be ue to obtain the epth inforation for recontructing the 3-D urface of an obect by the obtaine noral vector[4]. B. raining Algorith Bac-propagation learning i eploye for upervie training of the propoe oel to iniize the error function efine a E ( Rhybri Di i (8 i 1 where enote the nuber of total pixel of the -D iage, R i enote the i th output of the neural networ, an D i enote the i th eire output equal to the i th intenity of the original -D iage. For each -D iage, tarting at the input noe, a forwar pa i ue to calculate the activity level of all the noe in the networ to obtain the output. hen, tarting at the output noe, a bacwar pa i ue to calculate E ω, where ω enote the autable paraeter in the networ. he general paraeter upate rule i given by ω t + 1 ω t + ω t ( ( ( ω( t + η E ( ω t (9 he etail of the learning rule correponing to each autable paraeter are given below. C. he Output Layer he cobination ratio for each point an i calculate iteratively by + + η ( D Rhybri R 1,..., ( η ( D Rhybri R 1,..., (11 where D enote the th eire output; R hybri enote the th yte output; R enote the th iffue intenity obtaine fro the iffue ubnetwor; R enote the th pecular intenity obtaine fro the pecular ubnetwor; enote the total nuber of pixel in a -D iage, an η enote the learning rate of the neural networ. For a gray iage, the intenity value of a pixel i in the interval [0, 1]. o prevent the intenity value of R hybri fro exceeing the interval [0, 1], then the rule + 1 where >0 an >0, ut be enforce. herefore, the cobination ratio an i noralize by 118

4 Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, ,..., + 1,..., + D. Subnetwor (1 he noral vector calculate fro the ubnetwor correponing to the iffue coponent i enote a n ( 1 3 for the th point on the urface, an the noral vector calculate fro the ubnetwor correponing to the pecular coponent i enote a n ( 1 3 for the th point. he noral vector n an n are upate iteratively uing the graient etho a + + η ( D Rhybri 1,,3 (13 + ( t + η rh ( t ( D ( t Rhybri ( t 1,,3 (14 where enote the th eleent of illuinant irection ; h enote the th eleent of the halfway vector, an r enote the egree of the pecular equation. he upate an houl be noralize a follow: n 1,, 3 n (15 o obtain the reaonable noral vector of the urface fro the aaptive hybri-reflectance oel, n an n are copoe fro the hybri noral vector n of the urface on the th point by n n( t + 1 ( t n( t + 1 ( t + 1 (16 where an enote the cobination ratio for the iffue an pecular coponent. Since the tructure of the propoe neural networ i lie a irror in the center layer, the upate rule for the weight between Layer an 3 of the two ubnetwor enote a W an W can be calculate by the leat quare etho. Hence, W an W at tie t+1 can be calculate by 1 W ( V V V 1 W ( V V V (17 where V an V enote the weight between the output an central layer of the two ubnetwor for the iffue an pecular coponent, repectively. Aitionally, for fat convergence, the learning rate η of the neural networ i aaptive in the upating proce. If the current error i aller than the error of the previou two iteration, then the current irection of autent i correct. hu, the current irection houl be aintaine, an the tep ize houl be increae, to pee up convergence. By contrat, if the current error i larger than the error of the previou two iteration, then the tep ize ut be ecreae becaue the current autent i wrong. Otherwie, the learning rate oe not change. hu, the cot function E coul reach the iniu quicly an avoi ocillation aroun the local iniu. he autent rule of the learning rate i given a follow: If (Err (t-1 > Err an Err (t- > Err η(t+1 η + ξ, Ele If (Err (t-1 < Err an Err (t- < Err η(t+1 η ξ, where ξ i a given calar. Ele η(t+1 η IV. EXPERIMEN RESULS AND DISCUSSION Yale Databae ha been ue in thi proect an fro thi atabae two ataet have been coniere for training [5]. In the firt ataet a peron with fixe poe, 5 iage were electe with 5 ifferent illuinant irection. In the econ ataet five people with fixe poe, 3 iage were taen with 3 ifferent illuinant irection. Illuinant irection choen for ataet are ifferent. After the text eit ha been coplete, the paper i reay for the teplate. Duplicate the teplate file by uing the Save A coan, an ue the naing convention precribe by your conference for the nae of your paper. In thi newly create file, highlight all of the content an iport your prepare text file. You are now reay to tyle your paper; ue the croll own winow on the left of the MS Wor Foratting toolbar. A. Preproceing In the preproceing tage, the iage were croppe into 64X64 pixel. It wa ae into a ingle vector of ize herefore the firt atabae i of ize 3X4096 an the econ atabae i of ize 9X

5 Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, B. raining Reult he neural networ wa ipleente an the training of the networ wa tarte with the firt ataet. he reult of the training one o far are given below. Firt the training wa tarte with a fixe learning contant. It wa woring fine for higher value of error an later the convergence of error wa very low. hen the training wa one applying oentu. It reuce the error to oe lower value an it tarte egraing very lowly. hen aaptive learning etho wa eploye which howe that the convergence can happen fater. hu aaptive learning etho i a fater etho in error bac propagation algorith. Diffue Intenity Recontruction Figure 3 Efficiency plot with contant eata Efficiency plot of training with oentu Diffue Coponent error y-axi x-axi Figure 6 Recontruction with Diffue Coponent no. of epoche Figure 4 Efficiency plot with oentu Efficiency plot of training with ADAPIVE learning error Figure 7.Recontruction with Specular Coponent no. of epoche Figure 5 Efficiency plot with aaptive eata 10

6 Vincy Joeph et al /International Journal on Coputer Science an Engineering Vol.1(3, 009, IEEE International Conference on Control an Autoation Guangzhou, China - May 30 to June 1, 007 [] Wen-Chang Cheng, Neural-Networ-Bae Photoetric Stereo for 3D Surface Recontruction, 006 International Joint Conference on Neural Networ Sheraton Vancouver Wall Centre Hotel, Vancouver, BC, Canaa July 16-1, 006 [3] Chin-eng Lin,Wen-Chang Cheng, an Sheng-Fu Liang, Neural-Networ-Bae Aaptive Hybri-Reflectance Moel for 3- D Surface Recontruction, IEEE ranaction on Neural Networ, Vol.16, No. 6, Noveber 005. [4] Zhongquan Wu an Lingxiao Li, A line-integration bae etho for epth recovery fro urface noral, IEEE ranaction on Pattern Analyi an Machine Intelligence, Vol.43, No.1, July [5] S. Georghiae, P. N. Belhueur, an D. J. Kriegan, Fro few to any: illuination cone oel for face recognition uner variable lighting an poe, IEEE ranaction on Pattern Analyi an Machine Intelligence, vol. 3, No.06, June 001 Figure 8. Recontruction with Hybri Coponent V. CONCLUSION In thi paper a novel 3-D iage recontruction approach which conier both iffue an pecular coponent of the reflectance oel iultaneouly ha been propoe. wo neural networ with yetric tructure were ue to etiate thee two coponent eparately an to cobine the with an aaptive ratio for each point on the obect urface. hi paper alo attepte to reuce itortion caue by variable albeo variation by iviing each pixel intenity by correponing albeo value. hen, thee intenity value were fe into networ to learn the noral vector of urface by bac-propagation learning algorith. he paraeter uch a light ource an viewing irection can be obtaine fro the neural networ. he noral urface vector thu obtaine can then be applie to 3-D urface recontruction by integration etho. REFERENCES Shalini Bhatia wa born on Augut 08, She receive the B.E. egree in Coputer Engineering fro Sri Sant Gaanan Mahara College of Engineering, Aravati Univerity, Shegaon, Maharahtra, Inia in 1993, M.E. egree in Coputer Engineering fro haoal Shahani Engineering College, Mubai, Maharahtra, Inia in 003. She ha been aociate with haoal Shahani Engineering College ince 1995, where he ha wore a Lecturer in Coputer Engineering Departent fro Jan 1995 to Dec 004 an a Aitant Profeor fro Dec 004 to Dec 005. She ha publihe a nuber of technical paper in National an International Conference. She i a eber of CSI an SIGAI which i a part of CSI. Vincy Elizabeth Joeph wa born on February 5, 198. She receive the B.E. egree in Electronic an Counication Engineering fro College of Engineering, Kiangoor, Cochin Univerity of Science an echnology, Cochin, Kerala. She i puruing M.E. egree in Coputer Engineering fro haoal Shahani Engineering College, Mubai, Maharahtra, Inia.She i woring with St.Franci Intitute of echnology, Borivli (W Mubai fro the year 004 to 005 a Lecturer in Electronic an elecounication Departent an fro the year 005 a Lecturer in Coputer Engineering Departent. Her reearch interet inclue Iage Proceing, Neural Networ, Data Encryption an Data Copreion [1] Yuefang Gao, Jianzhong Cao, an Fei Luo, A Hybri-reflectanceoele an Neural-networ bae Shape fro Shaing Algorith, 11