Revealing Historical Background of Bayon Faces Using Classification

Transcription

1 * * * ** * ** 5 JSA 73 Revealig Historical Backgroud of Bayo Faces Usig Classificatio Mawo KAMAKURA* Takeshi OISHI* Ju TAKAMATSU* Katsushi IKEUCHI** *Istitute of Idustrial Sciece **Iterfaculty Iitiative i Iformatio Studies The Uiversity of Tokyo The Uiversity of Tokyo Digital 3D models of historic buildigs or cultural heritage objects are useful for preservatio. Not oly ca we store them permaetly, but the models ca supply a clear guidelie for the restoratio process. 3D models also provide sufficiet iformatio about geometrical characteristics that may help archaeologists to ispect ad classify the objects. The Bayo temple, which cosists of 5 towers, is oe of the represetative buildigs of the Agkor moumets i Cambodia. It is famous for its towers with four faces at the four cardial poits. Accordig to research by Japaese govermet team for Safeguardig Agkor (JSA), the faces ca be classified ito three groups, Deva, Devata, ad Asura, based o subjective criteria. I this paper, we eplore a more objective way to classify the faces by usig measured 3D geometrical models by a laser rage sesor [][] 5 73 Great Buddha Project[3] JSA [5] [6] [4] () JSA 40M60M () 45M

2 Fig. left: Bayo Temple, right: Bayo face Asura 35N Deva5S Devata50E [6] Fig. pictures, 3D models ad shapes lie of 3 types of Bayo faces Cyra500[7] Vivid90[8] 3

3 [9] [0] 4 [] M ref M tar i i= N N Fig.3 picture of laser rage sesor. 3 y i y i y 3i R t c M tar,i absolute orietatio problem[] [3] Fig.4 Outlie of makig 3D models. e ( R, t, c) = yi ( cri+ t) σ y = y i µ 6 T µ 3 µ y i y i USV i y i 4 S 5 det( y) 0 7 det( y) < 0 i= Rtc T R = USV t = µ crµ 3 y c = tr( DS) 4 σ σ = i µ 5 3

4 Normalizatio Fig.5 Outlie of ormalizatio method. JSA 6 8 Y Fig.6 Eamples of shade image ad depth image. Y X 33 Y R m G,G f ( ) Y P f ( ) > 0 P G f ( ) < 0 P G 7 f ( ) = + d JSA SB ST S S B T () () d = ( ( + )) Fig.7 Visualizatio of differeces betwee two classes. left: DevataDeva, right: DevaAsura 4

5 Fig.8 Result of liear discrimiat aalysis. Fig.9 dedrogram obtaied by hieratical cluster aalysis. 0 PCA Group0Group9Group Group 5

6 Fig.0 scatter diagram of HCA. Group 9 Group 8 Group 0 Group 7 Group 4 Group 4 JSA Fig. locatio of similar Bayo faces i map. Group Group 3 6 Fig. Visualizatio of the clusters ad their differeces. JSA JSA 3 6

7 7 Aalysis ad Machie Itelligece, vol.3, o.4, April 99. JSA [] KMarc Levoy et.al, "The Digital Michelagelo Project:3D Scaig of Large Statues", I Proceedigs of SIGGRAPH000 [] [3] Katsushi Ikeuchi, Atsushi Nakazawa, Kazuhide Hasegawa, Takeshi Oishi, "The Great Buddha Project: Modelig Cultural Heritage for VR Systems through Observatio," The secod IEEE ad ACM Iteratioal Symposium o Mied ad Augmeted Reality (ISMAR003), Oct 003. [4] K. Ikeuchi, K. Hasegawa, A. Nakazawa, J. Takamatsu, T. Oishi ad T. Masuda, Bayo Digital Archival Project, I Proceedigs of the Teth Iteratioal Coferece o Virtual System ad Multimedia, pages , November 004. [5] [6],,, 998,, pp ,,, 998. [7] [8] id/vivid90.html [9] T. Oishi, A. Nakazawa, R. Kurazume ad K. Ikeuchi, Fast Simultaeous Aligmet of Multiple Rage Images usig Ide Images, I Proc. 3D Digital Imagig ad Modelig, 005 [0] Ryusuke Sagawa, Takeshi Oishi, Atsushi Nakazawa, Ryo Kurazume, Katsushi Ikeuchi, "Iterative Refiemet of Rage Images with Aisotropic Error Distributio," Proc. of IEEE/RSJ Iteratioal Coferece o Itelliget Robots ad Systems, pp.79-85, 00. [] " ", Vol.J80-A, No.8, pp.5-30 (997.8) &, Vol.J80-D-II, No.8, pp (997.8) [] Berthold.K.P.Hor, Closed-form solutio of absolute orietatio usig uit quaterios, Joural of the Optical Society of America A, vol.5, o.7, pp.7-35, 987. [3] Shiji Umeyama, Least-Squares Estimatio of Trasformatio Parameters Betwee Two Poit Patters, IEEE Trasactios o Patter 7