Bilateral Mesh Denoising
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1 Outlne Blateral Meh Denong S. Flehman, I. Dror,, D. Cohen-Or Tel Avv Unverty Preented by Derek Bradley Motvaton Prevou ork Blateral Meh Denong Image Proeng Bakground Blateral Image Flterng Tranformng from Image to Mehe Meh Denong Reult Duon (Unle otherwe noted, all mage are from Flehman et al. Motvaton Prevou ork 3D annng reate noy mehe Smoothng an redue hgh frequeny noe Challenge: how do you know what noe and what are feature? Laplaan Smoothng v v + λ v v (, ( v v (, 3 4 Prevou ork Prevou ork eghted Laplaan Laplaan + Expanon v v v + λ v (, w (, w ( v v v v + µλ v (, ( v v (, ( µ λ v v 5 6
![Prevou ork Blateral Meh Denong Implt Farng (IF [Debrun 999] Implt ntegraton of the dffuon equaton Applaton of an mage moothng tehnque Verte are moved along ther normal](/docs-images/81/83011077/images/2-0.jpg "dreton X ( I + λdtl X ( I + λdtl X X n + n n+ n Explt Implt Anotrop Feature-Preervng Denong (AFP [Debrun 000] Feature deteted ung loal urvature Denoe ung weghted mean")
2 Prevou ork Blateral Meh Denong Implt Farng (IF [Debrun 999] Implt ntegraton of the dffuon equaton Applaton of an mage moothng tehnque Verte are moved along ther normal dreton X ( I + λdtl X ( I + λdtl X X n + n n+ n Explt Implt Anotrop Feature-Preervng Denong (AFP [Debrun 000] Feature deteted ung loal urvature Denoe ung weghted mean urvature moothng Penalze verte wth large rato between prnple urvature v v + d n Salar value d to be omputed for eah vertex Feature preervng Can be teratve or ngle-pa But frt ome mage proeng ba 7 8 Image Proeng Bakground Image Proeng Bakground An mage an array of nteger (0-55 [Toma and Manduh] v the urrent pxel N(v the et of neghbourng pxel of v I(v the ntenty of v 9 0 Blateral Image Flterng Goal: Smooth the mage ntente, but preerve trong edge (feature New ntenty weghted average of neghbour Two weght: Geometr: : Cloer pxel weghted hgher (loene moothng flter Photometr: : Strong hange n ntenty penalzed (mlarty weght funton Blateral Image Flterng Cloene Smoothng Flter d Gauan Funton [wkpeda.org]
3 Blateral Image Flterng Cloene Smoothng Flter d Gauan Flter Blateral Image Flterng Smlarty eght Funton Another Gauan funton x σ ( x e x σ ( x e x abolute dfferene n ntenty value Reult: pxel wth large hange n ntenty are weghted lower 3 4 Blateral Image Flterng Blateral Image Flterng Combnng the weght and normalzng: Iˆ( v p N ( v p N ( v ( p v ( I( v I( p I( p ( p v ( I( v I( p Reult: In prate, N(v defned by the et of pont: { q}, where v q < σ [Toma and Manduh] 5 6 Tranformng from Image to Mehe Tranformng from Image to Mehe Verte ntead of pxel Neghbourhood N(v,, defned the ame Cloene moothng flter: 3D Euldean dtane ntead of D Smlarty weght funton: Heght of neghbourng verte pxel ntente Dot produt between normal and (v-q( ued ntead of omputng the heght at q 7 8 3
4 Meh Denong Reult DenoePont(Vertex DenoePont(Vertex v, Normal n {q} neghbourhood(v neghbourhood(v K {q {q} um 0, normalzer 0 for : to K t v - q h <n, v - q> exp(exp(-t/(σ exp(exp(-h/(σ um + ( ( * * h normalzer + * end return Vertex v v + n * (um/normalzer (um/normalzer Mean Curvature Implt Farng 9 Blateral Denong Reult 0 Duon Iue when ung an magemage-baed tehnque on a meh: Only apple to manfold mehe Irregularty of mehe Shrnkage Vertex drft Handlng boundare Anotrop Denong of Heght Feld (AFP Blateral Denong Mrror neghbour at boundary verte Vrtual verte at nfnty (ued n th algorthm Duon Duon Settng the parameter (σ (σ, σ, # teraton UerUer-ated method σ and σ : Uer Independently, Jone et al. preent the ame algorthm wth mnor dfferene: elet mooth pont and radu on the meh Large σ few teraton, mall σ more teraton Small σ make ene large value an ro Surfae predtor Sngle pa feature lead to fater teraton maller neghbourhood < 6 teraton for all reult n the paper 3 Jone et al. Blateral Denong 4 4
5 Duon Dadvantage Aume well-behaved mehe Can reult n elf-ntereton Conluon Smple, effetve and fat algorthm for denong mehe Eay to mplement Take advantage of the ue of an mage proeng tehnque ould I mplement th algorthm? 5 6 Referene S. Flehman, I. Dror,, D. Cohen-Or. Blateral meh denong. SIGGRAPH 003. C. Toma,, R. Manduh.. Blateral flterng for gray and olor mage. ICCV 998. T. Jone, F. Durand, M. Debrun.. Non-teratve feature- preervng meh moothng. SIGGRAPH 003. M. Debrun,, M. Meyer, P. Shroder,, A.H. Barr. Implt farng of rregular mehe ung dffuon and urvature flow. SIGGRAPH 999. M. Debrun,, M. Meyer, P. Shroder,, A.H. Barr. Anotrop feature-preervng denong of heght feld and bvarate data. Graph Interfae
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