Multiresolution Point-set Surfaces Franois Duranleau Philippe - PowerPoint PPT Presentation

Multiresolution Point-set Surfaces François Duranleau Philippe Beaudoin Pierre Poulin Dép. d’informatique et de recherche opérationnelle GI 2008

Introduction def Outline 1 Introduction 2 Analysis 3 Synthesis 4 Results 5 Conclusion & Future Work 2

Introduction def Point-set Surfaces and Surface Editing • Point-set surfaces are becoming popular for shape modeling • Surface editing in the presence of fine geometric details can be problematic • Multiresolution representations for meshes are well known • Interest for multiresolution representation for point-set surfaces 3

Introduction def Decomposition 4

Introduction def Surface Editing 5

Introduction def Overview Analysis Synthesis Level L Level L smooth , Details L ⊖ ⊕ downsample upsample Level L − 1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 6

Introduction def Previous Work • Multiresolution meshes [Eck+ 95] [Lounsbery+ 97] [Zorin+ 97] [Kobbelt+ 98] [Guskov+ 99] [Lee+ 00] [Guskov+ 00] [Hubeli-Gross 01] ... • “Multiresolution” for points: mostly hierarchical structures geared for rendering [Pfister+ 00] [Rusinkiewicz+ 00] [Botsch+ 02] [Pajarola 03] [Park+ 04] [Pajarola+ 05] [Wu+ 05] ... 7

Introduction def Previous Work • Progressive point-set surfaces [Fleishman+ 03] [Singh-Narayanna 06] • Triangle fans [Linsen-Prautzsch 03] • Multiscale point-set surfaces [Pauly+ 06] [Zhang+ 05] 7

Introduction def Previous Work • Progressive point-set surfaces [Fleishman+ 03] [Singh-Narayanna 06] • Triangle fans [Linsen-Prautzsch 03] • Multiscale point-set surfaces [Pauly+ 06] [Zhang+ 05] + [Boubekeur+ 07] 7

Analysis def Outline 1 Introduction 2 Analysis 3 Synthesis 4 Results 5 Conclusion & Future Work 8

Analysis def Analysis Analysis Synthesis Level L Level L smooth , Details L ⊕ ⊖ downsample upsample Level L − 1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 9

Analysis def Analysis Analysis Synthesis Level L Level L smooth , Details L ⊕ ⊖ downsample upsample Level L − 1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 9

Analysis def Analysis Analysis Synthesis Level L Level L smooth , Details L ⊕ downsample upsample Level L-1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 9

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • MLS surfaces ⇒ smoothing by MLS projection 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • MLS surfaces ⇒ smoothing by MLS projection • Downsample point set before projection 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • MLS surfaces ⇒ smoothing by MLS projection • Downsample point set before projection • Similar to [Pauly+ 06], but constant downsampling factor 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • MLS surfaces ⇒ smoothing by MLS projection • Downsample point set before projection • Similar to [Pauly+ 06], but constant downsampling factor 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • Downsampling: same as smoothing 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • Downsampling: same as smoothing • However: 10

Analysis def Coarser Level Generation Level L smooth , Details L ⊖ downsample Level L-1 • Downsampling: same as smoothing • However: • Add extra refinement step using heuristics based on k -neighborhood analysis 10

Analysis def Detail Extraction Level L smooth , Details L downsample Level L − 1 11

Analysis def Detail Extraction Level L Level L smooth , Details L ⊕ downsample upsample Level L − 1 Level L − 1 • Main difficulty: represent detail information coherently with upsampling procedure 11

Analysis def Detail Extraction Level L smooth , Details L downsample Level L − 1 • Main difficulty: represent detail information coherently with upsampling procedure • Meshes profit from explicit connectivity information 11

Analysis def Detail Extraction Level L smooth , Details L downsample Level L − 1 • Main difficulty: represent detail information coherently with upsampling procedure • Meshes profit from explicit connectivity information • [Linsen-Prautzsch 03]: store full k -neighborhood 11

Analysis def Detail Extraction Level L smooth , Details L downsample Level L − 1 • Main difficulty: represent detail information coherently with upsampling procedure • Meshes profit from explicit connectivity information • [Linsen-Prautzsch 03]: store full k -neighborhood • Intrinsic reformulation [Boubekeur+ 07] 11

Analysis def Extraction Procedure Level L − 1 12

Analysis def Extraction Procedure Point from level L 12

Analysis def Extraction Procedure δ 1 Project on level L − 1 δ = geometric detail information 12

Analysis def Extraction Procedure δ 1 Project on level L − 1 2 Find a surrounding triangle 12

Analysis def Extraction Procedure δ 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Extraction Procedure δ ( t 0 , t 1 , t 2 , β 1 , β 2 , δ ) 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Extraction Procedure δ ( t 0 , t 1 , t 2 � �� � , β 1 , β 2 , δ ) 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Extraction Procedure δ ( t 0 , t 1 , t 2 , β 1 , β 2 � �� � , δ ) 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Extraction Procedure δ ( t 0 , t 1 , t 2 , β 1 , β 2 , ���� ) δ 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Extraction Procedure δ ˜ δ ˜ ( t 0 , t 1 , t 2 , β 1 , β 2 , δ, ���� ) δ 1 Project on level L − 1 2 Find a surrounding triangle 3 Reformulate projection relative to the triangle 12

Analysis def Triangle selection 13

Analysis def Triangle selection 13

Analysis def Triangle selection 13

Analysis def Triangle selection t 2 2 π − θ 2 θ t 1 t 0 13

Analysis def Triangle selection t 0 > π t 2 t 1 13

Analysis def Reformulation q ˜ δ r • Find a point r on the triangle such that q = r + ˜ δ n ( r ) for some ˜ δ ( n ( r ) = normal estimation at r ) 14

Analysis def Reformulation q ˜ δ r • Find a point r on the triangle such that q = r + ˜ δ n ( r ) for some ˜ δ • Iterative procedure (gory details in the paper) 14

Analysis def Reformulation q ˜ δ r • Find a point r on the triangle such that q = r + ˜ δ n ( r ) for some ˜ δ • Iterative procedure • β 1 , β 2 computed from r 14

Synthesis def Outline 1 Introduction 2 Analysis 3 Synthesis 4 Results 5 Conclusion & Future Work 15

Synthesis def Synthesis Analysis Synthesis Level L Level L smooth , Details L ⊕ ⊖ downsample upsample Level L − 1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 16

Synthesis def Synthesis Analysis Synthesis Level L Level L smooth , Details L ⊕ ⊖ downsample upsample Level L − 1 Level L − 1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 16

Synthesis def Synthesis Analysis Synthesis Level L Level L smooth , Details L ⊖ downsample upsample Level L − 1 Level L-1 . . . Level 1 Level 1 smooth , Details 1 ⊖ ⊕ downsample upsample Level 0 16

Synthesis def Synthesis Procedure ( t 0 , t 1 , t 2 , β 1 , β 2 , δ ) 17

Synthesis def Synthesis Procedure ( t 0 , t 1 , t 2 , β 1 , β 2 � , δ ) � �� 1 Compute base position 17

Synthesis def Synthesis Procedure ( t 0 , t 1 , t 2 , β 1 , β 2 , δ ) 1 Compute base position 2 Estimate normal direction at base position 17

Synthesis def Synthesis Procedure ( t 0 , t 1 , t 2 , β 1 , β 2 , δ ) 1 Compute base position 2 Estimate normal direction at base position 3 Intersect ray with surface (simplification of [Adamson-Alexa 04]) 17

Synthesis def Synthesis Procedure ˜ δ ˜ ( t 0 , t 1 , t 2 , β 1 , β 2 , δ, ���� ) δ 1 Compute base position 2 Estimate normal direction at base position 3 Intersect ray with surface (fast estimation with ˜ δ ) 17

Synthesis def Synthesis Procedure ( t 0 , t 1 , t 2 , β 1 , β 2 , δ ) 1 Compute base position 2 Estimate normal direction at base position 3 Intersect ray with surface 4 Estimate normal direction at intersection 17