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Surface Completion
Reporter: Zhonggui Chen2006.3.29
Outline
Background Overview Geometric method Volumetric method Image-based method Reference
Data acquisition
Background
Background Surface reconstruction
Surface Completion
Integrated into surface reconstruction algorithm
Considered as a post-processing
Requirements Robustness
The method should always produce a watertight surface for any input model.
Efficiency The method should be able to process huge
models within reasonable time and space. Accuracy
The method should preserve the geometry of the input model whenever possible.
Boundary condition Context condition
Classifications Geometric method
Operate directly on the polygons in the model
Volumetric method Convert a polygonal model into a volume
representation Image-based
Convert a polygonal model into a geometry image
Radial Basis Functions
J.C.Carr et al. Siggraph 2001
Signed-distance Function
Interpolation Problem
Given:
and
31{ }Ni iX x
1{ }Ni if
3:s
( ) , 1, , .i is x f i N ??
Output:3{ | ( ) 0}x s x
General form
e.g.
is a polynomial of low degreethe basic function is a real valued function
Radial Basis Function
( )p x
(2) 3BL ( )s
Evaluation
Evaluation
Greed algorithm
Procedure 1. Choose a subset from the interpolation nodes X a
nd fit an RBF only to these.2. Evaluate the residual, , at all nodes.3. If then stop.4. Else append new centers where is large.5. Re-fit RBF and goto 2.
Results
Summary
Repair holes with arbitrary topology
Holes are smoothly filled Approximate original surface
Filling Holes in Meshes
Peter Liepa. Eurographics Symposium on Geometry Prosessing 2
003
Pipeline
1. Hole identification2. Hole triangulation3. Mesh refinement 4. Mesh fairing
Triangulation of 3D Polygons
Minimum area triangulation Min-max dihedral angel
triangulation
Mesh Refinement
2. Edge Relaxation1. Subdivision
Fairing
Weighted umbrella-operator
Uniform : Scale-dependent :
U ( )v v v
Summary
Easy to implement Focus algorithm on holes Triangulation may self-intersect Can’t fill holes with islands Fairing weaken original surface
feature
Robust Repair of Polygonal Models
Tao Ju, Rice University, Siggraph 2004
Pipeline
I. Scan-conversionII. Sign generationIII. Surface reconstruction
Sign Generation
Cell faces containing an odd number of intersection edges
Patch Boundary Circles
Patching dual surface
Edges intersected with the model and the corresponding dual surface
Marching Cubes
Cube with signs at eight corners
Marching Cubes
Results
Results
Summary
Employ a space-efficient octree grid Produce closed, manifold surface for
any input model
Atomic Volumes for Mesh Completion
J. Podolak and S. Rusinkiewicz, SGP’05
A volume is atomic if it doesn’t intersect the polygons of the mesh.
Spatial Partitioning
Pipeline
In Cube
Out Cube
Hole Cube
Pipeline
Pipeline
Sink
(outside)
Source
(inside)
Pipeline
User Constraints
Results
Summary
Avoid changing, approximating or re-sampling the original mesh data
Incorporate user constraints Can’t process holes with islands
Geometry Completion and Detail Generation by Texture Synthesis
Minh X. Nguyen, Xiaoru Yan, Baoquan Chen. Pacific Graphics 200
5
Geometry Image
References Curless B., Levoy M.: A volumetric method for building compl
ex models from range images. In SIGGRAPH'96 Davis J., Marschner S., Garr M., Levoy M.: Filling holes in com
plex surfaces using volumetric diffusion, 2002. Fakir S. N., Greg T.: Simplification an repair of polygonal mod
els using volumetic techniques, TVCG. 9, 3(2003) J. C. Carr et al.: Reconstruction and representation of 3D obj
ects with radial basis functions. Siggraph’01. Joshua P., Szymon R., Atomic volumes for mesh completion.
Eurographics Symposium on Geometry Processing (2005) Ju T.: Robust repair of polygonal models. ACM Trans. Graph.
23, 3 (2004), 888-895.
References Kolluri R. K.: Spectral watertight surface reconstruction, 2003. Liepa P.: Filling holes in meshes. In Proceedings of the Eurogr
aphics/ACM SIGGRAPH symposium on Geometry processing (2003)
Minh X. N., Xiaoru Y., Baoqun C.: Geometry completion and detail generation by texture synthesis. PG’05.
Sharf A., Alexa M., Cohen-or D.: Context-based surface completion. ACM Trans. Graph. 23, 3 (2004), 878-887.
Verdera, J., Caselles, V., Bertalmio, M., , Sapiro, G.: In-painting surface holes. In: Proceedings of International Conference on Image Processing, pp. 903–906 (2003)
Thank you !