Reporter: Zhonggui Chen 2006.3.29 Surface Completion Reporter: Zhonggui Chen 2006.3.29

Outline Background Overview Geometric method Volumetric method Image-based method Reference

Background Data acquisition

Background Surface reconstruction

Surface Completion Integrated into surface reconstruction algorithm Considered as a post-processing

Requirements Robustness Efficiency Accuracy 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 Volumetric method Image-based 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 Output: ？

Radial Basis Function General form e.g. is a polynomial of low degree the basic function is a real valued function

Evaluation

Evaluation

Greed algorithm Procedure Choose a subset from the interpolation nodes X and fit an RBF only to these. Evaluate the residual, , at all nodes. If then stop. Else append new centers where is large. 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 2003

Pipeline Hole identification Hole triangulation Mesh refinement Mesh fairing

Triangulation of 3D Polygons Minimum area triangulation Min-max dihedral angel triangulation

Mesh Refinement 1. Subdivision 2. Edge Relaxation

Fairing Weighted umbrella-operator Uniform : Scale-dependent :

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 Scan-conversion Sign generation 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 创新点:1. 文章做得很细, 对怎样充分利用八叉树性质提高算法效率有很详细的讨论. 2. 对每个空间点作标记时, 先使对偶曲面封闭, 然后对每个空间点作inside还是outside标记. 3. 利用自己发表的曲面重建的新方法.

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 Hole Cube Out Cube In 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 2005

Geometry Image

Basic idea cut Gu et al. Siggraph 02 parametrize

Basic idea cut sample

Basic idea cut store render [r,g,b] = [x,y,z]

References Curless B., Levoy M.: A volumetric method for building complex models from range images. In SIGGRAPH'96 Davis J., Marschner S., Garr M., Levoy M.: Filling holes in complex surfaces using volumetric diffusion, 2002. Fakir S. N., Greg T.: Simplification an repair of polygonal models using volumetic techniques, TVCG. 9, 3(2003) J. C. Carr et al.: Reconstruction and representation of 3D objects 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 Eurographics/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)

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