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 !