Feature-Preserving Reconstruction of Singular Surfaces

with Tamal Dey, Qichao Que, Issam Safa, Lei Wang, Yusu WangComputer science and Engineering

The Ohio State University

Xiaoyin Ge

Problem statement

Surface reconstruction of singular surface

input output

Problem statement

Singular surface

A collection of smooth surface patches with boundaries.

glueintersectboundary

Motivation and Previous work

2D manifold reconstruction

[AB99] Surface reconstruction by Voronoi filtering. AMENTA N., BERN M.

[ACDL02] A simple algorithm for homeomorphic surface reconstruction. AMENTA N., et. al.

[BC02] Smooth surface reconstruction via natural neighbor interpolation of distance functions. BOISSONNAT et. Al

[ABCO01] Point set surfaces. ALEXA et. al. …

Motivation and Previous work

Feature aware method

[LCOL07] Data dependent MLS for faithful surface approximation. LIPMAN , et. al.

[ÖGG09] Feature preserving point set surfaces based on non-linear kernel regression, ÖZTIRELI, et.al

[CG06] Delaunay triangulation based surface reconstruction, CAZALS, et.al [FCOS05] Robust moving least-squares fitting with sharp features,

FLEISHMAN, et.al …

Motivation

Need a simple yet effective reconstruction algorithm for all three singular surfaces.

Our method: outline

Identify feature points

Reconstruct feature curves

Reconstruct singular surface

Our method: outline

Identify feature points

Reconstruct feature curves

Reconstruct singular surface

(I) Identify feature point

Gaussian-weighted graph Laplacian ( [BN02], Belkin-Niyogi, 2002)

(I) Identify feature point

Gaussian-weighted graph Laplacian ([BQWZ12])

Gaussian kernel

Position difference

(I) Identify feature point

Gaussian-weighted graph Laplacian, scaling ([BQWZ12])

boundarylow high

(I) Identify feature point

surf B

surf A

intersectionlow high

Gaussian-weighted graph Laplacian, scaling ([BQWZ12])

(I) Identify feature point

surf

A

surf B

glue (sharp feature)low high

Gaussian-weighted graph Laplacian, scaling ([BQWZ12])

(I) Identify feature point

surf

A

surf B

Gaussian-weighted graph Laplacian (scaling, [BQWZ12])

boundary

surf B

surf A

intersection sharp feature

Gaussian-weighted graph Laplacian

(I) Identify feature point

highlow

(I) Identify feature point

Gaussian-weighted graph Laplacian Advantage:

Simple Unified approach Robust to noise

Our method: outline

Identify feature points

Reconstruct feature curves

Reconstruct singular surface

(II) reconstruct feature curve

Graph method proposed by [GSBW11]

[ Data skeletonization via reeb graphs, Ge, et.al , 2011]

(II) reconstruct feature curve

Reeb graph ( from Rips-complex [DW11] )

Rips complexReeb graph(abstract)

Reeb graph(augmented)

(II) reconstruct feature curve

Reeb graph a noisy graph

feature points Reeb graph

(II) reconstruct feature curve

Graph simplification(denoise)

a zigzag graph

Graph smoothening [KWT88] Use snake to smooth out the graph

(II) reconstruct feature curve

graph energy

graph Laplacian

Graph smoothening Use snake to smoothen graph

graph Laplacian

(II) reconstruct feature curve

graph energy

align along feature

min( )

smoothen graph

(II) reconstruct feature curve

Graph smoothening Use snake to smooth out the graph

Our method: outline

Identify feature points

Reconstruct feature curves

Reconstruct singular surface

(III) Reconstruct singular surface

Reconstruction [CDR07][CDL07]

[CDL07] A Practical Delaunay Meshing Algorithm for a Large Class of Domains, Cheng, et.al

[CDR07] Delaunay Refinement for Piecewise Smooth Complexes, Cheng-Dey-Ramos, 2007

(III) Reconstruct singular surface

Weighted cocone

cocone weighted Delaunay[ACDL00] A simple algorithm for homeomorphic surface reconstruction, Amenta,-Choi-Dey -Leekha

(III) Reconstruct singular surface

Weighted cocone

un-weighted point

weighted point

(III) Reconstruct singular surface

Reconstruction Voronoi cell size weight∝ Give higher weight to points on the feature curve

Experiment results

ab

cd

a. Octaflower 107K

b. Fandisk 114K

c. SphCube 65K

d. Beetle 63K

Experiment results

Robust to noise

input with 1% noise result

Experiment results

Perform much better than un-weighted cocone

Cocone Our method

Conclusion and Future work

Conclusion Unified and simple method to handle all three

types of singular surfaces Robust to noise

Future work More robust system for real data Concave corner

Acknowledgement

We thank all people who have helped us to demonstrate this method !

Most of the models used in this paper are courtesy of

AIM@SHAPE Shape Repository. The authors acknowledge the support of NSF under grants CCF-1048983, CCF-1116258 and CCF-0915996.

Thank you!

Conclusion and Future work

Real scanned data