Iso-charts: Stretch-driven Mesh Parameterization using Spectral Analysis

Zhou, Kun; Synder, John; Guo, Baining; Shum, Heung-Yeung

Iso-charts: Stretch-driven Mesh Parameterization using Spectral Analysis

Files

047-056.pdf (7.2 MB)

Date

2004

Authors

Zhou, Kun
Synder, John
Guo, Baining
Shum, Heung-Yeung

Publisher

The Eurographics Association

Abstract

We describe a fully automatic method, called iso-charts, to create texture atlases on arbitrary meshes. It is the first to consider stretch not only when parameterizing charts, but also when forming charts. The output atlas bounds stretch by a user-specified constant, allowing the user to balance the number of charts against their stretch. Our approach combines two seemingly incompatible techniques: stretch-minimizing parameterization, based on the surface integral of the trace of the local metric tensor, and the "isomap" or MDS (multi-dimensional scaling) parameterization, based on an eigen-analysis of the matrix of squared geodesic distances between pairs of mesh vertices. We show that only a few iterations of nonlinear stretch optimization need be applied to the MDS parameterization to obtain low-stretch atlases. The close relationship we discover between these two parameterizations also allows us to apply spectral clustering based on MDS to partition the mesh into charts having low stretch. We also novelly apply the graph cut algorithm in optimizing chart boundaries to further minimize stretch, follow sharp features, and avoid meandering. Overall, our algorithm creates texture atlases quickly, with fewer charts and lower stretch than previous methods, providing improvement in applications like geometric remeshing. We also describe an extension, signal-specialized atlas creation, to efficiently sample surface signals, and show for the first time that considering signal stretch in chart formation produces better texture maps.

        @inproceedings{:10.2312/SGP/SGP04/047-056
,
booktitle = {Symposium on Geometry Processing
},
editor = {Roberto Scopigno and Denis Zorin
},
title = {{Iso-charts: Stretch-driven Mesh Parameterization using Spectral Analysis
}},
author = {Zhou, Kun and 
Synder, John and 
Guo, Baining and 
Shum, Heung-Yeung
},
year = {2004
},
publisher = {The Eurographics Association
},
ISSN = {1727-8384
},
ISBN = {3-905673-13-4
},
DOI = {/10.2312/SGP/SGP04/047-056
}
}