Principal curvatures from the integral invariant viewpoint

Helmut Pottmann; Johannes Wallner; Yongliang Yang; Yu Kun Lai; Shi Min Hu

doi:10.1016/j.cagd.2007.07.004

Principal curvatures from the integral invariant viewpoint

Helmut Pottmann^*, Johannes Wallner, Yongliang Yang, Yu Kun Lai, Shi Min Hu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

68 Scopus citations

Abstract

The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.

Original language	English (US)
Pages (from-to)	428-442
Number of pages	15
Journal	Computer Aided Geometric Design
Volume	24
Issue number	8-9
DOIs	https://doi.org/10.1016/j.cagd.2007.07.004
State	Published - Nov 2007
Externally published	Yes

Keywords

Integral invariants
Principal curvatures
Robustness

ASJC Scopus subject areas

Modeling and Simulation
Automotive Engineering
Aerospace Engineering
Computer Graphics and Computer-Aided Design

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10.1016/j.cagd.2007.07.004

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title = "Principal curvatures from the integral invariant viewpoint",

abstract = "The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.",

keywords = "Integral invariants, Principal curvatures, Robustness",

author = "Helmut Pottmann and Johannes Wallner and Yongliang Yang and Lai, {Yu Kun} and Hu, {Shi Min}",

year = "2007",

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doi = "10.1016/j.cagd.2007.07.004",

language = "English (US)",

volume = "24",

pages = "428--442",

journal = "Computer Aided Geometric Design",

issn = "0167-8396",

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T1 - Principal curvatures from the integral invariant viewpoint

AU - Pottmann, Helmut

AU - Wallner, Johannes

AU - Yang, Yongliang

AU - Lai, Yu Kun

AU - Hu, Shi Min

PY - 2007/11

Y1 - 2007/11

N2 - The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.

AB - The extraction of curvature information for surfaces is a basic problem of Geometry Processing. Recently an integral invariant solution of this problem was presented, which is based on principal component analysis of local neighborhoods defined by kernel balls of various sizes. It is not only robust to noise, but also adjusts to the level of detail required. In the present paper we show an asymptotic analysis of the moments of inertia and the principal directions which are used in this approach. We also address implementation and, briefly, robustness issues and applications.

KW - Integral invariants

KW - Principal curvatures

KW - Robustness

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U2 - 10.1016/j.cagd.2007.07.004

DO - 10.1016/j.cagd.2007.07.004

M3 - Article

AN - SCOPUS:35248855412

SN - 0167-8396

VL - 24

SP - 428

EP - 442

JO - Computer Aided Geometric Design

JF - Computer Aided Geometric Design

IS - 8-9

ER -

Principal curvatures from the integral invariant viewpoint

Abstract

Keywords

ASJC Scopus subject areas

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