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Author, Editor(s)

Author(s):

Jacobson, Alec
Weinkauf, Tino
Sorkine, Olga

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Not MPG Author(s):

Jacobson, Alec
Sorkine, Olga

BibTeX cite key*:

jacobson12a

Title

Title*:

Smooth Shape-Aware Functions with Controlled Extrema

Journal

Journal Title*:

Computer Graphics Forum

Journal's URL:


Download URL
for the article:

http://dx.doi.org/10.1111/j.1467-8659.2012.03163.x

Language:

English

Publisher

Publisher's
Name:

Blackwell Publ.

Publisher's URL:


Publisher's
Address:

Oxford, UK

ISSN:


Vol, No, pp, Date

Volume*:

31

Number:

5

Publishing Date:

July 2012

Pages*:

1577-1586

Number of
VG Pages:


Page Start:

1577

Page End:

1586

Sequence Number:


DOI:

10.1111/j.1467-8659.2012.03163.x

Note, Abstract, ©

Note:


(LaTeX) Abstract:

Functions that optimize Laplacian-based energies have become popular in geometry processing, e.g. for shape deformation, smoothing, multiscale kernel construction and interpolation. Minimizers of Dirichlet energies, or solutions of Laplace equations, are harmonic functions that enjoy the maximum principle, ensuring no spurious local extrema in the interior of the solved domain occur. However, these functions are only C0 at the constrained points, which often causes smoothness problems. For this reason, many applications optimize higher-order Laplacian energies such as biharmonic or triharmonic. Their minimizers exhibit increasing orders of continuity but lose the maximum principle and show oscillations. In this work, we identify characteristic artifacts caused by spurious local extrema, and provide a framework for minimizing quadratic energies on manifolds while constraining the solution to obey the maximum principle in the solved region. Our framework allows the user to specify locations and values of desired local maxima and minima, while preventing any other local extrema. We demonstrate our method on the smoothness energies corresponding to popular polyharmonic functions and show its usefulness for fast handle-based shape deformation, controllable color diffusion, and topologically-constrained data smoothing.

URL for the Abstract:


Categories,
Keywords:


HyperLinks / References / URLs:


Copyright Message:


Personal Comments:


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Access Level:

Internal

Correlation

MPG Unit:

Max-Planck-Institut für Informatik



MPG Subunit:

Computer Graphics Group

Audience:

Expert

Appearance:

MPII WWW Server, MPII FTP Server, MPG publications list, university publications list, working group publication list, Fachbeirat, VG Wort


BibTeX Entry:

@ARTICLE{jacobson12a,
AUTHOR = {Jacobson, Alec and Weinkauf, Tino and Sorkine, Olga},
TITLE = {Smooth Shape-Aware Functions with Controlled Extrema},
JOURNAL = {Computer Graphics Forum},
PUBLISHER = {Blackwell Publ.},
YEAR = {2012},
NUMBER = {5},
VOLUME = {31},
PAGES = {1577--1586},
ADDRESS = {Oxford, UK},
MONTH = {July},
DOI = {10.1111/j.1467-8659.2012.03163.x},
}


Entry last modified by Anja Becker, 12/18/2012
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Editor(s)
[Library]
Created
12/18/2012 01:59:18 PM
Revision
0.



Editor
Anja Becker



Edit Date
18.12.2012 14:03:21