 |
|
||||||||||
Symmetry Detection and Structure Discovery
"Symmetry is a complexity-reducing concept [...]; seek it everywhere. " - Alan J. Perlis
Short Summary
Symmetry and structural regularity are essential concepts in many
natural and man-made objects and play a crucial role in visual
perception, biology and physics, design, engineering, and art. This
project investigates computational methods to detect and enhance
symmetries and regular structures in geometric models.
Project Description
Symmetry detection and structure recovery have applications in shape
matching and retrieval, compression, geometric modeling and shape
design, and scientific data exploration.
We introduce a novel approach for detecting partial and
approximate symmetries in 3D shapes. The method employs a clustering
algorithm that aggregates local symmetry information in an
appropriately defined transformation space. We prove that this
algorithm finds the relevant symmetries of a given model with high
probability, given a suitably dense sampling. This work is complemented
by an optimization procedure that enhances imperfect symmetries by
deforming a shape towards a symmetric configuration. Currently we are
investigating a formal model of symmetry and a new methodology based on
compact generative models that allows a concise and semantically
meaningful way of representing digital geometry. Such a framework will
enable the analysis of the underlying design principles of geometric
shapes and facilitate novel geometry synthesis algorithms based on
procedural models derived from the extracted design rules.
Results
Regular structures discovered by our algorithm involve combinations of rotation, translation, and scaling of the repetitive elements.
Different 3D objects symmetrized with our algorithm. The transparent shapes indicate the original models. The example in the center shows a fully automatic correspondence computation that can be formulated as a symmetrization of the two poses of a scanned human.
Perfectly symmetric meshes can be obtained using symmetrizing deformations, symmetric sampling, and symmetry-aware meshing.
Symmetry Detection in an architectural model. The images in the center show the two most prominent symmetries. The image on the right shows the global symmetry structure.
Publications
Discovering Structural Regularity in 3D Geometry
Mark Pauly, Niloy J. Mitra, Johannes Wallner, Helmut Pottmann, Leonidas J. Guibas
ACM Transactions on Graphics (Proceedings of SIGGRAPH) 2008
[paper]
Symmetrization
Niloy J. Mitra, Leonidas J. Guibas, Mark Pauly
ACM Transactions on Graphics (Proceedings of SIGGRAPH) 2007
[paper]
[movie]
Partial and Approximate Symmetry Detection for 3D Geometry
Niloy J. Mitra, Leonidas J. Guibas, Mark Pauly
ACM Transactions on Graphics (Proceedings of SIGGRAPH) 2006
[paper]
Participating Researchers
Mark Pauly, Niloy Mitra, Leonidas Guibas, Johannes Wallner, Helmut Pottmann
Wichtiger Hinweis:
Diese Website wird in älteren Versionen von Netscape ohne
graphische Elemente dargestellt. Die Funktionalität der
Website ist aber trotzdem gewährleistet. Wenn Sie diese
Website regelmässig benutzen, empfehlen wir Ihnen, auf
Ihrem Computer einen aktuellen Browser zu installieren. Weitere
Informationen finden Sie auf
folgender
Seite.
Important Note:
The content in this site is accessible to any browser or
Internet device, however, some graphics will display correctly
only in the newer versions of Netscape. To get the most out of
our site we suggest you upgrade to a newer browser.
More
information
