Intrinsic signature and symmetry

Speaker:	Dr. Jian SUN
		Stanford University

Title:		"Intrinsic signature and symmetry"

Date:		Monday, 16 Feb 2009

Time:		4:00pm - 5:00pm

Venue:		Lecture Theater F
		(Leung Yat Sing Lecture Theater, near lifts 25/26)
		HKUST

Abstract:

Within the general framework of analyzing the properties of shapes which are
independent of the shape~Rs embedding, we have developed a novel method for
efficiently computing global symmetries of a shape which are invariant up to
isometry preserving transformations. Our approach is based on the observation
that the intrinsic symmetries of a shape are transformed into the Euclidean
symmetries in the signature space defined by the eigenfunctions of the
Laplace-Beltrami operator. We devise an algorithm which detects and computes the
isometric mappings from the shape onto itself. Our algorithm is both
computationally efficient and robust with respect to small non-isometric
deformations, even if they include topological changes.

The aforementioned method works very well when the whole object is intrinsically
symmetric. However, in practice objects are often partially symmetric. To tackle
this problem, we have developed an algorithm that detects partial intrinsic
similarities of shapes. Our method models the heat flow on the object and uses
the heat distribution as signature to characterize points and regions on the
shape. Using the multiscale nature of the heat distribution,
we are able to quantify the similarity between points at certain scale, and
determine, in particular, at which scale the point or region becomes unique.
This method can be used in data analysis, visualization and compression.


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Biography:

Dr. Jian SUN is a postdoctoral schoIar in Department of Computer Science
at Stanford University, working with Prof. Leonidas J. Guibas in his
Geometric Computation Group. He earned his Ph.D in Computer Science from
the Ohio State University under the supervision of Prof. Tamal K. Dey. Dr.
Sun's research interests include geometric algorithm and modeling,
computational geometry and topology, computer graphics and computational
biology. He holds an M.S. in Computer Science and B. E. in Mechanical
Engineering from Tsinghua University, Beijing China.