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Research Interests
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Geometric Modeling, Computer Graphics, Medical Imaging, Computer
Vision, Computational Conformal Geometry
Summary
of Ph D. Thesis: General Surface Geometric Structures and Their Applications
Geometric
structures are natural structures of surfaces, which enable different
geometries to be defined on the surfaces coherently and allow general planar
algorithmic constructions to be generalized onto the surfaces directly. For
example, all oriented surfaces have conformal structures. We can generalize
planar texture mapping, texture synthesis, remeshing
and mapping algorithms to surfaces based on their conformal structures without
angle distortion. Also polar form splines with planar
domains can be generalized to manifold splines on the
surfaces which admit affine structures and equipped with affine geometry.
Surface Ricci flow is a powerful and flexible
geometric analytic tool. It is a process that deforms the Riemannian metric of
the surface, with the deformation proportional to the Gaussian curvatures, and
the curvatures behaving like heat diffusion. Theoretically rigorous and
practically efficient methods using discrete Ricci flow have been invented to
compute general geometric structures for surfaces with arbitrary topologies,
like spherical structure, affine structure, hyperbolic structure, real
projective structure, and conformal structure. Differential
forms is also a very useful tool to compute surfaces
conformal structure and affine structure.
Applications
of surface geometric structures in Engineering field:
- Computer
Graphics:
Optimal global
conformal parameterization, Computing
geodesic spectra of surfaces, Computing shape
space.
- Geometric
Modeling:
Manifold splines
with single extraordinary point.
- Medical
Imaging: Conformal virtual
colon flattening.
- Computer
Vision: 3D surface matching and recognition
using conformal geometry.
Publications
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Discrete Surface Ricci Flow
M. Jin, J. Kim,
F. Luo and X. Gu, IEEE
Transaction on Visualization and Computer Graphics, Vol. 14, No. 5, 2008. [PDF] |
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Computing General Geometric Structures on Surfaces Using Ricci
Flow
M. Jin, F. Luo and X. Gu |
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Manifold Splines with Single Extraodinary Point
X. Gu, Y. He, M. Jin, F. Luo and
H. Qin X. Gu,
Y. He, M. Jin, F. Luo and H. Qin |
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Computing Shortest Cycles Using Universial
Covering Space
X. Yin, M. Jin
and X. Gu X. Yin, M. Jin and X. Gu |
Geometric Accuracy Analysis for Discrete Surface Approximation
J. Dai, W. Luo, M. Jin, W. Zeng, Y. He,
S-T. Yau and X. Gu |
Computing Geodesic Spectra of Surfaces
M. Jin, F. Luo, S-T. Yau and X. Gu |
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Conformal Geometry and Its Applications on
3D Shape Matching, Recognition and Stitching
S. Wang, Y. Wang, M. Jin, X. Gu
and D. Samaras S.
Wang, Y. Wang, M. Jin, X. Gu and D. Samaras |
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Discrete Surface Ricci Flow: Theory and Applications
M. Jin, J. Kim,
F. Luo and X. Gu |
Globally Optimal Surface Mapping for Surfaces with Arbitrary
Topology
X. Li, Y. Bao, X. Guo, M. Jin, X. Gu and H. Qin |
Computational Conformal Geometry Applied in Engineering Fields
X. Gu, M.Jin, J.Kim
and S.-T.Yau |
Computing Surface Hyperbolic Structure and Real Projective
Structure
M. Jin, F. Luo and X. Gu |
Conformal Virtual
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Topology-based Surface Mapping with Exact Feature Alignment
C. Carner, M. Jin, X. Gu and H.
Qin |
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Optimal Global Conformal Surface Parameterization
M. Jin, Y.
Wang, S-T. Yau and X. Gu M. Jin, Y. Wang, S-T. Yau and X. Gu |
