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- Jian Liang, Rongjie Lai, Tsz Wai Wong, Hongkai Zhao
- 2012 IEEE Conference on Computer Vision and…
- 2012

In this paper, we propose a general framework for approximating differential operator directly on point clouds and use it for geometric understanding on them. The discrete approximation of differential operator on the underlying manifold represented by point clouds is based only on local approximation using nearest neighbors, which is simple, efficient and… (More)

- Lok Ming Lui, Tsz Wai Wong, +4 authors Shing-Tung Yau
- J. Sci. Comput.
- 2012

In shape analysis, finding an optimal 1-1 correspondence between surfaces within a large class of admissible bijective mappings is of great importance. Such process is called surface registration. The difficulty lies in the fact that the space of all surface diffeomorphisms is a complicated functional space, making exhaustive search for the best mapping… (More)

- Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, Xianfeng Gu
- SIAM J. Imaging Sciences
- 2013

Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as three-dimensional coordinates each vertex is mapped to, which often requires lots of memory. This causes inconvenience in data transmission and data… (More)

- Lok Ming Lui, Tsz Wai Wong, Paul M. Thompson, Tony F. Chan, Xianfeng Gu, Shing-Tung Yau
- MICCAI
- 2010

We develop a new algorithm to automatically register hippocampal (HP) surfaces with complete geometric matching, avoiding the need to manually label landmark features. A good registration depends on a reasonable choice of shape energy that measures the dissimilarity between surfaces. In our work, we first propose a complete shape index using the Beltrami… (More)

- Lok Ming Lui, Ka Chun Lam, Tsz Wai Wong, Xianfeng Gu
- ArXiv
- 2012

Surface parameterizations and registrations are important in computer graphics and imaging, where 1-1 correspondences between meshes are computed. In practice, surface maps are usually represented and stored as 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenience in data transmission and data… (More)

- LOK MING LUI, TSZ WAI WONG, +4 authors SHING TUNG YAU
- 2009

We address the problem of detecting deformities on elastic surfaces. This is of great importance for shape analysis, with applications such as detecting abnormalities in biological shapes (e.g., brain structures). We propose an effective algorithm to detect abnormal deformations by generating quasi-conformal maps between the original and deformed surfaces.… (More)

- Tsz Wai Wong, Hongkai Zhao
- SIAM J. Imaging Sciences
- 2014

The manipulation of surface homeomorphisms is an important aspect in 3D modeling and surface processing. Every homeomorphic surface map can be considered as a quasiconformal map, with its local non-conformal distortion given by its Beltrami differential. As a generalization of conformal maps, quasiconformal maps are of great interest in mathematical study… (More)

- Lok Ming Lui, Tsz Wai Wong, Paul M. Thompson, Tony F. Chan, Xianfeng Gu, Shing-Tung Yau
- 2010 IEEE Computer Society Conference on Computer…
- 2010

Surface registration is widely used in machine vision and medical imaging, where 1-1 correspondences between surfaces are computed to study their variations. Surface maps are usually stored as the 3D coordinates each vertex is mapped to, which often requires lots of storage memory. This causes inconvenience in data transmission and data storage, especially… (More)

- Tsz Wai Wong, Hongkai Zhao
- SIAM J. Scientific Computing
- 2015

In this paper, we propose a novel algorithm for computing surface uniformization for surfaces with arbitrary topology. According to the celebrated uniformization theorem, all Riemann surfaces can be classified as elliptic, parabolic or hyperbolic. Our algorithm is able to work on all these cases by first constructing an initial map onto an appropriate… (More)

- Tsz Wai Wong, Xianfeng Gu, Tony F. Chan, Lok Ming Lui
- 2011 International Conference on Computer Vision
- 2011

In this paper, we propose novel algorithms for inpainting and refinement of diffeomorphisms. We first represent a diffeomorphism by its Beltrami coefficient. Then it is possible to refine and inpaint the diffeomorphism by processing this Beltrami coefficient. With the inpainted/refined Beltrami coefficient, we construct a new diffeomorphism using the exact… (More)