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Ka Chun Lam

Bio: Ka Chun Lam is an academic researcher from The Chinese University of Hong Kong. The author has contributed to research in topics: Matrix decomposition & Laplacian matrix. The author has an hindex of 10, co-authored 26 publications receiving 404 citations. Previous affiliations of Ka Chun Lam include California Institute of Technology.

Papers
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Journal ArticleDOI
TL;DR: FLASH is proposed, a fast algorithm to compute the optimized spherical harmonic parameterization with consistent landmark alignment for genus-0 closed brain surfaces with limited bijectivity under large deformations and slow computation.
Abstract: Surface registration between cortical surfaces is crucial in medical imaging for performing systematic comparisons between brains. Landmark-matching registration that matches anatomical features, called the sulcal landmarks, is often required to obtain a meaningful 1-1 correspondence between brain surfaces. This is commonly done by parameterizing the surface onto a simple parameter domain, such as the unit sphere, in which the sulcal landmarks are consistently aligned. Landmark-matching surface registration can then be obtained from the landmark aligned parameterizations. For genus-0 closed brain surfaces, the optimized spherical harmonic parameterization, which aligns landmarks to consistent locations on the sphere, has been widely used. This approach is limited by the loss of bijectivity under large deformations and the slow computation. In this paper, we propose FLASH, a fast algorithm to compute the optimized spherical harmonic parameterization with consistent landmark alignment. This is achieved by f...

121 citations

Journal ArticleDOI
TL;DR: This work proposes an effective algorithm for compressing surface homeomorphisms using Fourier approximation of the Beltrami representation, a complex-valued function defined on triangular faces of the surface mesh with supreme norm strictly less than 1.
Abstract: 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 storage. To tackle this problem, we propose an effective algorithm for compressing surface homeomorphisms using Fourier approximation of the Beltrami representation. The Beltrami representation is a complex-valued function defined on triangular faces of the surface mesh with supreme norm strictly less than 1. Under suitable normalization, there is a 1-1 correspondence between the set of surface homeomorphisms and the set of Beltrami representations. Hence, every bijective surface map is associated with a unique Beltrami representation. Conversely, given a Beltrami representation, the corresponding bijective surface map can be exactly reconstructed usin...

80 citations

Journal ArticleDOI
TL;DR: This paper proposes a special class of diffeomorphisms called the Teichmuller mappings (T-Maps), which under suitable conditions on the landmark constraints can be obtained, which minimizes the maximal conformality distortion.
Abstract: Registration, which aims to find an optimal 1-1 correspondence between shapes, is an important process in different research areas. Landmark-based surface registration has been widely studied to obtain a mapping between shapes that matches important features. Obtaining a unique and bijective surface registration that matches features consistently is generally challenging, especially when a large number of landmark constraints are enforced. This motivates us to search for a unique landmark matching surface diffeomorphism, which minimizes the local geometric distortion. For this purpose, we propose a special class of diffeomorphisms called the Teichmuller mappings (T-Maps). Under suitable conditions on the landmark constraints, a unique T-Map between two surfaces can be obtained, which minimizes the maximal conformality distortion. The conformality distortion measures how far the mapping deviates from a conformal mapping, and hence it measures the local geometric distortion. In this paper, we propose an eff...

78 citations

Journal ArticleDOI
TL;DR: A novel algorithm is presented to obtain diffeomorphic image or surface registrations with large deformations via quasi-conformal maps to minimize an energy functional involving a Beltrami coefficient term, which measures the distortion of the quasi- Conformal map.
Abstract: We present a new approach to obtain diffeomorphic registrations with large deformations using landmark and intensity information via quasi-conformal maps. The basic idea is to minimize an energy functional involving a Beltrami coefficient term, which measures the distortion of the quasi-conformal map. The Beltrami coefficient effectively controls the bijectivity and smoothness of the registration. In this paper, we first propose the quasi-conformal landmark registration (QCLR) algorithm to obtain diffeomorphic (1-1 and onto) registrations between images or surfaces. Using QCLR, landmark-aligned diffeomorphisms between images or surfaces can be obtained, even with a large geometric difference or a large number of landmark constraints. This algorithm is then extended to the quasi-conformal hybrid registration (QCHR) algorithm, which combines landmark and intensity (such as image intensity or surface curvature) information to achieve a more accurate registration result. Experiments have been carried out on b...

67 citations

Journal ArticleDOI
TL;DR: Zhang et al. as discussed by the authors generalized the standard conformality distortion defined for mappings between 2D spaces to the n-dimensional conformality distortions for a mapping f between ndimensional Euclidean spaces and proposed a variational model involving K(f) to tackle the landmark-matching problem in higher dimensional spaces.
Abstract: We propose a new method to obtain landmark-matching transformations between n-dimensional Euclidean spaces with large deformations. Given a set of feature correspondences, our algorithm searches for an optimal folding-free mapping that satisfies the prescribed landmark constraints. The standard conformality distortion defined for mappings between 2-dimensional spaces is first generalized to the n-dimensional conformality distortion K(f) for a mapping f between n-dimensional Euclidean spaces $$(n \ge 3)$$(n?3). We then propose a variational model involving K(f) to tackle the landmark-matching problem in higher dimensional spaces. The generalized conformality term K(f) enforces the bijectivity of the optimized mapping and minimizes its local geometric distortions even with large deformations. Another challenge is the high computational cost of the proposed model. To tackle this, we have also proposed a numerical method to solve the optimization problem more efficiently. Alternating direction method with multiplier is applied to split the optimization problem into two subproblems. Preconditioned conjugate gradient method with multi-grid preconditioner is applied to solve one of the sub-problems, while a fixed-point iteration is proposed to solve another subproblem. Experiments have been carried out on both synthetic examples and lung CT images to compute the diffeomorphic landmark-matching transformation with different landmark constraints. Results show the efficacy of our proposed model to obtain a folding-free landmark-matching transformation between n-dimensional spaces with large deformations.

30 citations


Cited by
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01 Apr 2003
TL;DR: The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it as mentioned in this paper, and also presents new ideas and alternative interpretations which further explain the success of the EnkF.
Abstract: The purpose of this paper is to provide a comprehensive presentation and interpretation of the Ensemble Kalman Filter (EnKF) and its numerical implementation. The EnKF has a large user group, and numerous publications have discussed applications and theoretical aspects of it. This paper reviews the important results from these studies and also presents new ideas and alternative interpretations which further explain the success of the EnKF. In addition to providing the theoretical framework needed for using the EnKF, there is also a focus on the algorithmic formulation and optimal numerical implementation. A program listing is given for some of the key subroutines. The paper also touches upon specific issues such as the use of nonlinear measurements, in situ profiles of temperature and salinity, and data which are available with high frequency in time. An ensemble based optimal interpolation (EnOI) scheme is presented as a cost-effective approach which may serve as an alternative to the EnKF in some applications. A fairly extensive discussion is devoted to the use of time correlated model errors and the estimation of model bias.

2,975 citations

01 Dec 1996

452 citations

Book ChapterDOI
01 Dec 1994
TL;DR: In this article, the authors discuss the advantages and disadvantages of finite element method and compare and contrast the Rayleigh comment on both the methods and explain the various teps involved in finite Element method and explain them through an Example.
Abstract: 1. If a displacement field is described as follows, u = (−x+2y+6xy)10 and v = (3x + 6y Determine the strain components v xx , v yy , and v xy at the point x = 1; y = 0. 2. Explain briefly about the following: (a) Variational method. (b) Importance of Boundary cond itions. 3. Discuss the following basic principles of finite element method. (a) Derivation of element stiffness matrix. (b) Assembly of Global stiffness Matrix. 4.What are the various teps involved in finite Element method and explain them through an Example 5. Compare and contrast the “Rayleigh comment on both the methods. 6. What are the various approximate methods of anal ysis and exp 7. (a) Explain the advantages and disadvantages of Finite Element Method. (b) What is meant by total potential of elastic str uc ure? Write the expression for total potential of a cantilever beam with uniformly dist ributed 8. In a plane strain problem, we have σx = 137.90*10 6 Pa σy= -68.95*10 Determine the value of the stress

200 citations

Journal ArticleDOI
TL;DR: This paper reviews the application of data-driven modeling and model learning procedures to different fields in science and engineering and finds the traditional approach seemed to be highly satisfactory.

142 citations

Journal ArticleDOI
TL;DR: FLASH is proposed, a fast algorithm to compute the optimized spherical harmonic parameterization with consistent landmark alignment for genus-0 closed brain surfaces with limited bijectivity under large deformations and slow computation.
Abstract: Surface registration between cortical surfaces is crucial in medical imaging for performing systematic comparisons between brains. Landmark-matching registration that matches anatomical features, called the sulcal landmarks, is often required to obtain a meaningful 1-1 correspondence between brain surfaces. This is commonly done by parameterizing the surface onto a simple parameter domain, such as the unit sphere, in which the sulcal landmarks are consistently aligned. Landmark-matching surface registration can then be obtained from the landmark aligned parameterizations. For genus-0 closed brain surfaces, the optimized spherical harmonic parameterization, which aligns landmarks to consistent locations on the sphere, has been widely used. This approach is limited by the loss of bijectivity under large deformations and the slow computation. In this paper, we propose FLASH, a fast algorithm to compute the optimized spherical harmonic parameterization with consistent landmark alignment. This is achieved by f...

121 citations