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Hongkai Zhao

Bio: Hongkai Zhao is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Inverse problem & Discretization. The author has an hindex of 41, co-authored 153 publications receiving 9211 citations. Previous affiliations of Hongkai Zhao include University of California, Los Angeles & Duke University.


Papers
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Journal ArticleDOI
TL;DR: In this paper, a coupled level set method for the motion of multiple junctions (of, e.g., solid, liquid, and grain boundaries), which follows the gradient flow for an energy functional consisting of surface tension and bulk energies, is developed.

1,158 citations

Journal ArticleDOI
TL;DR: A fast method to localize thelevel set method of Osher and Sethian and address two important issues that are intrinsic to the level set method, which reduces the computational effort by one order of magnitude, works in as much generality as the original one, and is conceptually simple and easy to implement.

1,131 citations

Journal ArticleDOI
TL;DR: Monotonicity and stability properties of the fast sweeping algorithm are proven and it is shown that 2 n Gauss-Seidel iterations is enough for the distance function in n dimensions.
Abstract: In this paper a fast sweeping method for computing the numerical solution of Eikonal equations on a rectangular grid is presented. The method is an iterative method which uses upwind difference for discretization and uses Gauss-Seidel iterations with alternating sweeping ordering to solve the discretized system. The crucial idea is that each sweeping ordering follows a family of characteristics of the corresponding Eikonal equation in a certain direction simultaneously. The method has an optimal complexity of O(N) for N grid points and is extremely simple to implement in any number of dimensions. Monotonicity and stability properties of the fast sweeping algorithm are proven. Convergence and error estimates of the algorithm for computing the distance function is studied in detail. It is shown that 2 n Gauss-Seidel iterations is enough for the distance function in n dimensions. An estimation of the number of iterations for general Eikonal equations is also studied. Numerical examples are used to verify the analysis.

998 citations

Journal ArticleDOI
TL;DR: A Godunov-type numerical flux is derived for the class of strictly convex, homogeneous Hamiltonians that includes H(p,q) and it is shown that convergence after a few iterations, even in rather difficult cases, is indicated.
Abstract: We derive a Godunov-type numerical flux for the class of strictly convex, homogeneous Hamiltonians that includes $H(p,q)=\sqrt{ap^{2}+bq^{2}-2cpq},$ $c^{2}

470 citations

Proceedings ArticleDOI
13 Jul 2001
TL;DR: The level set method and fast sweeping and tagging methods are used to reconstruct surfaces from a scattered data set and the reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density.
Abstract: We describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from a scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surface-like model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.

456 citations


Cited by
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28 Jul 2005
TL;DR: PfPMP1)与感染红细胞、树突状组胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作�ly.
Abstract: 抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1(PfPMP1)与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用,在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员,通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

18,940 citations

Journal ArticleDOI
TL;DR: A new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets is proposed, which can detect objects whose boundaries are not necessarily defined by the gradient.
Abstract: We propose a new model for active contours to detect objects in a given image, based on techniques of curve evolution, Mumford-Shah (1989) functional for segmentation and level sets. Our model can detect objects whose boundaries are not necessarily defined by the gradient. We minimize an energy which can be seen as a particular case of the minimal partition problem. In the level set formulation, the problem becomes a "mean-curvature flow"-like evolving the active contour, which will stop on the desired boundary. However, the stopping term does not depend on the gradient of the image, as in the classical active contour models, but is instead related to a particular segmentation of the image. We give a numerical algorithm using finite differences. Finally, we present various experimental results and in particular some examples for which the classical snakes methods based on the gradient are not applicable. Also, the initial curve can be anywhere in the image, and interior contours are automatically detected.

10,404 citations

Proceedings ArticleDOI
01 Jul 2000
TL;DR: A novel algorithm for digital inpainting of still images that attempts to replicate the basic techniques used by professional restorators, and does not require the user to specify where the novel information comes from.
Abstract: Inpainting, the technique of modifying an image in an undetectable form, is as ancient as art itself. The goals and applications of inpainting are numerous, from the restoration of damaged paintings and photographs to the removal/replacement of selected objects. In this paper, we introduce a novel algorithm for digital inpainting of still images that attempts to replicate the basic techniques used by professional restorators. After the user selects the regions to be restored, the algorithm automatically fills-in these regions with information surrounding them. The fill-in is done in such a way that isophote lines arriving at the regions' boundaries are completed inside. In contrast with previous approaches, the technique here introduced does not require the user to specify where the novel information comes from. This is automatically done (and in a fast way), thereby allowing to simultaneously fill-in numerous regions containing completely different structures and surrounding backgrounds. In addition, no limitations are imposed on the topology of the region to be inpainted. Applications of this technique include the restoration of old photographs and damaged film; removal of superimposed text like dates, subtitles, or publicity; and the removal of entire objects from the image like microphones or wires in special effects.

3,830 citations