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An Algorithmic Overview of Surface Registration . . .
 MEDICAL IMAGE ANALYSIS
, 2000
"... This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected ..."
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Cited by 92 (1 self)
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This paper presents a literature survey of automatic 3D surface registration techniques emphasizing the mathematical and algorithmic underpinnings of the subject. The relevance of surface registration to medical imaging is that there is much useful anatomical information in the form of collected surface points which originate from complimentary modalities and which must be reconciled. Surface registration
An efficient, interfacepreserving level set redistancing algorithm and its application to interfacial incompressible fluid flow
 SIAM Journal on Scientific Computing
, 1999
"... This paper is dedicated to the memory of Dr. Emad Fatemi, a very kind person and a truly original scientist. Abstract. In Sussman, Smereka, and Osher [J. Comp. Phys., 94 (1994), pp. 146–159], a numerical scheme was presented for computing incompressible air–water flows using the level set method. Cr ..."
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Cited by 84 (0 self)
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This paper is dedicated to the memory of Dr. Emad Fatemi, a very kind person and a truly original scientist. Abstract. In Sussman, Smereka, and Osher [J. Comp. Phys., 94 (1994), pp. 146–159], a numerical scheme was presented for computing incompressible air–water flows using the level set method. Crucial to the above method was a new iteration method for maintaining the level set function as the signed distance from the zero level set. In this paper we implement a “constraint ” along with higher order difference schemes in order to make the iteration method more accurate and efficient. Accuracy is measured in terms of the new computed signed distance function and the original level set function having the same zero level set. We apply our redistancing scheme to incompressible flows with noticeably better resolved results at reduced cost. We validate our results with experiment and theory. We show that our “distance level set scheme ” with the added constraint competes well with available interface tracking schemes for basic advection of an interface. We perform basic accuracy checks and more stringent tests involving complicated interfacial structures. As with all level set schemes, our method is easy to implement.
Structural Boundary Design Via Level Set And Immersed Interface Methods
, 1999
"... . We develop and test an algorithmic approach for the boundary design of elastic structures. The goal of our approach is twofold. First, to develop a method which allows one to rapidly solve the twodimensional Lame equations in abitrary domains and compute for example the stresses, and second, ..."
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Cited by 83 (4 self)
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. We develop and test an algorithmic approach for the boundary design of elastic structures. The goal of our approach is twofold. First, to develop a method which allows one to rapidly solve the twodimensional Lame equations in abitrary domains and compute for example the stresses, and second, to develop a systematic way of modifying the design towards optimizing chosen properties. At the core, our approach relies on two distinct steps. Given a design, we rst apply an Explicit Jump Immersed Interface Method for computing the stresses for a given design shape. We then use a narrow band level set method to perturb this shape and progress towards an improved design. The equations of 2D linear elastostatics in the displacement formulation on arbitrary domains are solved quickly by domain embedding and the use of fast elastostatic solvers. This eectively reduces the dimensionality of the problem by one. Once the stresses are found, the level set method, which represents the...
A Fast and Accurate SemiLagrangian Particle Level Set Method
 COMPUTERS AND STRUCTURES
, 2004
"... In this paper, we present an efficient semiLagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the p ..."
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Cited by 83 (11 self)
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In this paper, we present an efficient semiLagrangian based particle level set method for the accurate capturing of interfaces. This method retains the robust topological properties of the level set method without the adverse effects of numerical dissipation. Both the level set method and the particle level set method typically use high order accurate numerical discretizations in time and space, e.g. TVD RungeKutta and HJWENO schemes. We demonstrate that these computationally expensive schemes are not required. Instead, fast, low order accurate numerical schemes suffice. That is, the addition of particles to the level set method not only removes the difficulties associated with numerical diffusion, but also alleviates the need for computationally expensive high order accurate schemes. We use an efficient, first order accurate semiLagrangian advection scheme coupled with a first order accurate fast marching method to evolve the level set function. To accurately track the underlying flow characteristics, the particles are evolved with a second order accurate method. Since we avoid complex high order accurate numerical methods, extending the algorithm to arbitrary data structures becomes more feasible, and we show preliminary results obtained with an octreebased adaptive mesh.
Fast image and video colorization using chrominance blending
 IEEE TRANSACTIONS ON IMAGE PROCESSING
, 2004
"... Colorization, the task of coloring a grayscale image or video, involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions, such as red, green, and blue channels. Mapping between intensity and color is therefore not unique, and colorization is a ..."
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Cited by 81 (9 self)
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Colorization, the task of coloring a grayscale image or video, involves assigning from the single dimension of intensity or luminance a quantity that varies in three dimensions, such as red, green, and blue channels. Mapping between intensity and color is therefore not unique, and colorization is ambiguous in nature and requires some amount of human interaction or external information. A computationally simple yet effective approach of colorization is presented in this paper. The method is fast so it can be conveniently used “on the fly, ” permitting the user to interactively get the desired results promptly after providing a reduced set of chrominance scribbles. Based on concepts of luminanceweighted chrominance blending and fast intrinsic distance computations, high quality colorization results for still images and video are obtained at a fraction of the complexity and computational cost of previously reported techniques. Possible extensions of the algorithm here introduced included the capability of changing colors of an existing color image or video as well as changing the underlying luminance.
Optimal Algorithm for Shape from Shading and Path Planning
, 2001
"... An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A cons ..."
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Cited by 80 (2 self)
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An optimal algorithm for the reconstruction of a surface from its shading image is presented. The algorithm solves the 3D reconstruction from a single shading image problem. The shading image is treated as a penalty function and the height of the reconstructed surface is a weighted distance. A consistent numerical scheme based on Sethian’s fast marching method is used to compute the reconstructed surface. The surface is a viscosity solution of an Eikonal equation for the vertical light source case. For the oblique light source case, the reconstructed surface is the viscosity solution to a different partial differential equation. A modification of the fast marching method yields a numerically consistent, computationally optimal, and practically fast algorithm for the classical shape from shading problem. Next, the fast marching method coupled with a back tracking via gradient descent along the reconstructed surface is shown to solve the path planning problem in robot navigation.
Numerical Schemes for the HamiltonJacobi and Level Set Equations on Triangulated Domains
, 1997
"... Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations. Unf ..."
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Cited by 77 (8 self)
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Borrowing from techniques developed for conservation law equations, numerical schemes which discretize the HamiltonJacobi (HJ), level set, and Eikonal equations on triangulated domains are presented. The first scheme is a provably monotone discretization for certain forms of the HJ equations. Unfortunately, the basic scheme lacks proper Lipschitz continuity of the numerical Hamiltonian. By employing a "virtual" edge ipping technique, Lipschitz continuity of the numerical flux is restored on acute triangulations. Next, schemes are introduced and developed based on the weaker concept of positive coefficient approximations for homogeneous Hamiltonians. These schemes possess a discrete maximum principle on arbitrary triangulations and naturally exhibit proper Lipschitz continuity of the numerical Hamiltonian. Finally, a class of PetrovGalerkin approximations are considered. These schemes are stabilized via a leastsquares bilinear form. The PetrovGalerkin schemes do not possess a discrete...
Modeling Holes and Inclusions by Level Sets in the Extended Finite Element Method
, 2000
"... A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (Osher and Sethian, 1988) to the eXtended Finite Element Method (XFEM) (Moes et al., 1999). In the XFEM, the finite ..."
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Cited by 75 (11 self)
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A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (Osher and Sethian, 1988) to the eXtended Finite Element Method (XFEM) (Moes et al., 1999). In the XFEM, the finite element approximation is enriched by additional functions through the notion of partition of unity. The level set method is used for representing the location of holes and material interfaces, and in addition, the level set function is used to develop the local enrichment for material interfaces. Numerical examples in 2dimensional linear elastostatics are presented to demonstrate the accuracy and potential of the new technique.
3D distance fields: A survey of techniques and applications
 IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS
, 2006
"... A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the ..."
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Cited by 74 (3 self)
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A distance field is a representation where, at each point within the field, we know the distance from that point to the closest point on any object within the domain. In addition to distance, other properties may be derived from the distance field, such as the direction to the surface, and when the distance field is signed, we may also determine if the point is internal or external to objects within the domain. The distance field has been found to be a useful construction within the areas of computer vision, physics, and computer graphics. This paper serves as an exposition of methods for the production of distance fields, and a review of alternative representations and applications of distance fields. In the course of this paper, we present various methods from all three of the above areas, and we answer pertinent questions such as How accurate are these methods compared to each other? How simple are they to implement?, and What is the complexity and runtime of such methods?
Spatially adaptive techniques for level set methods and incompressible flow
 Comput. Fluids
"... Since the seminal work of [92] on coupling the level set method of [69] to the equations for twophase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes ..."
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Cited by 73 (15 self)
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Since the seminal work of [92] on coupling the level set method of [69] to the equations for twophase incompressible flow, there has been a great deal of interest in this area. That work demonstrated the most powerful aspects of the level set method, i.e. automatic handling of topological changes such as merging and pinching, as well as robust geometric information such as normals and curvature. Interestingly, this work also demonstrated the largest weakness of the level set method, i.e. mass or information loss characteristic of most Eulerian capturing techniques. In fact, [92] introduced a partial differential equation for battling this weakness, without which their work would not have been possible. In this paper, we discuss both historical and most recent works focused on improving the computational accuracy of the level set method focusing in part on applications related to incompressible flow due to both its popularity and stringent accuracy requirements. Thus, we discuss higher order accurate numerical methods such as HamiltonJacobi WENO [46], methods for maintaining a signed distance function, hybrid methods such as the particle level set method [27] and the coupled level set volume of fluid method [91], and adaptive gridding techniques such as the octree approach to free surface flows proposed in [56].