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27
A Fast Marching Level Set Method for Monotonically Advancing Fronts
 PROC. NAT. ACAD. SCI
, 1995
"... We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential eq ..."
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Cited by 561 (22 self)
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We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential equation for a propagating level set function, and use techniques borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, and accurate determination of geometric properties such as curvature and normal direction are naturally obtained in this setting. In this paper, we describe a particular case of such methods for interfaces whose speed depends only on local position. The technique works by coupling work on entropy conditions for interface motion, the theory of viscosity solutions for HamiltonJacobi equations and fast adaptive narrow band level set methods. The technique is applicable to a variety of problems, including shapefromshading problems, lithog...
Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2000
"... 8.997> 1INTRODUCTION T HE problem of detecting and tracking moving objects has a wide variety of applications in computer vision such as coding, video surveillance, monitoring, augmented reality, and robotics. Additionally, it provides input to higher level vision tasks, such as 3D reconstruct ..."
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Cited by 236 (4 self)
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8.997> 1INTRODUCTION T HE problem of detecting and tracking moving objects has a wide variety of applications in computer vision such as coding, video surveillance, monitoring, augmented reality, and robotics. Additionally, it provides input to higher level vision tasks, such as 3D reconstruction and 3D representation. This paper addresses the problem using boundarybased information to detect and track several nonrigid moving objects over a sequence of frames acquired by a static observer. During the last decade, a large variety of motion detection algorithms have been proposed. Early approaches for motion detection rely on the detection of temporal changes. Such methods [1] employ a thresholding technique over the interframe difference, where pixelwise differences or block differences (to increase robustness) have been considered. The difference map is usually binarized using a predefined threshold value to obtain the motion/nomotion classi
Global Minimum for Active Contour Models: A Minimal Path Approach
, 1997
"... A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the ..."
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Cited by 228 (70 self)
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A new boundary detection approach for shape modeling is presented. It detects the global minimum of an active contour model’s energy between two end points. Initialization is made easier and the curve is not trapped at a local minimum by spurious edges. We modify the “snake” energy by including the internal regularization term in the external potential term. Our method is based on finding a path of minimal length in a Riemannian metric. We then make use of a new efficient numerical method to find this shortest path. It is shown that the proposed energy, though based only on a potential integrated along the curve, imposes a regularization effect like snakes. We explore the relation between the maximum curvature along the resulting contour and the potential generated from the image. The method is capable to close contours, given only one point on the objects’ boundary by using a topologybased saddle search routine. We show examples of our method applied to real aerial and medical images.
ThreeDimensional Face Recognition
, 2005
"... An expressioninvariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expressioninvariant representations of faces using the bendinginvariant canonical forms approach. The re ..."
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Cited by 138 (23 self)
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An expressioninvariant 3D face recognition approach is presented. Our basic assumption is that facial expressions can be modelled as isometries of the facial surface. This allows to construct expressioninvariant representations of faces using the bendinginvariant canonical forms approach. The result is an efficient and accurate face recognition algorithm, robust to facial expressions, that can distinguish between identical twins (the first two authors). We demonstrate a prototype system based on the proposed algorithm and compare its performance to classical face recognition methods. The numerical methods employed by our approach do not require the facial surface explicitly. The surface gradients field, or the surface metric, are sufficient for constructing the expressioninvariant representation of any given face. It allows us to perform the 3D face recognition task while avoiding the surface reconstruction stage.
Expressioninvariant 3D face recognition
, 2003
"... We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the ..."
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Cited by 105 (17 self)
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We present a novel 3D face recognition approach based on geometric invariants introduced by Elad and Kimmel. The key idea of the proposed algorithm is a representation of the facial surface, invariant to isometric deformations, such as those resulting from different expressions and postures of the face. The obtained geometric invariants allow mapping 2D facial texture images into special images that incorporate the 3D geometry of the face. These signature images are then decomposed into their principal components. The result is an efficient and accurate face recognition algorithm that is robust to facial expressions. We demonstrate the results of our method and compare it to existing 2D and 3D face recognition algorithms.
Texture mapping using surface flattening via multidimensional scaling
 IEEE Transactions on Visualization and Computer Graphics
, 2002
"... AbstractÐWe present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from ..."
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Cited by 102 (23 self)
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AbstractÐWe present a novel technique for texture mapping on arbitrary surfaces with minimal distortions by preserving the local and global structure of the texture. The recent introduction of the fast marching method on triangulated surfaces made it possible to compute a geodesic distance map from a given surface point in O…n lg n † operations, where n is the number of triangles that represent the surface. We use this method to design a surface flattening approach based on multidimensional scaling �MDS). MDS is a family of methods that map a set of points into a finite dimensional flat �Euclidean) domain, where the only given data is the corresponding distances between every pair of points. The MDS mapping yields minimal changes of the distances between the corresponding points. We then solve an ªinverseº problem and map a flat texture patch onto the curved surface while preserving the structure of the texture. Index TermsÐTexture mapping, multidimensional scaling, fast marching method, Geodesic distance, Euclidean distance. æ 1
Two new methods for simulating photolithography development
 in 3D
, 1996
"... Two methods are presented for simulating the development of photolithographic profiles during the resist dissolution phase. These algorithms are the volumeoffluid I algorithm. and the steady levelset algorithm. These methods are compared with the raytrace, cell and levelset techniques employed ..."
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Cited by 67 (1 self)
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Two methods are presented for simulating the development of photolithographic profiles during the resist dissolution phase. These algorithms are the volumeoffluid I algorithm. and the steady levelset algorithm. These methods are compared with the raytrace, cell and levelset techniques employed in SAMPLE3D 2. The volumeoffluid algorithm employs an Euclidean Grid with volume fractions. At each time step, the surface is reconstructed by computing an approximation of the tangent plane of the surface in each cell that contains a value between 0 and 1. The geometry constructed in this manner is used to determine flow velocity vectors and the flux across each edge. The material is then advanced by a split advection scheme 3, The steady Level Set algorithm is an extension of the Iterati ve Level Set algorithm 2,4. The steady Level Set algorithm combines Fast Level Set concepts 5 and a technique for finding zero residual solutions to the eikonal function 6. The etch time for each cell is calculated in a time ordered manner. Use of heap sorting data structures allows the algorithm to execute extremely quickly. A similar technique was submitted by J. Sethian in 7,8. Comparisons of the methods have been performed and the results are shown.
An Overview of Level Set Methods for Etching, Deposition, and Lithography Development
 IEEE Transactions on Semiconductor Devices
, 1996
"... The range of surface evolution problems in etching, deposition, and lithography development oers signicant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specically designed for proles which can develop sharp corners, change topology, and undergo ord ..."
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Cited by 26 (1 self)
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The range of surface evolution problems in etching, deposition, and lithography development oers signicant challenge for numerical methods in front tracking. Level set methods for evolving interfaces are specically designed for proles which can develop sharp corners, change topology, and undergo orders of magnitude changes in speed. They are based on solving a HamiltonJacobi type equation for a level set function, using techniques borrowed from hyperbolic conservation laws. Over the past few years, a body of level set methods have been developed with application to microfabrication problems. In this paper, we give an overview of these techniques, describe the implementation in etching, deposition, and lithography simulations, and present a collection of fast level set methods, each aimed at a particular application. In the case of photoresist development and isotropic etching/deposition, the fast marching level set method, introduced by Sethian in [40, 39], can track the threedim...
Three dimensional traveltime computation using the Fast Marching Method
 INTERNAT. MTG. OF SOC. EXPL. GEOPHYS
, 1998
"... We present a fast algorithm for solving the eikonal equation in three dimensions, based on the Fast Marching Method (FMM). The algorithm is of order O(N log N ), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system, and ..."
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Cited by 24 (4 self)
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We present a fast algorithm for solving the eikonal equation in three dimensions, based on the Fast Marching Method (FMM). The algorithm is of order O(N log N ), where N is the total number of grid points in the computational domain. The algorithm can be used in any orthogonal coordinate system, and globaly constructs the solution to the eikonal equation for each point in the coordinate domain. The method is unconditionally stable, and constructs solutions consistent with the exact solution for arbitrarily large gradient jumps in velocity. In addition, the method resolves any overturning propagation wavefronts. We begin with the mathematical foundation for solving the eikonal equation using the Fast Marching Method, and follow with the numerical details. We show examples of traveltime propagation through the SEG/EAGE Salt model using point source and plane wave intial conditions, and analyze the error in constant velocity media. The algorithm allows for any shape of the initial wavef...