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324
An Experimental Comparison of MinCut/MaxFlow Algorithms for Energy Minimization in Vision
 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE
, 2001
"... After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time compl ..."
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Cited by 1311 (54 self)
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After [10, 15, 12, 2, 4] minimum cut/maximum flow algorithms on graphs emerged as an increasingly useful tool for exact or approximate energy minimization in lowlevel vision. The combinatorial optimization literature provides many mincut/maxflow algorithms with different polynomial time complexity. Their practical efficiency, however, has to date been studied mainly outside the scope of computer vision. The goal of this paper
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2002
"... We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2phase segmentation, developed by ..."
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Cited by 493 (21 self)
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We propose a new multiphase level set framework for image segmentation using the Mumford and Shah model, for piecewise constant and piecewise smooth optimal approximations. The proposed method is also a generalization of an active contour model without edges based 2phase segmentation, developed by the authors earlier in T. Chan and L. Vese (1999. In ScaleSpace'99, M. Nilsen et al. (Eds.), LNCS, vol. 1682, pp. 141151) and T. Chan and L. Vese (2001. IEEEIP, 10(2):266277). The multiphase level set formulation is new and of interest on its own: by construction, it automatically avoids the problems of vacuum and overlap; it needs only log n level set functions for n phases in the piecewise constant case; it can represent boundaries with complex topologies, including triple junctions; in the piecewise smooth case, only two level set functions formally suffice to represent any partition, based on The FourColor Theorem. Finally, we validate the proposed models by numerical results for signal and image denoising and segmentation, implemented using the Osher and Sethian level set method.
Graph Cuts and Efficient ND Image Segmentation
, 2006
"... Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graphcuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features ..."
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Cited by 304 (7 self)
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Combinatorial graph cut algorithms have been successfully applied to a wide range of problems in vision and graphics. This paper focusses on possibly the simplest application of graphcuts: segmentation of objects in image data. Despite its simplicity, this application epitomizes the best features of combinatorial graph cuts methods in vision: global optima, practical efficiency, numerical robustness, ability to fuse a wide range of visual cues and constraints, unrestricted topological properties of segments, and applicability to ND problems. Graph cuts based approaches to object extraction have also been shown to have interesting connections with earlier segmentation methods such as snakes, geodesic active contours, and levelsets. The segmentation energies optimized by graph cuts combine boundary regularization with regionbased properties in the same fashion as MumfordShah style functionals. We present motivation and detailed technical description of the basic combinatorial optimization framework for image segmentation via s/t graph cuts. After the general concept of using binary graph cut algorithms for object segmentation was first proposed and tested in Boykov and Jolly (2001), this idea was widely studied in computer vision and graphics communities. We provide links to a large number of known extensions based on iterative parameter reestimation and learning, multiscale or hierarchical approaches, narrow bands, and other techniques for demanding photo, video, and medical applications.
A Riemannian Framework for Tensor Computing
 INTERNATIONAL JOURNAL OF COMPUTER VISION
, 2006
"... Positive definite symmetric matrices (socalled tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affineinvariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of ..."
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Cited by 282 (27 self)
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Positive definite symmetric matrices (socalled tensors in this article) are nowadays a common source of geometric information. In this paper, we propose to provide the tensor space with an affineinvariant Riemannian metric. We demonstrate that it leads to strong theoretical properties: the cone of positive definite symmetric matrices is replaced by a regular manifold of constant curvature without boundaries (null eigenvalues are at the infinity), the geodesic between two tensors and the mean of a set of tensors are uniquely defined, etc. We have
Stability of Persistence Diagrams
, 2005
"... The persistence diagram of a realvalued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result ..."
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Cited by 222 (24 self)
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The persistence diagram of a realvalued function on a topological space is a multiset of points in the extended plane. We prove that under mild assumptions on the function, the persistence diagram is stable: small changes in the function imply only small changes in the diagram. We apply this result to estimating the homology of sets in a metric space and to comparing and classifying geometric shapes.
VectorValued Image Regularization with PDEs: A Common Framework for Different Applications
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... We address the problem of vectorvalued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new reg ..."
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Cited by 178 (8 self)
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We address the problem of vectorvalued image regularization with variational methods and PDE's. From the study of existing formalisms, we propose a unifying framework based on a very local interpretation of the regularization processes. The resulting equations are then specialized into new regularization PDE's and corresponding numerical schemes that respect the local geometry of vectorvalued images. They are finally applied on a wide variety of image processing problems, including color image restoration, inpainting, magnification and flow visualization.
Filling Holes In Complex Surfaces Using Volumetric Diffusion
, 2001
"... We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation al ..."
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Cited by 173 (2 self)
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We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as knownempty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold noninterpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes. By showing results for complex range scans, we demonstrate that our algorithm produces holefree surfaces that are plausible, visually acceptable, and usually close to the intended geometry.
S.: Geometric surface smoothing via anisotropic diffusion of normals
 Visualization Conference, IEEE (2002
"... All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately. ..."
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Cited by 106 (14 self)
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All intext references underlined in blue are linked to publications on ResearchGate, letting you access and read them immediately.
Level set surface editing operators
 SIGGRAPH
, 2002
"... Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework fo ..."
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Cited by 102 (10 self)
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Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines predefined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, selfintersection cannot occur, which guarantees the generation of physicallyrealizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scanconverted models.