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272
ApertureAngle and HausdorffApproximation of Convex Figures ∗
"... The aperture angle α(x, Q) of a point x ̸ ∈ Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q ⊂ C is the minimum ..."
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The aperture angle α(x, Q) of a point x ̸ ∈ Q in the plane with respect to a convex polygon Q is the angle of the smallest cone with apex x that contains Q. The aperture angle approximation error of a compact convex set C in the plane with respect to an inscribed convex polygon Q ⊂ C is the minimum
Convex Optimization for Image Segmentation
"... Segmentation is one of the fundamental low level problems in computer vision. Extracting objects from an image gives rise to further high level processing as well as image composing. A segment not always has to correspond to a real world object, but can fulfill any coherency criterion (e.g. similar ..."
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of these problems. Continuous energy minimization provides an elegant way to model a problem like image segmentation. If the problem is convex, there are powerful optimization algorithms available. Additionally, we are guaranteed to find the globally optimal solution. We give an extensive introduction to convex
Depth And Motion Discontinuities
, 1999
"... Depth and motion discontinuities arise wherever a light ray incident on a camera sensor meets a discrete change in the depth or motion of the surfaces in the world. Because these discontinuities tend to coincide with occlusions and with the boundaries of objects, they provide useful information for ..."
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Cited by 25 (1 self)
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Depth and motion discontinuities arise wherever a light ray incident on a camera sensor meets a discrete change in the depth or motion of the surfaces in the world. Because these discontinuities tend to coincide with occlusions and with the boundaries of objects, they provide useful information for a number of applications in computer vision, such as camera control, compression, and tracking. Moreover, because they have simple, precise definitions depending only upon the physics of the scene, they are unaffected by subjective considerations. The first part of this thesis presents an algorithm to detect depth discontinuities from a stereo pair of images by matching pixels in corresponding scanlines and then propagating information between those scanlines. It uses a new measure of pixel dissimilarity that is provably insensitive to image sampling. The algorithm is fast and is shown to produce good results on difficult images containing untextured, slanted surfaces. Then some work aimed a...
Optimization · Manifold valued
"... Abstract We introduce a general framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation TV S 1, as well as cyclic versions of quadratic regularization, HuberTV and MumfordShah regularity. The key idea ..."
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Abstract We introduce a general framework for regularization of signals with values in a cyclic structure, such as angles, phases or hue values. These include the total cyclic variation TV S 1, as well as cyclic versions of quadratic regularization, HuberTV and MumfordShah regularity. The key
HamiltonPerelman’s Proof of the Poincaré Conjecture and The Geometrization Conjecture
, 2006
"... In this paper, we provide an essentially selfcontained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of threemanifolds. In particular, we give a detailed exposition of a complete pro ..."
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Cited by 20 (0 self)
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In this paper, we provide an essentially selfcontained and detailed account of the fundamental works of Hamilton and the recent breakthrough of Perelman on the Ricci flow and their application to the geometrization of threemanifolds. In particular, we give a detailed exposition of a complete proof of the Poincaré conjecture due to Hamilton and Perelman.
Phase separation in random cluster models I: uniform upper bounds on local deviation
, 1001
"... This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioningthe planarFortuinKasteleynrandomcluster model on the presence of an open dual circuit Γ0 encircling the origin and enclosing an area of at least (or exa ..."
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Cited by 4 (2 self)
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, this being the maximum distance from a point in the circuit Γ0 to the boundary ∂conv () Γ0 of the circuit’s convex hull; and in a longitudinal sense by what we term maximum facet length, MFL () Γ0, namely, the length of the longest line segment of which the polygon ∂conv () Γ0 is formed. The principal
Improvements in Pose Invariance and Local Description for Gaborbased 2D Face Recognition
, 2008
"... A mi familia Automatic face recognition has attracted a lot of attention not only because of the large number of practical applications where human identification is needed but also due to the technical challenges involved in this problem: large variability in facial appearance, nonlinearity of fac ..."
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linearity of face manifolds and high dimensionality are some the most critical handicaps. In order to deal with the above mentioned challenges, there are two possible strategies: the first is to construct a “good ” feature space in which the manifolds become simpler (more linear and more convex). This scheme
Statistical Shape Knowledge in Variational Image Segmentation
"... this paper is derived from completely different considerations  namely from correspondences to simple parametric density estimates in appropriate feature spaces  we will show that in the case of the Gaussian kernel (C.2), there are certain similarities of the final expression to other extensions ..."
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Cited by 10 (0 self)
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this paper is derived from completely different considerations  namely from correspondences to simple parametric density estimates in appropriate feature spaces  we will show that in the case of the Gaussian kernel (C.2), there are certain similarities of the final expression to other extensions of the Parzen estimator
Results 1  10
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272