Traditional gradient domain seamless image cloning is a time consuming task,requiring the solving of Poisson's equations whenever the shape or position of the cloned region changes.Recently,a more efficient altern...Traditional gradient domain seamless image cloning is a time consuming task,requiring the solving of Poisson's equations whenever the shape or position of the cloned region changes.Recently,a more efficient alternative,the mean-value coordinates(MVCs) based approach,was proposed to interpolate interior pixels by a weighted combination of values along the boundary.However,this approach cannot faithfully preserve the gradient in the cloning region.In this paper,we introduce harmonic cloning,which uses harmonic coordinates(HCs) instead of MVCs in image cloning.Benefiting from the non-negativity and interior locality of HCs,our interpolation generates a more accurate harmonic field across the cloned region,to preserve the results with as high a quality as with Poisson cloning.Furthermore,with optimizations and implementation on a graphic processing unit(GPU),we demonstrate that,compared with the method using MVCs,our harmonic cloning gains better quality while retaining real-time performance.展开更多
In this paper,we study the expansions of Ricci flat metrics in harmonic coordinates about the infinity of ALE(Asymptotically Local Euclidean)manifolds.
In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.
The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As...The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.展开更多
In this article, we extend the Weyl Schouten Theorem for a C0＇1 A W2＇2 manifold only under the assumptions on scalar curvature. Also we obtain a regularity of a C0＇1 V/W2＇2 manifold by conformal transformation und...In this article, we extend the Weyl Schouten Theorem for a C0＇1 A W2＇2 manifold only under the assumptions on scalar curvature. Also we obtain a regularity of a C0＇1 V/W2＇2 manifold by conformal transformation under some assumptions on Weyl curvature and scalar curvature.展开更多
The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned ...Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.展开更多
基金supported in part by the National Natural Science Foundation of China (No. 60903037)the National Basic Research Program (973) of China (No. 2009CB320803)
文摘Traditional gradient domain seamless image cloning is a time consuming task,requiring the solving of Poisson's equations whenever the shape or position of the cloned region changes.Recently,a more efficient alternative,the mean-value coordinates(MVCs) based approach,was proposed to interpolate interior pixels by a weighted combination of values along the boundary.However,this approach cannot faithfully preserve the gradient in the cloning region.In this paper,we introduce harmonic cloning,which uses harmonic coordinates(HCs) instead of MVCs in image cloning.Benefiting from the non-negativity and interior locality of HCs,our interpolation generates a more accurate harmonic field across the cloned region,to preserve the results with as high a quality as with Poisson cloning.Furthermore,with optimizations and implementation on a graphic processing unit(GPU),we demonstrate that,compared with the method using MVCs,our harmonic cloning gains better quality while retaining real-time performance.
文摘In this paper,we study the expansions of Ricci flat metrics in harmonic coordinates about the infinity of ALE(Asymptotically Local Euclidean)manifolds.
基金Supported by the NNSF of China (10671066)the NSF of Shandong Province (Q2008A08)Scientific Research Foundation of QFNU
文摘In this article, we introduce the Hausdorff convergence to derive a differentiable sphere theorem which shows an interesting rigidity phenomenon on some kind of manifolds.
基金Supported by the Program for New Century Excellent Talents in University under Grant No.NCET-10-0702the National Basic Research Program of China(973 Program)under Grant No.2013CB328904the Ph.D.Programs Foundation of Ministry of Education of China under Grant No.20110184110016
文摘The harmonic metric for Schwarzschild black hole with a uniform velocity is presented. In the limit of weak field and low velocity, this metric reduces to the post-Newtonian approximation for one moving point mass. As an application, we derive the dynamics of particle and photon in the weak-field limit for the moving Schwarzschild black hole with an arbitrary velocity. It is found that the relativistic motion of gravitational source can induce an additional centripetal force on the test particle, which may be comparable to or even larger than the conventional Newtonian gravitational force.
文摘In this article, we extend the Weyl Schouten Theorem for a C0＇1 A W2＇2 manifold only under the assumptions on scalar curvature. Also we obtain a regularity of a C0＇1 V/W2＇2 manifold by conformal transformation under some assumptions on Weyl curvature and scalar curvature.
基金supported by the National Natural Science Foundation of China (No. 10671066)the Scientific Research Foundation of Qufu Normal University and the Shanghai and Shandong Priority Academic Discipline
文摘The authors introduce the Hausdorff convergence to discuss the differentiable sphere theorem with excess pinching. Finally, a type of rigidity phenomenon on Riemannian manifolds is derived.
基金supported by National Natural Science Foundation of China (Grant No.10871069)the Youth Natural Science Foundation of Shandong Province (Grant No. Q2008A08)the Youth Foundation of Qufu Normal University
文摘Let Mn be a compact, simply connected n (≥3)-dimensional Riemannian manifold without bound-ary and Sn be the unit sphere Euclidean space Rn+1. We derive a differentiable sphere theorem whenever themanifold concerned satisfies that the sectional curvature KM is not larger than 1, while Ric(M)≥n+2 4 and the volume V (M) is not larger than (1 + η)V (Sn) for some positive number η depending only on n.
