As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot...As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.展开更多
In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global pr...In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.展开更多
An approach to contour extraction and feature point detection in the 3-D fragment reassembly is proposed. A simple and effective technique is used for building the intrinsic topology of the fragment data suitable for ...An approach to contour extraction and feature point detection in the 3-D fragment reassembly is proposed. A simple and effective technique is used for building the intrinsic topology of the fragment data suitable for contour extraction. For the scanned data in which the topology is difficult to be achieved, the corresponding solutions are given to manage this problem. A robust approach is used for the curvature and torsion calculation of the discrete contour in a 3-D space. Finally, a method is developed for detecting feature points of the fragment contour based on total curvature. Therefore, the contour description combines the simple global information with local feature points. Experiments with real contour curves extracted from 3-D fragments demonstrate that the proposed method is robust and efficient.展开更多
This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the charac...This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.展开更多
We proved that there exists a family of complete oriented minimal surfaces in R3 with finite total curvature-4nπ,each of which has 0 genus and two ends,and both of the ends have winding order n,where n ∈ N,and discu...We proved that there exists a family of complete oriented minimal surfaces in R3 with finite total curvature-4nπ,each of which has 0 genus and two ends,and both of the ends have winding order n,where n ∈ N,and discussed the symmetric property for special parameters.展开更多
The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacel...The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacelike condition means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve γ under consideration. The assumption of index 1 is equivalent to saying that γ winds around some timelike axis with winding number 1. This reversed Fenchel-type inequality is proved by constructing a ruled spacelike surface with the given curve as boundary and applying the Gauss-Bonnet formula. As a by-product, this shows the existence of a maximal surface with γ as the boundary.展开更多
Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M...Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .展开更多
文摘As an important part of water level warning in water conservancy projects,often due to the influence of environmental factors such as light and stains,the acquired water gauge images have sticky,broken and bright spot conditions,which affect the identification of water gauges.To solve this problem,a water gauge image denoising model based on improved adaptive total variation is proposed.Firstly,the regular term exponent in the adaptive total variational equation is changed to an inverse cosine function;secondly,the differential curvature is used to distinguish the image noise points and increase the smoothing strength at the noise points;finally,according to the characteristics of the gradient mode and adaptive gradient threshold after Gaussian filtering,the New model can adaptively denoise in the smooth area and protect the edge area,so as to have the characteristics of both edge-preserving denoising.The experimental results show that the new model has a great improvement in image vision,higher iteration efficiency and an average increase of 1.6 dB in peak signal-to-noise ratio,and an average increase of 9%in structural similarity,which is more beneficial to practical applications.
文摘In this paper, we derive an elementary identity for smooth solutions of the following equation:$$\Delta u\left( x \right) + K\left( x \right)e^{2u\left( x \right)} = 0\,{\rm in}\,R^2 $$and use it to get some global properties of the solutions.
文摘An approach to contour extraction and feature point detection in the 3-D fragment reassembly is proposed. A simple and effective technique is used for building the intrinsic topology of the fragment data suitable for contour extraction. For the scanned data in which the topology is difficult to be achieved, the corresponding solutions are given to manage this problem. A robust approach is used for the curvature and torsion calculation of the discrete contour in a 3-D space. Finally, a method is developed for detecting feature points of the fragment contour based on total curvature. Therefore, the contour description combines the simple global information with local feature points. Experiments with real contour curves extracted from 3-D fragments demonstrate that the proposed method is robust and efficient.
基金supported by the National Natural Science Foundation of China(No.61602269)the China Postdoctoral Science Foundation(No.2015M571993)+1 种基金the Shandong Provincial Natural Science Foundation of China(No.ZR2017MD004)the Qingdao Postdoctoral Application Research Funded Project
文摘This paper develops a variational model for image noise removal using total curvature(TC), which is a high-order regularizer. The TC has the advantage of preserving image feature. Unfortunately, it also has the characteristics of nonlinear, non-convex and non-smooth. Consequently, the numerical computation with the curvature regularization is difficult. In order to conquer the computation problem, the proposed model is transformed into an alternating optimization problem by importing auxiliary variables. Furthermore, based on alternating direction method of multipliers, we design a fast numerical approximation iterative scheme for proposed model. Finally, numerous experiments are implemented to indicate the advantages of the proposed model in image edge preserving, image contrast and corners preserving. Meanwhile, the high computational efficiency of the designed model is verified by comparing with traditional models, including the total variation(TV) and total Laplace(TL) model.
基金Supported by the Specific Research Fund of the Doctoral Program of Higher Education of China (Grant No.20050141011)the MATH+X Project offered by Dalian University of Technology (Grant No.MXDUT073005)the Science Fund of Dalian University of Technology
文摘We proved that there exists a family of complete oriented minimal surfaces in R3 with finite total curvature-4nπ,each of which has 0 genus and two ends,and both of the ends have winding order n,where n ∈ N,and discussed the symmetric property for special parameters.
基金supported by the National Natural Science Foundation of China(No.11471021)the Fundamental Research Funds for the Central Universities of China(No.531107050874)
文摘The authors generalize the Fenchel theorem for strong spacelike closed curves of index 1 in the 3-dimensional Minkowski space, showing that the total curvature must be less than or equal to 2π. Here the strong spacelike condition means that the tangent vector and the curvature vector span a spacelike 2-plane at each point of the curve γ under consideration. The assumption of index 1 is equivalent to saying that γ winds around some timelike axis with winding number 1. This reversed Fenchel-type inequality is proved by constructing a ruled spacelike surface with the given curve as boundary and applying the Gauss-Bonnet formula. As a by-product, this shows the existence of a maximal surface with γ as the boundary.
文摘Some properties of the pseudo umbilical surface M in R 4 are discussed and thus the lower for the tolal mean curvature of M is estimated. On the basis of the estimation and by using the Gauss map of M , a sufficient condition is given for M as a flat torus in R 4 .
