In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set approaches.To the best of our knowledge,the proposed prior is the firs...In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set approaches.To the best of our knowledge,the proposed prior is the first one which can work for high dimensional objects.Convexity prior is very useful for object completion in computer vision.It is a very challenging task to represent high dimensional convex objects.In this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function.Then,the second order condition of convex functions is used to characterize the shape convexity equivalently.We apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three constraints.An algorithm based on the alternating direction method of multipliers is presented for the optimization problem.Numerical experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.展开更多
Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax ...Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax rule. Theorem of the convergence for the algorithm is proved. Finally, a numerical example about two-stage convex recourse problem shows the essential character and the efficiency.展开更多
In counter-rotating electrochemical machining （CRECM）, a revolving cathode tool with hollow windows of various shapes is used to fabricate convex structures on a revolving part. During this process, the anode workpi...In counter-rotating electrochemical machining （CRECM）, a revolving cathode tool with hollow windows of various shapes is used to fabricate convex structures on a revolving part. During this process, the anode workpiece and the cathode tool rotate relative to each other at the same rotation speed. In contrast to the conventional schemes of ECM machining with linear motion of a block tool electrode, this scheme of ECM is unique, and has not been adequately studied yet. In this paper, the finite element method （FEM） is used to simulate the anode shaping process during CRECM, and the simulation process which involves a meshing model, a moving boundary, and a simulation algorithm is described. The simulated anode profiles of the convex structure at different processing times show that the CRECM process can be used to fabricate convex structures of various shapes with different heights. Besides, the variation of the inter-electrode gap indicates that this process can also reach a relative equilibrium state like that in conventional ECM. A rectangular convex and a circular convex are successfully fabricated on revolving parts. The experimental results indicate relatively good agreement with the simulation results. The proposed simulation process is valid for convex shaping prediction and feasibility studies as well.展开更多
In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon....In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.展开更多
Nowadays, manufacturing processes are carried out at speeds that they themselves demand and subject to rigorous standards to maintain the quality of materials. An important step to define the quality of products in me...Nowadays, manufacturing processes are carried out at speeds that they themselves demand and subject to rigorous standards to maintain the quality of materials. An important step to define the quality of products in metalworking is the casting process, which principal focus is seeking control and monitoring of properties of materials. Nevertheless, it is not easy due to the high temperatures and gas produced in the vessel. Although some researchers have been attempting to solve these problems, it is difficult to carry out due to hard conditions. This article proposes the analysis of the surface of the liquid metal, that is, the slag on the surface, which is considered as connected spaces characterized by the topology of their discrete surface. These spaces are described through Fast Fourier Transform, associating changes of intensities to the frequency domain and obtaining main features of these frequencies, these features are used to define an enveloping shape that represents the liquid metal. Finally, the results obtained are presented, which, according to them shows that it is possible to characterize the slag, and by which it is possible to spatially locate the molten metal liquid in the refractory. Therefore, this research serves as the basis for the development of new algorithms for level detection and measurement, preventing overflows and damage to refractories.展开更多
基金supported by RG(R)-RC/17-18/02-MATHHKBU 12300819+2 种基金NSF/RGC grant N-HKBU214-19RC-FNRA-IG/19-20/SCI/01supported by Programs for Science and Technology Development of Henan Province(192102310181)。
文摘In this work,we present a new method for convex shape representation,which is regardless of the dimension of the concerned objects,using level-set approaches.To the best of our knowledge,the proposed prior is the first one which can work for high dimensional objects.Convexity prior is very useful for object completion in computer vision.It is a very challenging task to represent high dimensional convex objects.In this paper,we first prove that the convexity of the considered object is equivalent to the convexity of the associated signed distance function.Then,the second order condition of convex functions is used to characterize the shape convexity equivalently.We apply this new method to two applications:object segmentation with convexity prior and convex hull problem(especially with outliers).For both applications,the involved problems can be written as a general optimization problem with three constraints.An algorithm based on the alternating direction method of multipliers is presented for the optimization problem.Numerical experiments are conducted to verify the effectiveness of the proposed representation method and algorithm.
文摘Two-stage problem of stochastic convex programming with fuzzy probability distribution is studied in this paper. Multicut L-shaped algorithm is proposed to solve the problem based on the fuzzy cutting and the minimax rule. Theorem of the convergence for the algorithm is proved. Finally, a numerical example about two-stage convex recourse problem shows the essential character and the efficiency.
基金supported by the Program for New Century Excellent Talents in University of China(NCET-10-0074)
文摘In counter-rotating electrochemical machining （CRECM）, a revolving cathode tool with hollow windows of various shapes is used to fabricate convex structures on a revolving part. During this process, the anode workpiece and the cathode tool rotate relative to each other at the same rotation speed. In contrast to the conventional schemes of ECM machining with linear motion of a block tool electrode, this scheme of ECM is unique, and has not been adequately studied yet. In this paper, the finite element method （FEM） is used to simulate the anode shaping process during CRECM, and the simulation process which involves a meshing model, a moving boundary, and a simulation algorithm is described. The simulated anode profiles of the convex structure at different processing times show that the CRECM process can be used to fabricate convex structures of various shapes with different heights. Besides, the variation of the inter-electrode gap indicates that this process can also reach a relative equilibrium state like that in conventional ECM. A rectangular convex and a circular convex are successfully fabricated on revolving parts. The experimental results indicate relatively good agreement with the simulation results. The proposed simulation process is valid for convex shaping prediction and feasibility studies as well.
文摘In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.
文摘Nowadays, manufacturing processes are carried out at speeds that they themselves demand and subject to rigorous standards to maintain the quality of materials. An important step to define the quality of products in metalworking is the casting process, which principal focus is seeking control and monitoring of properties of materials. Nevertheless, it is not easy due to the high temperatures and gas produced in the vessel. Although some researchers have been attempting to solve these problems, it is difficult to carry out due to hard conditions. This article proposes the analysis of the surface of the liquid metal, that is, the slag on the surface, which is considered as connected spaces characterized by the topology of their discrete surface. These spaces are described through Fast Fourier Transform, associating changes of intensities to the frequency domain and obtaining main features of these frequencies, these features are used to define an enveloping shape that represents the liquid metal. Finally, the results obtained are presented, which, according to them shows that it is possible to characterize the slag, and by which it is possible to spatially locate the molten metal liquid in the refractory. Therefore, this research serves as the basis for the development of new algorithms for level detection and measurement, preventing overflows and damage to refractories.
