An image filter based on nonlinear discontinuous partial differential equation （PDE） is presented. It models a class of morphological image filters called the level set method for gray image processing. We discuss t...An image filter based on nonlinear discontinuous partial differential equation （PDE） is presented. It models a class of morphological image filters called the level set method for gray image processing. We discuss the theoretical aspects of this PDE. The switch signal is controlled by the discontinuous right hand of PDE. We propose a discrete algorithm for its numerical solution and corresponding filter implementation. The study provides insights via several experiments. These types of filters are very useful in numerical image analyses.展开更多
In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. Th...In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.展开更多
A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanizati...A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.展开更多
This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers ...This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.展开更多
We present a general framework for a higher-order spline level-set （HLS） method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formu...We present a general framework for a higher-order spline level-set （HLS） method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solving this partial differential equation using a C2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated their individual atomic coordinates which is the construction of biomolecule and solvated radii as prerequisites. surfaces （an implicit solvation interface） with展开更多
基金Supported by the National Natural Science Foundation of China (60808010)
文摘An image filter based on nonlinear discontinuous partial differential equation （PDE） is presented. It models a class of morphological image filters called the level set method for gray image processing. We discuss the theoretical aspects of this PDE. The switch signal is controlled by the discontinuous right hand of PDE. We propose a discrete algorithm for its numerical solution and corresponding filter implementation. The study provides insights via several experiments. These types of filters are very useful in numerical image analyses.
基金supported by PRIN-MIUR-Cofin 2006,project,by"Progetti Strategici EF2006"University of Bologna,and by University of Bologna"Funds for selected research topics"
文摘In this work we consider the problem of shape reconstruction from an unorganized data set which has many important applications in medical imaging, scientific computing, reverse engineering and geometric modelling. The reconstructed surface is obtained by continuously deforming an initial surface following the Partial Differential Equation (PDE)-based diffusion model derived by a minimal volume-like variational formulation. The evolution is driven both by the distance from the data set and by the curvature analytically computed by it. The distance function is computed by implicit local interpolants defined in terms of radial basis functions. Space discretization of the PDE model is obtained by finite co-volume schemes and semi-implicit approach is used in time/scale. The use of a level set method for the numerical computation of the surface reconstruction allows us to handle complex geometry and even changing topology,without the need of user-interaction. Numerical examples demonstrate the ability of the proposed method to produce high quality reconstructions. Moreover, we show the effectiveness of the new approach to solve hole filling problems and Boolean operations between different data sets.
文摘A symbolic computation method to decide whether the solutions to the system Of linear partial differential equation is complete via using differential algebra and characteristic set is presented. This is a mechanization method, and it can be carried out on the computer in the Maple environment.
基金This work was supported in part by a National Key Basic Research Project of China(No.G19980306)the National Natural Science Foundation of China(Grant No.69725002).
文摘This paper presents an algorithm to reduce a nonlinear algebraic partial differential equation system into the involutive characteristic set with respect to an abstract involutive prolongation direction, which covers the existing algorithms based on Riquier method, Thomas method, and Pommaret method. It also provides new algorithms for computing involutive characteristic sets due to the existence of new involutive directions. Experiments show that these new algorithms may be used to significantly reduce the computational steps in Wu-Ritt's characteristic set method for algebraic partial differential equations.
基金Bajaj is supported in part by NSF of USA under Grant No. CNS-0540033NIH under Grant Nos. P20-RR020647, R01- EB00487, R01-GM074258, R01-GM07308.+2 种基金Xu and Zhang are supported by the National Natural Science Foundation of China under Grant No. 60773165the National Basic Research 973 Program of China under Grant No. 2004CB318000. Zhang is also supported by Beijing Educational Committee Foundation under Grant No. KM200811232009.
文摘We present a general framework for a higher-order spline level-set （HLS） method and apply this to biomolecule surfaces construction. Starting from a first order energy functional, we obtain a general level set formulation of geometric partial differential equation, and provide an efficient approach to solving this partial differential equation using a C2 spline basis. We also present a fast cubic spline interpolation algorithm based on convolution and the Z-transform, which exploits the local relationship of interpolatory cubic spline coefficients with respect to given function data values. One example of our HLS method is demonstrated their individual atomic coordinates which is the construction of biomolecule and solvated radii as prerequisites. surfaces （an implicit solvation interface） with
