传统Voronoi图对大量点集进行Voronoi划分时会产生Voronoi单元格数过多的现象,导致难以适用于地理信息系统、生物医学等诸多领域。为了解决这个问题,提出一种自适应基于密度的聚类算法(Density-Based Spatial Clustering of Application...传统Voronoi图对大量点集进行Voronoi划分时会产生Voronoi单元格数过多的现象,导致难以适用于地理信息系统、生物医学等诸多领域。为了解决这个问题,提出一种自适应基于密度的聚类算法(Density-Based Spatial Clustering of Applications with Noise,DBSCAN)的Voronoi图。阐述了Voronoi单元合并的现象,证明了其发生的充要条件,提出该Voronoi图的生成算法并进行仿真。通过显微镜下嗜中性粒细胞、我国地表火点数据对算法进行验证,结果表明,该算法能够有效解决点集规模较大时,Voronoi图划分过于细致的问题,突破了传统Voronoi图单点对单点的划分形式。此外,该算法拓宽了Voronoi图在图形图像处理、生物医学、地理信息系统等领域的应用。展开更多
Path prediction of flexible needles based on the Fokker-Planck equation and disjunctive Kriging model is proposed to improve accuracy and consider the nonlinearity and anisotropy of soft tissues.The stochastic differe...Path prediction of flexible needles based on the Fokker-Planck equation and disjunctive Kriging model is proposed to improve accuracy and consider the nonlinearity and anisotropy of soft tissues.The stochastic differential equation is developed into the Fokker-Planck equation with Gaussian noise,and the position and orientation probability density function of flexible needles are then optimized by the stochastic differential equation.The probability density function obtains the mean and covariance of flexible needle movement and helps plan puncture paths by combining with the probabilistic path algorithm.The weight coefficients of the ordinary Kriging are extended to nonlinear functions to optimize the planned puncture path,and the Hermite expansion is used to calculate nonlinear parameter values of the disjunctive Kriging optimization model.Finally,simulation experiments are performed.Detailed comparison results under different path planning maps show that the kinematics model can plan optimal puncture paths under clinical requirements with an error far less than 2 mm.It can effectively optimize the path prediction model and help improve the target rate of soft tissue puncture with flexible needles through data analysis and processing of the mean value and covariance parameters derived by the probability density and disjunctive Kriging algorithms.展开更多
文摘传统Voronoi图对大量点集进行Voronoi划分时会产生Voronoi单元格数过多的现象,导致难以适用于地理信息系统、生物医学等诸多领域。为了解决这个问题,提出一种自适应基于密度的聚类算法(Density-Based Spatial Clustering of Applications with Noise,DBSCAN)的Voronoi图。阐述了Voronoi单元合并的现象,证明了其发生的充要条件,提出该Voronoi图的生成算法并进行仿真。通过显微镜下嗜中性粒细胞、我国地表火点数据对算法进行验证,结果表明,该算法能够有效解决点集规模较大时,Voronoi图划分过于细致的问题,突破了传统Voronoi图单点对单点的划分形式。此外,该算法拓宽了Voronoi图在图形图像处理、生物医学、地理信息系统等领域的应用。
基金The National Natural Science Foundation of China(No.61903175,62163024,62163026)the Academic and Technical Leaders Foundation of Major Disciplines of Jiangxi Province under Grant(No.20204BCJ23006).
文摘Path prediction of flexible needles based on the Fokker-Planck equation and disjunctive Kriging model is proposed to improve accuracy and consider the nonlinearity and anisotropy of soft tissues.The stochastic differential equation is developed into the Fokker-Planck equation with Gaussian noise,and the position and orientation probability density function of flexible needles are then optimized by the stochastic differential equation.The probability density function obtains the mean and covariance of flexible needle movement and helps plan puncture paths by combining with the probabilistic path algorithm.The weight coefficients of the ordinary Kriging are extended to nonlinear functions to optimize the planned puncture path,and the Hermite expansion is used to calculate nonlinear parameter values of the disjunctive Kriging optimization model.Finally,simulation experiments are performed.Detailed comparison results under different path planning maps show that the kinematics model can plan optimal puncture paths under clinical requirements with an error far less than 2 mm.It can effectively optimize the path prediction model and help improve the target rate of soft tissue puncture with flexible needles through data analysis and processing of the mean value and covariance parameters derived by the probability density and disjunctive Kriging algorithms.
