scholarly journals An ADMM-based scheme for distance function approximation

2019 ◽  
Vol 84 (3) ◽  
pp. 983-996
Author(s):  
Alexander Belyaev ◽  
Pierre-Alain Fayolle
Keyword(s):  
Variational Problem ◽  
Distance Function ◽  
Function Approximation ◽  
Numerical Experiments ◽  
Domain Boundary ◽  
Estimation Method ◽  
Surface Curvature ◽  
Binary Image ◽  
Function Estimation ◽  
Curvature Estimation

Abstract A novel variational problem for approximating the distance function (to a domain boundary) is proposed. It is shown that this problem can be efficiently solved by ADMM. A review of several other variational and PDE-based methods for distance function estimation is presented. Advantages of the proposed distance function estimation method are demonstrated by numerical experiments. Applications of the method to the problems of surface curvature estimation and computing the skeleton of a binary image are shown.

The Cumulant Generating Function Estimation Method

1997 ◽  
Vol 13 (2) ◽  
pp. 170-184 ◽  
Author(s):  
John L. Knight ◽  
Stephen E. Satchell
Keyword(s):  
Characteristic Function ◽  
Density Function ◽  
Generating Function ◽  
Estimation Method ◽  
Empirical Characteristic Function ◽  
Function Estimation ◽  
Asymptotic Equivalence ◽  
Cumulant Generating Function ◽  
Worked Example ◽  
Step Procedure

This paper deals with the use of the empirical cumulant generating function to consistently estimate the parameters of a distribution from data that are independent and identically distributed (i.i.d.). The technique is particularly suited to situations where the density function is unknown or unbounded in parameter space. We prove asymptotic equivalence of our technique to that of the empirical characteristic function and outline a six-step procedure for its implementation. Extensions of the approach to non-i.i.d. situations are considered along with a discussion of suitable applications and a worked example.

Estimation and Display of Triangular Mesh Curvature in Reverse Engineering

2010 ◽  
Vol 136 ◽  
pp. 95-102
Author(s):  
Hui Cun Shen ◽  
J.J. Nie ◽  
W.S. Zong ◽  
J. Wang ◽  
B.G. Yang
Keyword(s):  
Reverse Engineering ◽  
Surface Fitting ◽  
Triangular Mesh ◽  
Surface Curvature ◽  
Estimation Methods ◽  
Quadric Surface ◽  
Fitting Method ◽  
Curvature Estimation ◽  
Curvature Group ◽  
Paraboloid Surface

The estimation of triangular mesh curvature is implemented by establishing local quadric surface at vertexes of mesh. Deduction course of quadric surface curvature calculation is presented. Errors and complexity of two curvature estimation methods, which are the ecumenical quadric surface fitting method and the quadric paraboloid surface fitting method respectively, are compared. Technique for curvature group display is put forward. This technique can display features of mesh distinctly, even though the curvature values of mesh distribute non-uniformly in their variety range.

scholarly journals Spatial Analogues of Numerical Quasiconformal Mapping Methods for Solving Problems of Bursts Parameters Identification

2020 ◽  
pp. 11-14
Author(s):  
Mykhailo Boichura
Keyword(s):  
Image Reconstruction ◽  
Quasiconformal Mapping ◽  
Numerical Experiments ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Parameters Identification ◽  
Dimensional Case ◽  
Flow Function ◽  
Flow Lines ◽  
Tomographic Data

An approach to solving the problem of image reconstruction based on applied quasipotential tomographic data in the three-dimensional case is developed. It is based on the synthesis of spatial analogues of numerical quasiconformal mapping methods and algorithm for identifying the parameters of local bursts of homogeneous materials using similar methods on the plane. The peculiarity of the corresponding algorithm is taking into account (for each of the appropriate injections) the presence of only equipotential lines (with given values of the flow function or distributions of local velocities on them) and flow lines (with known potential distributions on them) at the domain boundary. Numerical experiments of simulative restoration of the environment structure are carried out.

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