THE INVARIATOR DESIGN: AN UPDATE

Author:

Cruz-Orive Luis Manuel,Gual-Arnau Ximo

Abstract

The invariator is a method to generate a test line within an isotropically oriented plane through a fixed point, in such a way that the test line is effectively motion invariant in three dimensional space. Generalizations exist for non Euclidean spaces. The invariator design is convenient to estimate surface area and volume simultaneously. In recent years a number of new results have appeared which call for an updated survey. We include two new estimators, namely the a posteriori weighting estimator for surface area and volume, and the peak-and-valley formula for surface area.

Publisher

Slovenian Society for Stereology and Quantitative Image Analysis

Subject

Computer Vision and Pattern Recognition,Acoustics and Ultrasonics,Radiology, Nuclear Medicine and imaging,Instrumentation,Materials Science (miscellaneous),General Mathematics,Signal Processing,Biotechnology

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. STEREOLOGY: A HISTORICAL SURVEY;Image Analysis & Stereology;2017-12-18

2. ON THE PRECISION OF THE NUCLEATOR;Image Analysis & Stereology;2017-06-23

3. Gauss–Bonnet formulae and rotational integrals in constant curvature spaces;Differential Geometry and its Applications;2017-02

4. Rotation Invariant Valuations;Lecture Notes in Mathematics;2017

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