Bayesian approach to circle diameter estimation from chord lengths

Abstract

. This study presents a method for estimating circle diameters based on chord length measurements, which proves particularly valuable for analyzing 2D cross-sections of three-dimensional structures where direct diameter measurement is impossible. The method employs a Bayesian approach that incorporates both the geometric properties of circle chords and prior assumptions about diameter distributions. The author developed a Python algorithm that requires only input data in the form of measured chord lengths and automatically computes the most probable diameter value, its confidence boundaries, and measurement accuracy estimates. Key advantages of the proposed solution include a user-friendly implementation with no need for complex computations, independence from specialized software, open-source availability (via a public repository), and reliable performance even with limited measurement data. Potential applications span multiple disciplines, including materials science (microstructure analysis), nanotechnology (nanoparticle characterization), and stereology (3D parameter reconstruction from 2D sections). The method’s principal innovation lies in its optimal combination of theoretical rigor and practical accessibility, making it an effective research tool. By enabling accurate diameter estimation from chord measurements, it overcomes a fundamental challenge in stereometric analysis of circular objects. The algorithm’s robustness with small datasets and its open availability position it as a valuable resource for researchers across relevant fields.

In the Introduction section, we review the literature and state the aim and objectives; Materials and Methods describes the uncertainty assessment and numerical implementation; Results and Discussion presents the simulation statistics and a real-data example; the Conclusions highlight the universality and practical value of the proposed algorithm.