Accurate coupled lines fitting in an errors-in-variables framework

• Published in: Survey review - Directorate of Overseas Surveys Vol. 50; no. 362; pp. 386 - 396
• Main Authors: Zhou, Yongjun, Gong, Jinghai, Fang, Xing
• Format: Journal Article
• Language: English
• Published: Taylor & Francis 03.09.2018
• Subjects: Coupled lines; Errors-in-variables model; Regular polygon; Weighted total least squares
• ISSN: 0039-6265; 1752-2706
• DOI: 10.1080/00396265.2017.1281095

For the purpose of accurate measurement of regular polygons, the boundary lines with parallel, perpendicular or given angles are defined as coupled lines. Provided that the noisy data points are measured from each line without outliers, an accurate and numerical reliable weighted total least squares (WTLS) method is proposed for two dimensional coupled lines fitting task. The underlying problem is modelled within an errors-in-variables framework by assuming all the coordinates are subject to random errors. In order to overcome the possible ill-posedness, the lines are parameterised as constrained Hessian normal form instead of the intercept and slope one. A generic WTLS algorithm is derived in case of the random columns are corrupted by fully correlated errors. Special case that the data are corrupted by homocedastic errors are considered and solved with less computational expenses. A single line fitting and a simulated regular hexagon fitting examples are performed with comparisons and discussions. The proposed methods can be used for accurate regular polygon measurement in vision metrology or reverse engineering.