Error analysis for circle fitting algorithms

By Ali A. Al-Sharadqah, Nikolai I. Chernov. 2009

213 citations recorded by the source corpus.

We study the problem of fitting circles (or circular arcs) to data points observed with errors in both variables. A detailed error analysis for all popular circle fitting methods – geometric fit, Kasa fit, Pratt fit, and Taubin fit – is presented. Our error analysis goes deeper than the traditional expansion to the leading order. We obtain higher order terms, which show exactly why and by how much circle fits differ from each other. Our analysis allows us to construct a new algebraic (non-iterative) circle fitting algorithm that outperforms all the existing methods, including the (previously regarded as unbeatable) geometric fit.

Subfields: Biomedical Engineering, Computer Vision and Pattern Recognition, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/d20ce855fa22b9af4e57c5ae030f38b90187ee58

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Biomedical Engineering

1. Rex A. Kerr
2. Catharine H. Rankin
3. Stuart J. Robbins
4. A. Giles
5. N. A. Swierczek

In Computer Vision and Pattern Recognition

1. M. Wulder
2. Rex A. Kerr
3. Catharine H. Rankin
4. Stuart J. Robbins
5. A. Giles
6. N. A. Swierczek

In Mechanical Engineering

1. Juha Hyyppä
2. Rex A. Kerr
3. Harri Kaartinen
4. Catharine H. Rankin
5. Xinlian Liang
6. Stuart J. Robbins
7. A. Giles
8. Xiaowei Yu

Citations in the corpus

• High-Throughput Behavioral Analysis in C. elegans (2011, methodology): “To speed computation, circular arcs are fit using the HyperFit method with zero essential bias 25 .”
• Accurate derivation of stem curve and volume using backpack mobile laser scanning (2020, background): “Thus, the hyperaccurate fit is a clear improvement over the simple Kåsa fit (Kåsa, 1976) that tends to underestimate the radius for short and noisy arcs (see, e.g., Pratt, 1987; Al-Sharadqah and Chernov, 2009), and it is also a slight improvement over the Pratt fit (Pratt, 1987).”
• A New Global Database of Lunar Impact Craters >1–2 km: 1. Crater Locations and Sizes, Comparisons With Published Databases, and Global Analysis (2019, methodology): “A second fit was done using a singular-value decomposition implementation of the Taubin (1991) implicit fit, considered by some to be the best algebraic circle fit (Al-Sharadqah & Chernov, 2009).”