Draft:Eriksson-Jemsson approximation

Eriksson-Jemsson approximation

Background

The Eriksson-Jemsson approximation is an algorithm used for circle fitting in the context of LiDAR-data. The algorithm is mainly used for its simplicity and reduced time complexity over other fitting-algorithms such as the one described in Circle Fitting.

The algorithm

The algorithm fits a circle $(x-x_{0})^{2}+(y-y_{0})^{2}=r^{2}$ , where $(x_{0},y_{0})$ is the circle center and $r$ is the radius, to $n$ data points $(x_{i},y_{i}),i=1,...,n$.

Given that the data points are order by ascending angle $\theta _{i}=arg(x_{i},y_{i})$, the circle center $(x_{0},y_{0})$ is calculated by

$(x_{0},y_{0})=\left({\frac {x_{1}+x_{n}}{2}},{\frac {y_{1}+y_{n}}{2}}\right)$

and the radius

$r={\frac {\sqrt {(x_{n}-x_{1})^{2}+(y_{n}-y_{1})^{2}}}{2}}$.

References

Circle Fitting (nu-msr.github.io)