Circle is a non-linear geometry that has a non-linear mathematical model. In this post, a closed-form and deterministic method to fit a circle from points (e.g., obtained from a measurement) by using direct least-square (DLS) estimation method is presented.

Data filtering is a process to reduce noises or supress certain components or information contained in measurement data by using a specific kernel (filter).

Any iterative optimisation algorithms, used to optimise non-linear and multi-modal objective functions, always require an initial solution estimation.

The fitting process for non-linear geometry is more complex than that for the linear geometry fitting. Non-linear geometry includes circle (2D and 3D), sphere, cylinder, cone and torus as well as more complex geometries such as free-form surfaces.

The least-squared fitting of linear geometry is solved by transforming a non-linear objective function of residuals into a linear objective function of the residuals.