radiusthat

Radiusthat is a term used in statistics and computational geometry to denote an estimator of the radius of a geometric object, typically a circle in two dimensions or a sphere in higher dimensions, inferred from a set of sample points. The concept is commonly employed when the center of the object and its boundary are not directly observed but must be inferred from noisy data.

Estimators for radiusthat include algebraic circle or sphere fitting methods, which linearize the problem to estimate center and radius, and geometric (nonlinear) least-squares approaches that minimize the residual distance from the data to the ideal boundary. In two dimensions, classic methods include Kasa's circle fit and Taubin's refinement, among others. In higher dimensions, equivalent sphere-fitting methods apply.

When the center is unknown, radiusthat is typically paired with c_hat, an estimator of the center, obtained by similar fitting procedures. Robust variants aim to reduce influence of outliers, using loss functions that down-weight distant points or using RANSAC-style procedures.

Applications span computer vision, robotics, quality control, and pattern recognition, where the size of an object must be estimated from incomplete or noisy data. Limitations include sensitivity to outliers, sampling bias, and identifiability issues when the data do not constrain the radius well. Radiusthat remains an area of ongoing methodological development.