Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. We present here a closed-form solution to the least-squares problem for three or more points. Currently, various empirical, graphical and numerical iterative ...

Finding the relationship between two coordinate systems using pairs of measurements of the coordinates of a number of points in both systems is a classic photogrammetric task. It finds applications in stereophotogrammetry and in robotics. We present here a closed-form solution to the least-squares problem for three or more points. Currently, various empirical, graphical and numerical iterative ...

We study theoretical and computational aspects of the least squares fit (LSF) of circles and circular arcs. First we discuss the existence and uniqueness of LSF and various parametrization schemes. Then we evaluate several popular circle fitting algorithms and propose a new one that surpasses the existing methods in reliability. We also discuss and compare direct (algebraic) circle fits.

After diagnose the model and something was detected, there needs an adjustment for model fitting. For example, if non-equal variance happens, either use the transformation of response or other choices. If there are influential points in the dataset, we may try to avoid its influence by different fitting method (Robust Methods). If the relation between response and predictors are absolute not li...