Abstract: We will introduce Errors-in-Variables models (EIV) and its applications in geometric estimation, which is a widely known topic in computer vision and pattern recognition. In geometric estimation, two types of problems will be discussed: (1) Fitting geometric curves such as circles, and ellipses to a set of experimental observations whose both coordinates are contaminated by noisy errors. (2) Other applications in computer vision such as 'Fundamental Matrix' estimation and 'Homography' computation that are essential in 3D-reconstruction.



Some theoretical results in circle and ellipse fitting will be addressed first. These results lead to some methodological questions that require further investigation. Therefore, we developed our unconventional statistical analysis that allowed us to effectively assess EIV parameter estimates. We validated this approach through a series of numerical tests. We theoretically compared the most popular fits for circles and ellipses with each other and we showed why and by how much each fit differs from others. Our theoretical comparison leads to new unbeatable fits with superior characteristics that surpass all existing fits theoretically and experimentally.