Covariance estimation for minimal geometry solvers via scaled unscented transformation

• Scaled unscented transformation (SUT) for minimal geometry solvers (MGS).
• SUT vs. first-order-propagation (FOP) in uncertainty estimation of MGS.
• Since MGS are highly nonlinear, SUT is a better uncertainty estimator than FOP.

Covariance is a well-established characterisation of the output uncertainty for estimators dealing with noisy data. It is conventionally estimated via first-order forward propagation (FOP) of input covariance. However, since FOP employs a local linear approximation of the estimator, its reliability is compromised in the case of nonlinear transformations. An alternative method, scaled unscented transformation (SUT) is known to cope with such cases better. However, despite the nonlinear nature of many vision problems, its adoption remains limited. This paper investigates the application of SUT on common minimal geometry solvers, a class of algorithms at the core of many applications ranging from image stitching to film production and robot navigation. The contributions include an experimental comparison of SUT against FOP on synthetic and real data, and practical suggestions for adapting the original SUT to the geometry solvers. The experiments demonstrate the superiority of SUT to FOP as a covariance estimator, over a range of scene types and noise levels, on synthetic and real data.