MUSE: Robust Surface Fitting using Unbiased Scale Estimates

Despite many successful applications of robust statistics, they have yet to be completely adapted to many computer vision problems. Range reconstruction, particularly in unstructured environments, requires a robust estimator that not only tolerates a large outlier percentage but also tolerates several discontinuities, extracting multiple surfaces in an image region. Observing that random outliers and/or points from across discontinuities increase a hypothesized fit’s scale estimate (standard deviation of the noise), our new operator, called MUSE (Minimum Unbiased Scale Estimator), evaluates a hypothesized fit over potential inlier sets via an objective function of unbiased scale estimates. MUSE extracts the single best fit from the data by minimizing its objective function over a set of hypothesized fits and can sequentially extract multiple surfaces from an image region. We show MUSE to be effective on synthetic data modelling small scale discontinuities and in preliminary experiments on complicated range data.