Robust fitting of multiple structures: The statistical learning approach

We propose an unconventional but highly effective approach to robust fitting of multiple structures by using statistical learning concepts. We design a novel Mercer kernel for the robust estimation problem which elicits the potential of two points to have emerged from the same underlying structure. The Mercer kernel permits the application of well-grounded statistical learning methods, among which nonlinear dimensionality reduction, principal component analysis and spectral clustering are applied for robust fitting. Our method can remove gross outliers and in parallel discover the multiple structures present. It functions well under severe outliers (more than 90% of the data) and considerable inlier noise without requiring elaborate manual tuning or unrealistic prior information. Experiments on synthetic and real problems illustrate the superiority of the proposed idea over previous methods.