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.