Interacting Geometric Priors For Robust Multi-Model Fitting: Supplementary Material

where l is a positive spatial smoothness penalty, G(fp, fq) is a function measuring the geometric inconsistency between fp and fq . Under the condition that l ≥ G(., .) ≥ 0, function (6) is submodular, and can be minimised by using graph-cut based methods (e.g., PEARL [1]). However, the condition l ≥ G(., .) ≥ 0 clearly limits the effect of the geometric consistency since the penalty G(., .) is bounded by l. Indeed, we have tried PEARL with the piecewise smooth function (6), yet the benefit of the geometric consistency is diminishing. More importantly, in the applications where the smoothness assumption is not valid (e.g., vanishing point detection), it is impossible to penalise the geometric inconsistency using (6) because the smoothness cost is set to zero (i.e., l = 0). III. PLANAR SURFACE RECONSTRUCTION FROM 3D POINT CLOUDS.