  We propose a novel method to fit and segment multi-structural data via convex
relaxation. Unlike greedy methods --which maximise the number of inliers-- this
approach efficiently searches for a soft assignment of points to models by
minimising the energy of the overall classification. Our approach is similar to
state-of-the-art energy minimisation techniques which use a global energy.
However, we deal with the scaling factor (as the number of models increases) of
the original combinatorial problem by relaxing the solution. This relaxation
brings two advantages: first, by operating in the continuous domain we can
parallelize the calculations. Second, it allows for the use of different
metrics which results in a more general formulation.
  We demonstrate the versatility of our technique on two different problems of
estimating structure from images: plane extraction from RGB-D data and
homography estimation from pairs of images. In both cases, we report accurate
results on publicly available datasets, in most of the cases outperforming the
state-of-the-art.
