  We present an efficient deterministic hypothesis generation algorithm for
robust fitting of multiple structures based on the maximum feasible subsystem
(MaxFS) framework. Despite its advantage, a global optimization method such as
MaxFS has two main limitations for geometric model fitting. First, its
performance is much influenced by the user-specified inlier scale. Second, it
is computationally inefficient for large data. The presented MaxFS-based
algorithm iteratively estimates model parameters and inlier scale and also
overcomes the second limitation by reducing data for the MaxFS problem. Further
it generates hypotheses only with top-n ranked subsets based on matching scores
and data fitting residuals. This reduction of data for the MaxFS problem makes
the algorithm computationally realistic. Our method, called iterative MaxFS
with inlier scale estimation and subset updating (IMaxFS-ISE-SU) in this paper,
performs hypothesis generation and fitting alternately until all of true
structures are found. The IMaxFS-ISE-SU algorithm generates substantially more
reliable hypotheses than random sampling-based methods especially as
(pseudo-)outlier ratios increase. Experimental results demonstrate that our
method can generate more reliable and consistent hypotheses than random
sampling-based methods for estimating multiple structures from data with many
outliers.
