  In this paper, we propose a novel hierarchical representation via message
propagation (HRMP) method for robust model fitting, which simultaneously takes
advantages of both the consensus analysis and the preference analysis to
estimate the parameters of multiple model instances from data corrupted by
outliers, for robust model fitting. Instead of analyzing the information of
each data point or each model hypothesis independently, we formulate the
consensus information and the preference information as a hierarchical
representation to alleviate the sensitivity to gross outliers. Specifically, we
firstly construct a hierarchical representation, which consists of a model
hypothesis layer and a data point layer. The model hypothesis layer is used to
remove insignificant model hypotheses and the data point layer is used to
remove gross outliers. Then, based on the hierarchical representation, we
propose an effective hierarchical message propagation (HMP) algorithm and an
improved affinity propagation (IAP) algorithm to prune insignificant vertices
and cluster the remaining data points, respectively. The proposed HRMP can not
only accurately estimate the number and parameters of multiple model instances,
but also handle multi-structural data contaminated with a large number of
outliers. Experimental results on both synthetic data and real images show that
the proposed HRMP significantly outperforms several state-of-the-art model
fitting methods in terms of fitting accuracy and speed.
