Identifying the underlying models in a set of data points contaminated by noise and outliers, leads to a highly complex multi-model fitting problem. This problem can be posed as a clustering problem by the projection of higher order affinities between data points into a graph, which can then be clustered using spectral clustering. Calculating all possible higher order affinities is computationally expensive. Hence in most cases only a subset is used. In this paper, we propose an effective sampling method to obtain a highly accurate approximation of the full graph required to solve multi-structural model fitting problems in computer vision. The proposed method is based on the observation that the usefulness of a graph for segmentation improves as the distribution of hypotheses (used to build the graph) approaches the distribution of actual parameters for the given data. In this paper, we approximate this actual parameter distribution using a k-th order statistics based cost function and the samples are generated using a greedy algorithm coupled with a data sub-sampling strategy. The experimental analysis shows that the proposed method is both accurate and computationally efficient compared to the state-of-the-art robust multi-model fitting techniques. The code is publicly available from https://github.com/RuwanT/model-fitting-cbs.
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