Hypergraph Modelling for Geometric Model Fitting

TL;DR

This paper introduces a hypergraph-based approach for fitting and segmenting multi-structural data, effectively handling outliers and estimating multiple model parameters simultaneously.

Contribution

It presents a novel hypergraph model and partition algorithm that improve multi-structure model fitting and segmentation in complex, noisy datasets.

Findings

Outperforms previous methods on synthetic data

Effective in estimating multiple models simultaneously

Robust to heavy outliers

Abstract

In this paper, we propose a novel hypergraph based method (called HF) to fit and segment multi-structural data. The proposed HF formulates the geometric model fitting problem as a hypergraph partition problem based on a novel hypergraph model. In the hypergraph model, vertices represent data points and hyperedges denote model hypotheses. The hypergraph, with large and "data-determined" degrees of hyperedges, can express the complex relationships between model hypotheses and data points. In addition, we develop a robust hypergraph partition algorithm to detect sub-hypergraphs for model fitting. HF can effectively and efficiently estimate the number of, and the parameters of, model instances in multi-structural data heavily corrupted with outliers simultaneously. Experimental results show the advantages of the proposed method over previous methods on both synthetic data and real images.