Nonnegative Matrix Underapproximation for Robust Multiple Model Fitting

TL;DR

This paper introduces an efficient algorithm for nonnegative matrix underapproximation, enhancing data interpretability and robustness in multiple model fitting, with applications in climate data analysis and computer vision.

Contribution

The paper proposes a novel, efficient NMU algorithm that improves robustness and sparsity in nonnegative matrix factorization for multiple model fitting tasks.

Findings

Outperforms existing methods in estimating multiple fundamental matrices.

Provides state-of-the-art results in homography estimation.

Demonstrates effectiveness on climate data analysis.

Abstract

In this work, we introduce a highly efficient algorithm to address the nonnegative matrix underapproximation (NMU) problem, i.e., nonnegative matrix factorization (NMF) with an additional underapproximation constraint. NMU results are interesting as, compared to traditional NMF, they present additional sparsity and part-based behavior, explaining unique data features. To show these features in practice, we first present an application to the analysis of climate data. We then present an NMU-based algorithm to robustly fit multiple parametric models to a dataset. The proposed approach delivers state-of-the-art results for the estimation of multiple fundamental matrices and homographies, outperforming other alternatives in the literature and exemplifying the use of efficient NMU computations.