Deterministic Hypothesis Generation for Robust Fitting of Multiple Structures

TL;DR

This paper introduces a deterministic algorithm for robustly fitting multiple structures in data with high outlier ratios, combining local hypothesis generation with iterative refinement for improved stability and efficiency.

Contribution

The proposed method uses local MaxFS hypotheses and IRL1 refinement to outperform random sampling methods in robustness and computational efficiency for multiple-structure fitting.

Findings

More reliable hypotheses than random sampling methods.

Effective in high outlier scenarios.

Significantly more efficient than global optimization approaches.

Abstract

We present a novel algorithm for generating robust and consistent hypotheses for multiple-structure model fitting. Most of the existing methods utilize random sampling which produce varying results especially when outlier ratio is high. For a structure where a model is fitted, the inliers of other structures are regarded as outliers when multiple structures are present. Global optimization has recently been investigated to provide stable and unique solutions, but the computational cost of the algorithms is prohibitively high for most image data with reasonable sizes. The algorithm presented in this paper uses a maximum feasible subsystem (MaxFS) algorithm to generate consistent initial hypotheses only from partial datasets in spatially overlapping local image regions. Our assumption is that each genuine structure will exist as a dominant structure in at least one of the local regions. To refine initial hypotheses estimated from partial datasets and to remove residual tolerance dependency of the MaxFS algorithm, iterative re-weighted L1 (IRL1) minimization is performed for all the image data. Initial weights of IRL1 framework are determined from the initial hypotheses generated in local regions. Our approach is significantly more efficient than those that use only global optimization for all the image data. Experimental results demonstrate that the presented method can generate more reliable and consistent hypotheses than random-sampling methods for estimating single and multiple structures from data with a large amount of outliers. We clearly expose the influence of algorithm parameter settings on the results in our experiments.