arXiv:2603.14796v1 Announce Type: new 
Abstract: To achieve outlier-robust geometric estimation, robust objective functions are generally employed to mitigate the influence of outliers. The widely used consensus maximization(CM) is highly robust when paired with global branch-and-bound(BnB) search. However, CM relies solely on inlier counts and is sensitive to the inlier threshold. Besides, the discrete nature of CM leads to loose bounds, necessitating extensive BnB iterations and computation cost. Truncated losses(TL), another continuous alternative, leverage residual information more effectively and could potentially overcome these issues. But to our knowledge, no prior work has systematically explored globally minimizing TL with BnB and its potential for enhanced threshold resilience or search efficiency. In this work, we propose GTM, the first unified BnB-based framework for globally-optimal TL loss minimization across diverse geometric problems. GTM involves a hybrid solving design: given an n-dimensional problem, it performs BnB search over an (n-1)-dimensional subspace while the remaining 1D variable is solved by bounding the objective function. Our hybrid design not only reduces the search space, but also enables us to derive Lipschitz-continuous bounding functions that are general, tight, and can be efficiently solved by a classic global Lipschitz solver named DIRECT, which brings further acceleration. We conduct a systematic evaluation on various BnB-based methods for CM and TL on the robust linear regression problem, showing that GTM enjoys remarkable threshold resilience and the highest efficiency compared to baseline methods. Furthermore, we apply GTM on different geometric estimation problems with diverse residual forms. Extensive experiments demonstrate that GTM achieves state-of-the-art outlier-robustness and threshold-resilience while maintaining high efficiency across these estimation tasks.

تم تقديم إطار عمل جديد يسمى الحد الأدنى العالمي للخسائر المقيدة (GTM) لتعزيز تقدير الهندسة المقاوم للقيم الشاذة من خلال تقليل الخسائر المقيدة بشكل منهجي باستخدام نهج البحث العالمي عن طريق التفرع والتقييد. تهدف هذه الطريقة إلى تحسين مقاومة العتبة وكفاءة البحث مقارنة بتقنيات تعظيم الإجماع التقليدية، التي تكون حساسة لعوامل الإدخال وتتطلب حسابات واسعة.

Se ha introducido un nuevo marco llamado Minimización Global de Pérdidas Truncadas (GTM) para mejorar la estimación geométrica robusta a valores atípicos mediante la minimización sistemática de pérdidas truncadas utilizando un enfoque de búsqueda global por ramificación y acotación. Este método busca mejorar la resiliencia al umbral y la eficiencia de búsqueda en comparación con las técnicas de maximización de consenso tradicionales, que son sensibles a los umbrales de inliers y requieren un cálculo extenso.

Un nouveau cadre appelé Minimisation Globale des Pertes Truncées (GTM) a été introduit pour améliorer l'estimation géométrique robuste aux valeurs aberrantes en minimisant systématiquement les pertes truncées à l'aide d'une approche de recherche globale par branchement et bornage. Cette méthode vise à améliorer la résilience aux seuils et l'efficacité de recherche par rapport aux techniques de maximisation de consensus traditionnelles, qui sont sensibles aux seuils d'inliers et nécessitent des calculs étendus.

A new framework called Global Truncated Loss Minimization (GTM) has been introduced to enhance outlier-robust geometric estimation by systematically minimizing truncated losses using a global branch-and-bound search approach. This method aims to improve threshold resilience and search efficiency compared to traditional consensus maximization techniques, which are sensitive to inlier thresholds and require extensive computation.