Minimal Constraint Relaxation for Multiview Autocalibration

摘要

Polynomial systems in multiview geometry are often over-constrained, and naively removing equations can lead to unstable or inconsistent solutions. We revisit this issue through constraint relaxation---selectively removing equations to obtain a finite set of isolated (and, ideally, well-conditioned) solutions. Focusing on the three-view Kruppa equations for autocalibration, we introduce a minimal relaxation framework for identifying subsets of constraints leading to geometrically valid solutions. Using both symbolic computation and numerical homotopy continuation methods, we enumerate and classify all possible relaxation patterns arising from our formulation of Kruppa's equations, isolating all patterns that yield finitely-many solutions. In experiments with synthetic and real images, we demonstrate empirically that specific relaxations are well-conditioned and consistently outperform multiple baselines, including a more classical Kruppa formulation. Overall, our findings establish the minimal relaxation framework as a practical tool in multiview geometry computation.