Publications
WORKSHOP (INTERNATIONAL) Multi-Square-Up Homotopy Continuation for Robust Relative Pose
Norio Kosaka, Genki Osada, Shuhei Nishimura, Shinichi Higashino, Shuji Yamaguchi
Structure-from-Motion in the Age of Deep Learning (SfM-ADL)
September 28, 2026
Robust calibrated relative-pose estimation repeatedly invokes a five-point solver inside RANSAC, but the algebraic presentation solved by that backend is usually fixed. Classical five-point solvers are highly optimised and already return multiple roots for their chosen formulation; we instead study variability from the squared-up presentation of the redundant cubic essential-matrix system obtained after five-point nullspace substitution. Although all square-ups preserve the exact solutions of the full system, their excess-root structure and numerical conditioning can differ, so finite-precision continuation and filtering may yield non-identical retained candidate sets. We present MS-HC-RANSAC, a multi-square-up homotopy-continuation hypothesis generator for robust relative pose. For each minimal sample, MS-HC-RANSAC solves a compact fixed ensemble of square-ups, maps roots to projective essential matrices, clusters and ranks candidates by the full coefficient-normalised residual, and uses cross-square-up recurrence only as a residual-gated tie-breaker. Final model selection remains standard geometric scoring over all correspondences. Controlled synthetic and real-image experiments show that HC-based hypothesis generation changes the candidate pool reaching fixed-budget RANSAC, improves support and selected accuracy metrics over a matched low-budget OpenCV baseline, and reveals metric-dependent multi-square-up gains. High-iteration OpenCV and USAC/MAGSAC remain much stronger practical references, positioning MS-HC-RANSAC as an algebraic diagnostic and stabilisation mechanism rather than a real-time replacement for hand-optimised five-point solvers.
Paper :
Multi-Square-Up Homotopy Continuation for Robust Relative Pose
(external link)
PDF : Multi-Square-Up Homotopy Continuation for Robust Relative Pose