稳健局部优化的正确实现

中文摘要 AI 辅助

RANSAC评分和局部优化（LO）对鲁棒性提出了不同的要求，这促使我们将假设选择与细化分离。我们系统地隔离了鲁棒损失形状、错误指定的内点尺度以及优化策略对本质矩阵、基础矩阵和单应性估计的影响。一种轮廓边际评分对 nuisance 内点尺度进行边际化，并选择一个内点分区，从中我们估计设置LO损失宽度的尺度；这使得LO对指定过大的内点尺度具有鲁棒性，而指定过小的尺度则会降低选择本身的性能。细化需要来自种子当前拒绝的对应点的梯度：从当前残差重新加权的优化器会停留在其种子上，而具有宽吸引域的方法能恢复强烈扰动的种子，但会降低准确评分选择的假设的性能，因此仅凭吸引域大小不足以评估RANSAC LO。联合半二次优化平衡了这两者，并且是跨模型类最一致的策略。与轮廓边际评分匹配的优化器，其评分从不降低，却未能达到最佳精度，这对评分和细化目标应匹配的处方提出了挑战。基于这些发现，我们的RANSAC在PhotoTourism上将最先进的RANSAC的本质矩阵姿态误差中位数从2.23度降低到1.58度（当内点尺度正确指定时），并在内点尺度严重错误指定（128倍过大）时从38度降低到6.2度。

英文摘要

RANSAC scoring and local optimization (LO) impose different robustness requirements, motivating the separation of hypothesis selection from refinement. We systematically isolate the effects of robust-loss shape, incorrectly specified inlier scales, and optimization strategy on essential matrix, fundamental matrix, and homography estimation. A profile-marginal score marginalizes the nuisance inlier scale and selects an inlier partition, from which we estimate the scale that sets the LO loss width; this makes LO robust to an inlier scale specified too large, whereas one specified too small degrades selection itself. Refinement needs gradient from correspondences the seed currently rejects: optimizers that reweight from current residuals stay pinned to their seed, whereas methods with broad basins recover strongly perturbed seeds yet degrade accurate score-selected hypotheses, so basin size alone is insufficient to assess RANSAC LO. Joint half-quadratic optimization balances the two and is the most consistent strategy across model classes. An optimizer matched to the profile-marginal score, which never decreases it, does not reach the best accuracy, challenging the prescription that scoring and refinement objectives should match. Composed from these findings, our RANSAC reduces the median essential-matrix pose error of a state-of-the-art RANSAC on PhotoTourism from 2.23 degrees to 1.58 degrees with a correctly specified inlier scale and from 38 degrees to 6.2 degrees when it is grossly misspecified (128x too large).

发表机构

• Kiel University（基尔大学）

机构由 AI 辅助整理，请以论文原文为准。