渐进性优化的尺度自适应Cauchy稳健估计模型及其应用

doi:10.11947/j.AGCS.2023.20210415

摘要/Abstract

摘要： 稳健估计技术在几何建模与平差处理中至关重要。传统加权迭代法无法处理高粗差比率(≥50%)问题;随机采样一致性方法(RANSAC)仅能获得近似解且时间复杂度高。本文提出一种渐进优化的尺度自适应Cauchy稳健估计模型。首先,通过在Cauchy核函数中引入控制参数(尺度因子)来调节其稳健性;其次,利用控制参数过滤掉一部分大残差观测值,降低真实粗差比率。所提模型采用由粗到精的迭代加权最小二乘法(IRLS)进行渐进优化,在迭代过程中不断减小控制参数来提升模型对高粗差比率的稳健性。同时,本文给出了其在经典摄影测量任务中的应用,包括误匹配剔除、后方交会及点云配准。试验结果表明,对非对抗性粗差(non-adversarial outliers),该模型能有效处理高达80%的粗差点并且其运行效率比RANSAC快2~3个数量级。

关键词: 稳健估计, 粗差观测, 图像匹配, 后方交会, 点云配准

Abstract: Robust estimation is a basic technology in geometric processing and survey adjustment. Traditional iteratively reweighted least squares (IRLS) cannot handle problems with high outlier rates (≥50%); Random sampling consensus (RANSAC) type algorithms can only obtain approximate solutions and are time consuming. This paper proposes a progressively optimized scale-adaptive Cauchy robust estimation model. First, a scale parameter is introduced into the typical Cauchy kernel function to control its robustness. Second, the proposed method uses the control parameter to filter out some observations with the large residuals in each iteration and reduce the true outlier rate. Then, a “coarse to fine” IRLS method is used for optimization in a progressive manner. In the iterative process, the control parameter is continuously reduced to improve the robustness. This paper also applies the proposed model in several important tasks of photogrammetry, including mismatch removal, image orientation, and point cloud registration. Extensive experiments show that the proposed model is robust to more than 80% outliers when the gross errors conform to an approximately uniform or random distribution, and is 2~3 orders of magnitude faster than RANSAC.

Key words: robust estimation, gross errors, image matching, space resection, point cloud registration

中图分类号:

P231

李加元, 张永军, 艾明耀, 胡庆武. 渐进性优化的尺度自适应Cauchy稳健估计模型及其应用[J]. 测绘学报, 2023, 52(1): 61-70.

LI Jiayuan, ZHANG Yongjun, AI Mingyao, HU Qingwu. Scale-adaptive Cauchy robust estimation based on progressive optimization and its applications[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52(1): 61-70.

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