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收稿日期：2023-10-17，
修回日期：2024-01-04，
纸质出版日期：2024-10-16
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目的
2
全局式从运动恢复结构（structure from motion， SfM）通过运动平均一次性恢复所有相机的绝对位姿，效率相对较高。运动平均中的平移平均主要负责解算相机在世界坐标系下的绝对位置，其求解过程因尺度歧义性、估计敏感性和求解不确定性的影响而较为困难。本文提出了一种基于增量尺度估计的平移平均方法，在消除尺度歧义性的同时提升了求解鲁棒性与准确性。
方法
2
本文将平移平均问题解耦为3个子问题：1）局部绝对尺度的增量式估计；2）全局绝对尺度的增量式估计；3）基于
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优化的尺度已知的绝对位置估计。
结果
2
在1DSfM数据集上进行对比实验，基线解算精度明显提升，解算相机百分比的均值达到96%。当引入两种不同的绝对旋转进行计算时，其绝对位置中值误差仅略差于BATA（bilinear angle-based translation averaging）与CReTA（correspondence reweighted translation averaging），排名第3，均值误差改善更为明显，分别排名第1和第2。相较于原始方法，本文方法在相机解算数量与位置解算精度上均有较大提升。
结论
2
本文方法综合了尺度分离思想与增量式参数估计思想，既消除了尺度歧义性，又保证了鲁棒性与高效性，求解所得的相机绝对位置稳定可靠。
Objective
2
The structure from motion （SfM） technique serves as the fundamental step in the sparse reconstruction process， finding extensive applications in remote sensing mapping， indoor modeling， augmented reality， and ancient architecture preservation. SfM technology retrieves camera poses from images， encompassing two main categories： incremental and global approaches. The global SfM， in contrast to the iterative nature of incremental SfM， simultaneously estimates the absolute poses of all cameras through motion averaging， resulting in relatively high efficiency. However， it still encounters challenges regarding robustness and accuracy. Rotation averaging and translation averaging constitute crucial components within the motion averaging. Compared with rota
tion averaging， translation averaging is more difficult due to the following three reasons： 1） Only relative translation directions could be recovered by essential matrix estimation and decomposition， i.e.， the produced relative translations are scale ambiguous. 2） Only cameras in the same parallel rigid component could their absolute locations be uniquely determined by translation averaging， while for rotation averaging， the requirement simply degenerates to the connected component. 3） Compared with relative rotation， the estimation accuracy of relative translation is more vulnerable to the feature point mismatches and more likely to be outlier contaminated. In traditional approaches， the translation averaging method based on scale separation （
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） calculates the relative baseline length between cameras before estimating the absolute locations， eliminates the scale ambiguity， and the solving range is no longer constrained by the camera triplet， but its robustness and accuracy still need to be improved. Incremental translation averaging （ITA） introduces the idea of incremental parameter estimation into the translation averaging process for the first time， which has good robustness and high accuracy. However， its solving process depends on camera triplets and may suffer from degeneracy during collinear camera motion. To solve the above problems， this study proposes a translation averaging method based on incremental scale estimation （
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）， which eliminates the scale ambiguity and enhances the method's robustness and result accuracy.
Method
2
Incremental SfM has been proven to be highly accurate and robust， making it a preferred choice for many applications. It has shown to be particularly effective in handling large datasets and overcoming the challenges posed by complex real-world scenarios. Recognizing its potential， researchers have sought to transfer the incremental parameter estimation ideology to other related tasks， such as incremental rotation averaging （IRA） and ITA. In particular， IRA is designed to estimate the camera absolute rotations incrementally and efficiently. Meanwhile， ITA is performed for the camera absolute locations， enabling it to handle outliers effectively and avoid error propagation. Overall， the adoption of incremental parameter estimation ideology for motion averaging tasks demonstrates the versatility and effectiveness of this approach. With its ability to handle complex datasets and overcome a range of challenges， the incremental parameter estimation ideology holds great promise for future research in the field of 3D reconstruction and beyond. In this study，
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is proposed by incorporating the scale separation strategy and incremental parameter estimation ideology. Specifically， the translation averaging problem is decomposed into three sub-ones and sequentially solved： 1） incremental estimation of local absolute scale， 2） incremental estimation of global absolute scale， 3） scale-aware absolute location estimation based on
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optimization. The input of our proposed method is the pairwise scale invariant feature transform point matches， and its output is the absolute camera locations. First， the relative motion between cameras is obtained by estimating and decomposing the essential matrix. Next， the two-view triangulation is performed to calculate the relative depths in the local coordinate system. On the basis of depth ratios， incremental estimations are conducted for the local and global absolute scales. Subsequently， the relative baseline length between cameras is computed， and rotation averaging is performed for abs
olute rotation estimation， enabling the final scale-aware absolute location estimation.
Result
2
We performed experimental tests to evaluate the selection of scale distance function and scale distance threshold. The experimental results confirmed that the normalized perfect square deviation function effectively eliminates the impact of scaling effects. Furthermore， the incremental scale estimation method shows good robustness and insensitivity to scale distance threshold and achieves remarkably higher baseline accuracy compared with
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. The experiments were conducted on the 1DSfM dataset. In comparison with various state-of-the-art methods including bilinear angle-based translation averaging （BATA）， correspondence reweighted translation averaging （CReTA）， ITA， and
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， our proposed method exhibited the following performance： 1） In terms of the number of cameras solved， the average percentage of successfully solved cameras using the proposed method is 96%. 2） The median error of absolute location estimation is slightly worse than that of BATA and CReTA and ranks third overall under different absolute rotations. 3） In terms of the mean error in absolute location estimation， the proposed method has remarkable advantages， ranking first and second respectively. Compared with the original
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， the method in this study has a great improvement in the number of cameras solved and the accuracy of locations estimated.
Conclusion
2
The proposed method combines the concept of scale separation with incremental parameter estimation. By integrating these two ideas， our method effectively eliminates scale ambiguity while ensuring the effectiveness of outlier rejection and maintaining a concise solving process. As a result， the obtained absolute camera locations are stable and reliable.
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