视觉SLAM：旋转平均优化法替代BA
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"本文探讨了视觉SLAM中bundle adjustment（BA）的传统作用以及其存在的问题，并提出了一种替代的优化方法，即通过旋转平均来仅优化相机的定向，从而避免传统BA的一些难题。"
在视觉SLAM（Simultaneous Localization And Mapping，同时定位与建图）系统中，bundle adjustment是关键步骤，用于从特征轨迹中估计相机的6自由度（6DOF）运动轨迹和3D地图。在现代SLAM管道中，BA通常在每次新数据帧加入时执行，以提高估计的精度。然而，这种方法存在两个主要缺陷：首先，对BA的良好初始化要求对所有变量，尤其是地图，进行精确估计并随时间维护，这使得整个算法变得复杂；其次，BA内在地需要足够的基线来估计3D结构，因此在缓慢移动或纯旋转运动期间，SLAM算法可能会遇到困难。
作者Alvaro Parra Bustos、Tat-Jun Chin、Anders Eriksson和Ian Reid提出了一种不同的SLAM优化核心策略。他们建议用旋转平均代替传统的bundle adjustment。旋转平均允许系统逐步优化相机的方向，而不是同时优化方向和位置。通过这种方式，他们可以避免在低速或纯旋转运动中遇到的问题，因为这些情况下的基线可能不足。
在优化相机方向后，他们利用一种准凸形式来估算相机位置和3D点。这种方法的优点在于它能够解决BA中的部分难题，尤其是在动态变化的环境或困难的运动条件下。通过只优化旋转，可以减少计算负担，同时仍然能够获得准确的定位和地图重建结果。
此外，这种方法还有可能提高SLAM系统的实时性能和鲁棒性。由于不需要像BA那样维护和更新复杂的3D地图，因此在资源受限的设备上，如无人机或移动机器人，这种优化方法可能更具优势。
该研究提供了一个有前景的SLAM优化策略，它可以改进当前依赖于bundle adjustment的SLAM系统的性能，特别是在处理低速和旋转运动场景时。通过专注于相机定向的优化，该方法有望简化SLAM算法，提高其在实际应用中的效率和可靠性。
Visual SLAM: Why Bundle Adjust?
´
Alvaro Parra Bustos
1
, Tat-Jun Chin
1
, Anders Eriksson
2
and Ian Reid
1
Abstract— Bundle adjustment plays a vital role in feature-
based monocular SLAM. In many modern SLAM pipelines,
bundle adjustment is performed to estimate the 6DOF camera
trajectory and 3D map (3D point cloud) from the input feature
tracks. However, two fundamental weaknesses plague SLAM
systems based on bundle adjustment. First, the need to care-
fully initialise bundle adjustment means that all variables, in
particular the map, must be estimated as accurately as possible
and maintained over time, which makes the overall algorithm
cumbersome. Second, since estimating the 3D structure (which
requires sufficient baseline) is inherent in bundle adjustment,
the SLAM algorithm will encounter difficulties during periods
of slow motion or pure rotational motion.
We propose a different SLAM optimisation core: instead of
bundle adjustment, we conduct rotation averaging to incremen-
tally optimise only camera orientations. Given the orientations,
we estimate the camera positions and 3D points via a quasi-
convex formulation that can be solved efficiently and globally
optimally. Our approach not only obviates the need to estimate
and maintain the positions and 3D map at keyframe rate (which
enables simpler SLAM systems), it is also more capable of
handling slow motions or pure rotational motions.
I. INTRODUCTION
Let u
i, j
be the 2D coordinates of the i-th scene point
as seen in the j-th image Z
j
. Given a set {u
i, j
} of obser-
vations, structure-from-motion (SfM) aims to estimate the
3D coordinates X = {X
i
} of the scene points and 6DOF
poses {(R
j
,t
j
)} of the images {Z
j
} that agree with the
observations. The bundle adjustment (BA) formulation is
min
{X
i
},{(R
j
,t
j
)}
∑
i, j
u
i, j
− f (X
i
| R
j
,t
j
)
2
2
,
(1)
where f (X
i
| R
j
,t
j
) is the projection of X
i
onto Z
j
(assuming
calibrated cameras). In practice, not all X
i
are visible in every
Z
j
, thus some of the (i, j) terms are dropped. For ease of
exposition, we follow [1] and regard the image set {Z
j
} as
inputs to BA, bearing in mind that the effective inputs are
the observations {u
i, j
} and the visibility matrix.
As a non-linear least squares problem, (1) is usually solved
by gradient descent methods, e.g., Levenberg-Marquardt,
which require initialisation for all unknowns. Thus, apart
from the images {Z
j
}, the total inputs to a BA instance
typically include the initial values for {(R
j
,t
j
)} and X.
BA is justifiable in the maximum likelihood sense if the
errors due to the uncertainty in localising the feature points
{u
i, j
} are Normally distributed. However, it is not obvious
that available feature detectors satisfy this property [2], [3],
[4]. While this does not reduce the usefulness of BA, its
statistical validity should not be taken for granted.
1
School of Computer Science, The University of Adelaide.
2
School of Electrical Engineering and Computer Science, Queensland
University of Technology
Algorithm 1 BA-SLAM (adapted from [1]).
1: X ← Initialise points(Z
0
).
2: for each keyframe step t = 1, 2,. .. do
3: s ← t −(window size) + 1.
4: if a number of n ≥ 1 points left field of view then
5: X ← X ∪ initialise n new points(Z
t
).
6: end if
7: R
s:t
,t
s:t
,X ← BA(R
s:t
,t
s:t
,X,Z
0:t
).
8: if loop is detected in Z
t
then
9: R
1:t
,t
1:t
,X ← BA(R
1:t
,t
1:t
,X,Z
0:t
).
10: end if
11: end for
A. BA-SLAM
Roughly speaking, monocular feature-based SLAM [5]
(henceforth, “SLAM”) is the execution of SfM incrementally
to process streaming input images Z
0:t
, where
Z
0:t
= {Z
0
,Z
1
,...,Z
t
}. (2)
Several influential works [6], [7], [1], [8] have cemented the
importance of BA in SLAM. Algorithm 1, which is adapted
from [1, Table 1], describes a SLAM optimisation core based
on BA over keyframes. Specifically:
• In Step 5, new scene points are “spawned” if the current
frame Z
t
does not adequately observe the map X.
• In Step 7 (a.k.a. local mappping), BA is used to estimate
the camera trajectory and 3D map in the current time
window. Often, local mapping is preceded by camera
tracking to accurately initialise the current pose (R
t
,t
t
).
See [1, Sec. 5.3] or [8, Sec. V] for examples.
• In Step 9 (a.k.a. loop closure), a system-wide BA is
executed to reoptimise all the variables and redistribute
accumulated drift errors. Implicit in Algorithm 1 is the
introduction of covisibility information between Z
t
and
older keyframes, prior to BA. Often, Step 9 is preceded
by pose graph optimisation [9], [10], [11], [12] to give
a more accurate initialisation of the poses.
Note that Algorithm 1 is merely a “basic recipe” for SLAM.
In practice, “what will make or break a real-time SLAM
system are all the (often heuristic) nitty-gritty details” [13],
e.g., how to select features/keyframes, how to update the
covisibility graph, how to select/merge/prune 3D points, etc.
However, since our focus is on optimisation, Algorithm 1 is
sufficient to capture the core algorithmic elements of SLAM
systems based on BA, such as ORB-SLAM [8].
arXiv:1902.03747v2 [cs.CV] 14 Jun 2019
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