Bundle adjustment (BA) is the standard way to optimise camera poses and to
produce sparse representations of a scene. However, as the number of camera
poses and features grows, refinement through bundle adjustment becomes
inefficient. Inspired by global motion averaging methods, we propose a new
bundle adjustment objective which does not rely on image features' reprojection
errors yet maintains precision on par with classical BA. Our method averages
over relative motions while implicitly incorporating the contribution of the
structure in the adjustment. To that end, we weight the objective function by
local hessian matrices - a by-product of local bundle adjustments performed on
relative motions (e.g., pairs or triplets) during the pose initialisation step.
Such hessians are extremely rich as they encapsulate both the features' random
errors and the geometric configuration between the cameras. These pieces of
information propagated to the global frame help to guide the final optimisation
in a more rigorous way. We argue that this approach is an upgraded version of
the motion averaging approach and demonstrate its effectiveness on both
photogrammetric datasets and computer vision benchmarks.

本文提出了一种新的捆绑调整目标，它不依赖于图像特征的重新投影误差，同时保持与传统捆绑调整相当的精度，通过平均相对运动和局部海森矩阵的加权目标函数，从而隐含地考虑结构信息，利用全局对齐来引导最终优化。

使用相对运动海森矩阵的无意义全局捆绑调整

Pointless Global Bundle Adjustment With Relative Motions Hessians

A recent numerical study observed that neural network classifiers enjoy a
large degree of symmetry in the penultimate layer. Namely, if $h(x) = Af(x) +b$
where $A$ is a linear map and $f$ is the output of the penultimate layer of the
network (after activation), then all data points $x_{i, 1}, \dots, x_{i, N_i}$
in a class $C_i$ are mapped to a single point $y_i$ by $f$ and the points $y_i$
are located at the vertices of a regular $k-1$-dimensional standard simplex in
a high-dimensional Euclidean space.
We explain this observation analytically in toy models for highly expressive
deep neural networks. In complementary examples, we demonstrate rigorously that
even the final output of the classifier $h$ is not uniform over data samples
from a class $C_i$ if $h$ is a shallow network (or if the deeper layers do not
bring the data samples into a convenient geometric configuration).

神经网络分类器的倒数第二层在高维空间中呈现出较大的对称性，通过仅仅简述深度网络的玩具模型，证明了即使是分类器的最终输出在某些条件下也不会对来自于同一类中的数据样本一致，这里的条件包括分类器是浅层网络或深层网络无法将样本带入适当的几何配置。