In this paper we introduce a general framework for analyzing the numerical
conditioning of minimal problems in multiple view geometry, using tools from
computational algebra and Riemannian geometry. Special motivation comes from
the fact that relative pose estimation, based on standard 5-point or 7-point
Random Sample Consensus (RANSAC) algorithms, can fail even when no outliers are
present and there is enough data to support a hypothesis. We argue that these
cases arise due to the intrinsic instability of the 5- and 7-point minimal
problems. We apply our framework to characterize the instabilities, both in
terms of the world scenes that lead to infinite condition number, and directly
in terms of ill-conditioned image data. The approach produces computational
tests for assessing the condition number before solving the minimal problem.
Lastly synthetic and real data experiments suggest that RANSAC serves not only
to remove outliers, but also to select for well-conditioned image data, as
predicted by our theory.

本文介绍了一个使用计算代数和黎曼几何工具来分析多视角几何中最小问题的数值条件的通用框架。我们从标准的 5 点或 7 点随机采样一致性（RANSAC）算法在相对姿态估计时的失败情况出发，即使在没有离群值和足够数据支持假说的情况下。我们认为这些情况是由于 5 点和 7 点最小问题的固有不稳定性引起的。我们将我们的框架应用于表征造成条件数无穷大的世界场景，以及直接在图像数据中表征病态。该方法产生了在求解最小问题之前评估条件数的计算测试。最后，合成和真实数据的实验证明，RANSAC 不仅可以去除离群值，还可选择具有良好条件的图像数据，如我们的理论所预测。

多视几何中的条件数、相对姿态估计的不稳定性和 RANSAC

Condition numbers in multiview geometry, instability in relative pose  estimation, and RANSAC

We study the problem of shape generation in 3D mesh representation from a few
color images with known camera poses. While many previous works learn to
hallucinate the shape directly from priors, we resort to further improving the
shape quality by leveraging cross-view information with a graph convolutional
network. Instead of building a direct mapping function from images to 3D shape,
our model learns to predict series of deformations to improve a coarse shape
iteratively. Inspired by traditional multiple view geometry methods, our
network samples nearby area around the initial mesh's vertex locations and
reasons an optimal deformation using perceptual feature statistics built from
multiple input images. Extensive experiments show that our model produces
accurate 3D shape that are not only visually plausible from the input
perspectives, but also well aligned to arbitrary viewpoints. With the help of
physically driven architecture, our model also exhibits generalization
capability across different semantic categories, number of input images, and
quality of mesh initialization.

使用图卷积网络从多角度图像中预测一系列形状变形，以进一步提高 3D 网格表征的形状质量，从而获得高精确度、高可靠性且具有普适性的 3D 模型。

Pixel2Mesh++: 多视角下基于变形的 3D 网格生成

Pixel2Mesh++: Multi-View 3D Mesh Generation via Deformation

The objective of this work is to infer the 3D shape of an object from a
single image. We use sculptures as our training and test bed, as these have
great variety in shape and appearance.
To achieve this we build on the success of multiple view geometry (MVG) which
is able to accurately provide correspondences between images of 3D objects
under varying viewpoint and illumination conditions, and make the following
contributions: first, we introduce a new loss function that can harness
image-to-image correspondences to provide a supervisory signal to train a deep
network to infer a depth map. The network is trained end-to-end by
differentiating through the camera. Second, we develop a processing pipeline to
automatically generate a large scale multi-view set of correspondences for
training the network. Finally, we demonstrate that we can indeed obtain a depth
map of a novel object from a single image for a variety of sculptures with
varying shape/texture, and that the network generalises at test time to new
domains (e.g. synthetic images).

本文的研究目的是从单个图像中推断出物体的三维形状，为了实现这一目标，本文使用雕塑作为实验数据集，并基于多视角几何（MVG）的成功经验，提出了一种新的损失函数，利用图像与图像之间的对应关系训练深度网络，完成端到端的单张图像深度估计任务。同时，为了自动地生成大规模的多视图对应数据集，本文提出了一种数据处理方法。在多种雕塑的数据集上的实验表明，本方法可以从单张图像中推断出新物体的三维形状，并且在测试时可以泛化到新的领域（如合成图像）中。