Natural Light Uncalibrated Photometric Stereo (NaUPS) relieves the strict
environment and light assumptions in classical Uncalibrated Photometric Stereo
(UPS) methods. However, due to the intrinsic ill-posedness and high-dimensional
ambiguities, addressing NaUPS is still an open question. Existing works impose
strong assumptions on the environment lights and objects' material, restricting
the effectiveness in more general scenarios. Alternatively, some methods
leverage supervised learning with intricate models while lacking
interpretability, resulting in a biased estimation. In this work, we proposed
Spin Light Uncalibrated Photometric Stereo (Spin-UP), an unsupervised method to
tackle NaUPS in various environment lights and objects. The proposed method
uses a novel setup that captures the object's images on a rotatable platform,
which mitigates NaUPS's ill-posedness by reducing unknowns and provides
reliable priors to alleviate NaUPS's ambiguities. Leveraging neural inverse
rendering and the proposed training strategies, Spin-UP recovers surface
normals, environment light, and isotropic reflectance under complex natural
light with low computational cost. Experiments have shown that Spin-UP
outperforms other supervised / unsupervised NaUPS methods and achieves
state-of-the-art performance on synthetic and real-world datasets. Codes and
data are available at this https URL

Spin-UP 是一种非监督方法，通过减少未知量并提供可靠的先验知识，使用旋转平台上的对象图像捕获新颖的设置来解决在各种自然光环境和对象下的 Natural Light Uncalibrated Photometric Stereo 的困难。

自然光未校准的自旋光对光度立体的应用

Spin-UP: Spin Light for Natural Light Uncalibrated Photometric Stereo

The limited angle Radon transform is notoriously difficult to invert due to
the ill-posedness. In this work, we give a mathematical explanation that the
data-driven approach based on deep neural networks can reconstruct more
information in a stable way compared to traditional methods.

基于深度神经网络的数据驱动方法相较于传统方法，能够更稳定地重建有限角度 Radon 变换中的信息。

有限角度层析成像中的数据驱动方法的鲁棒性

Robustness of the data-driven approach in limited angle tomography

There has been continued interest in seeking a theorem describing optimal
low-rank approximations to tensors of order 3 or higher, that parallels the
Eckart-Young theorem for matrices. In this paper, we argue that the naive
approach to this problem is doomed to failure because, unlike matrices, tensors
of order 3 or higher can fail to have best rank-r approximations. The
phenomenon is much more widespread than one might suspect: examples of this
failure can be constructed over a wide range of dimensions, orders and ranks,
regardless of the choice of norm (or even Bregman divergence). Moreover, we
show that in many instances these counterexamples have positive volume: they
cannot be regarded as isolated phenomena. In one extreme case, we exhibit a
tensor space in which no rank-3 tensor has an optimal rank-2 approximation. The
notable exceptions to this misbehavior are rank-1 tensors and order-2 tensors.
In a more positive spirit, we propose a natural way of overcoming the
ill-posedness of the low-rank approximation problem, by using weak solutions
when true solutions do not exist. In our work we emphasize the importance of
closely studying concrete low-dimensional examples as a first step towards more
general results. To this end, we present a detailed analysis of equivalence
classes of 2-by-2-by-2 tensors, and we develop methods for extending results
upwards to higher orders and dimensions. Finally, we link our work to existing
studies of tensors from an algebraic geometric point of view. The rank of a
tensor can in theory be given a semialgebraic description; i.e., can be
determined by a system of polynomial inequalities. In particular we make
extensive use of the 2-by-2-by-2 hyperdeterminant.

本文讨论了针对高于三阶的张量的最优低秩逼近定理。我们提出了使用弱解来克服低秩逼近问题的不适定性，并从代数几何的角度将我们的工作与张量的现有研究联系起来。