Accurate lighting estimation is challenging yet critical to many computer
vision and computer graphics tasks such as high-dynamic-range (HDR) relighting.
Existing approaches model lighting in either frequency domain or spatial domain
which is insufficient to represent the complex lighting conditions in scenes
and tends to produce inaccurate estimation. This paper presents NeedleLight, a
new lighting estimation model that represents illumination with needlets and
allows lighting estimation in both frequency domain and spatial domain jointly.
An optimal thresholding function is designed to achieve sparse needlets which
trims redundant lighting parameters and demonstrates superior localization
properties for illumination representation. In addition, a novel spherical
transport loss is designed based on optimal transport theory which guides to
regress lighting representation parameters with consideration of the spatial
information. Furthermore, we propose a new metric that is concise yet effective
by directly evaluating the estimated illumination maps rather than rendered
images. Extensive experiments show that NeedleLight achieves superior lighting
estimation consistently across multiple evaluation metrics as compared with
state-of-the-art methods.

本文介绍一种新的光照估计模型 NeedleLight，其中需要用到 needlets 来表示照明，并允许同时在频域和空间域进行照明估计。通过设计最优阈值函数来实现稀疏的 needlets，并利用基于最优输运理论的新型球形传输损失来指导对空间信息的考虑。在实验中，该模型的估计能力在多个评估指标下均优于其他先进方法。

球面传输损失下的稀疏小针灯估计

Sparse Needlets for Lighting Estimation with Spherical Transport Loss

We investigate invariant random fields on the sphere using a new type of
spherical wavelets, called needlets. These are compactly supported in frequency
and enjoy excellent localization properties in real space, with
quasi-exponentially decaying tails. We show that, for random fields on the
sphere, the needlet coefficients are asymptotically uncorrelated for any fixed
angular distance. This property is used to derive CLT and functional CLT
convergence results for polynomial functionals of the needlet coefficients:
here the asymptotic theory is considered in the high-frequency sense. Our
proposals emerge from strong empirical motivations, especially in connection
with the analysis of cosmological data sets.

使用新型球面小波 ——needlets，我们研究了球面上的不变随机场，证明了对于球面上的随机场，needlet 系数在任何固定角距离处渐近不相关。利用此性质，我们得出了 needlet 系数的多项式函数的中心极限定理（CLT）和函数 CLT 收敛性结果，本论文的建议是根据实证动机提出的，特别是与宇宙学数据集的分析有关。