  Inferring the scene illumination from a single image is an essential yet
challenging task in computer vision and computer graphics. Existing works
estimate lighting by regressing representative illumination parameters or
generating illumination maps directly. However, these methods often suffer from
poor accuracy and generalization. This paper presents Geometric Mover's Light
(GMLight), a lighting estimation framework that employs a regression network
and a generative projector for effective illumination estimation. We
parameterize illumination scenes in terms of the geometric light distribution,
light intensity, ambient term, and auxiliary depth, which can be estimated by a
regression network. Inspired by the earth mover's distance, we design a novel
geometric mover's loss to guide the accurate regression of light distribution
parameters. With the estimated light parameters, the generative projector
synthesizes panoramic illumination maps with realistic appearance and
high-frequency details. Extensive experiments show that GMLight achieves
accurate illumination estimation and superior fidelity in relighting for 3D
object insertion. The codes are available at
\href{https://github.com/fnzhan/Illumination-Estimation}{https://github.com/fnzhan/Illumination-Estimation}.
