Geometric Constrained Non-Line-of-Sight Imaging

TL;DR

This work tackles non-line-of-sight imaging under sparse, short-exposure data by jointly reconstructing volumetric albedo and surface details through a 2D depth/albedo representation. It introduces a geometric prior that regularizes surface normals via the Frobenius norm of the shape operator on the depth map and couples it with a TV prior on albedo, enabling accurate, high-resolution reconstructions with significantly reduced computation. The authors develop an ADMM/FISTA-based solver that alternates updates for $u$, $\tau$, $D$, and $I$ using FFTs and shrinkage, achieving robust performance on synthetic and real data and demonstrating up to 30x speedups over prior surface-reconstruction approaches. The approach excels under sparse illumination and low exposure, offering practical impact for rapid, high-detail NLOS imaging and opening avenues to further improvements via conformal geometry for one-to-one surface-to-map mappings.

Abstract

Normal reconstruction is crucial in non-line-of-sight (NLOS) imaging, as it provides key geometric and lighting information about hidden objects, which significantly improves reconstruction accuracy and scene understanding. However, jointly estimating normals and albedo expands the problem from matrix-valued functions to tensor-valued functions that substantially increasing complexity and computational difficulty. In this paper, we propose a novel joint albedo-surface reconstruction method, which utilizes the Frobenius norm of the shape operator to control the variation rate of the normal field. It is the first attempt to apply regularization methods to the reconstruction of surface normals for hidden objects. By improving the accuracy of the normal field, it enhances detail representation and achieves high-precision reconstruction of hidden object geometry. The proposed method demonstrates robustness and effectiveness on both synthetic and experimental datasets. On transient data captured within 15 seconds, our surface normal-regularized reconstruction model produces more accurate surfaces than recently proposed methods and is 30 times faster than the existing surface reconstruction approach.

Figures (13)

• Figure 1: Illustration of our geometric constrained non-line-of-sight imaging framework, where (a) NLOS system, (b) projection of volumetric albedo to albedo image (left side) and depth image (bottom), and (c) illustration of shape operator on surface.
• Figure 2: The projection operator between volumetric albedo and 2D albedo map.
• Figure 3: Performance of our SLCT model in terms of both SSIM and PSNR with different model parameters $\rho$, $\sigma$, $\lambda$, and $\eta$.
• Figure 4: Performance of our SLCT model in terms of both SSIM and PSNR with different algorithm parameters $r_1$, $r_2$, and $r_3$.
• Figure 5: Evaluation of model performance with different powers of $u$.