[Paper Review] Two-Dimensional Non-Line-of-Sight Scene Estimation from a Single Edge Occluder

Sheila W. Seidel, John Murray–Bruce+4 more|arXiv (Cornell University)|Jan 1, 2020

Advanced Optical Sensing TechnologiesPhysics and Astronomy36 references46 citations

TL;DR

The paper introduces a forward model and two inversion algorithms to reconstruct a 2D plan-view of a hidden scene from a single penumbra photograph induced by a wall edge, including a CRB analysis of feasibility.

ABSTRACT

Passive non-line-of-sight imaging methods are often faster and stealthier than their active counterparts, requiring less complex and costly equipment. However, many of these methods exploit motion of an occluder or the hidden scene, or require knowledge or calibration of complicated occluders. The edge of a wall is a known and ubiquitous occluding structure that may be used as an aperture to image the region hidden behind it. Light from around the corner is cast onto the floor forming a fan-like penumbra rather than a sharp shadow. Subtle variations in the penumbra contain a remarkable amount of information about the hidden scene. Previous work has leveraged the vertical nature of the edge to demonstrate 1D (in angle measured around the corner) reconstructions of moving and stationary hidden scenery from as little as a single photograph of the penumbra. In this work, we introduce a second reconstruction dimension: range measured from the edge. We derive a new forward model, accounting for radial falloff, and propose two inversion algorithms to form 2D reconstructions from a single photograph of the penumbra. Performances of both algorithms are demonstrated on experimental data corresponding to several different hidden scene configurations. A Cramer-Rao bound analysis further demonstrates the feasibility (and utility) of the 2D corner camera.

Motivation & Objective

• Motivate passive NLOS imaging using ubiquitous wall edges as apertures to image hidden scenes.
• Extend prior 1D angle reconstructions to 2D by incorporating range information via observed penumbra falloff.
• Develop a forward model that links a single floor photograph to hidden-scene radiosity and depth.
• Propose and compare two inversion algorithms for 2D plan-view reconstruction.
• Provide experimental validation and CRB-based feasibility analysis for edge-based NLOS imaging.

Proposed method

• Derive a forward model where the floor radiosity is the sum of visible and hidden contributions and express the hidden contribution as an integral over angle and range (Equations 1–8).
• Discretize the hidden region into angular wedges with per-wedge range variables to obtain a nonlinear forward model (Equation 9).
• Perform Cramér–Rao bound analysis for single and multiple hidden targets to quantify angular and range estimation limits with and without the edge occluder (Section III).
• Propose a polar-grid linearization approach that recasts the problem as y = A c + (V ∘ D(ρ)) s_h + ε (Equation 23).
• Develop an alternating optimization method that first estimates high-resolution angle information and then refines per-target ranges (Section IV).
• Address ambient floor albedo and near/far-field lighting via a structured A matrix and sparsity-promoting recovery (Equation 22 and related discussion).

Experimental results

Research questions

• RQ1 Can a wall edge provide 2D (angle and range) reconstruction of hidden scenes from a single penumbra photograph?
• RQ2 How does the edge occluder affect the CRB for estimating hidden-target range and angle compared to no occluder?
• RQ3 What reconstruction strategies (polar-grid vs. alternating angle-range) yield accurate 2D plan-view representations?
• RQ4 How do ambient light and floor albedo influence the feasibility and accuracy of the 2D NLOS reconstruction?
• RQ5 What is the performance when reconstructing multiple hidden targets behind an edge occluder?

Key findings

• CRB analysis shows that the corner dramatically improves angular resolution (five to seven orders of magnitude better) for angle estimation, with range estimation showing smaller but still meaningful gains.
• Edge occluder enables near-circular to line-like uncertainty regions in angle-radial space, collapsing angle uncertainty and isolating range information through radial falloff.
• Two reconstruction approaches are demonstrated: a polar-grid linear model and a sparsity-promoting, alternating angular/range method, both producing 2D plan-view reconstructions from a single penumbra photograph.
• Experimental results validate 2D reconstructions across several hidden-scene configurations and colors, confirming feasibility of 2D NLOS imaging with an edge occluder.
• CRB-based insights suggest the corner camera is feasible for 2D reconstruction, particularly improving angular estimation, with range estimation being more challenging but still attainable.