Fig. 1: Two-edge-resolved NLOS imaging scenario and hidden scene representation.

a Depiction of the imaging scenario and proposed projected-elevation spherical coordinate. With the origin at the upper-left corner of the door frame, a hidden scene point is identified by its range ρ, azimuth θ, and projected-elevation ψ. b Shows the projected-elevation ψ in the proposed projected-elevation spherical coordinate system, it is the projection of the conventional elevation angle of spherical coordinates onto the xz-plane and is such that \(\tan (\psi )=\tan (\varphi )\sec (\theta )\). (For clarity, the z-axis is flipped from (a) to point upward.) c Elemental surface representation resulting from 10 equal divisions of azimuth and projected-elevation axes with fixed range, ρ. Indicated by the red dot is an example surface element whose centre is at (ρ, θ, ψ) = (1, 11π/40, 13π/40) and angular extents equal π/20 along azimuth and projected-elevation. d, e Depict the changes in the observed measurement due to a hidden point source (red dot) moving from its position in (d) to a new position in (e) such that its range and projected-elevation angle are fixed and only its azimuthal angle changes. The light from a hidden scene point is occluded by the doorway edges to create an illuminated region of trapezoidal shape on the ceiling. The observation in (d) has an illuminated trapezoidal region whose slanted edge is steeper than that of (e) because the azimuthal angle of the point source increases from (d) to (e); the heights of the illuminated trapezoid portions in (d) and (e) are otherwise equal because the projected-elevation angle is unchanged.