Occlusion Fields: An Implicit Representation for Non-Line-of-Sight Surface Reconstruction

Non-line-of-sight reconstruction (NLoS) is a novel indirect imaging modality that aims to recover objects or scene parts outside the field of view from measurements of light that is indirectly scattered off a directly visible, diffuse wall. Despite recent advances in acquisition and reconstruction techniques, the well-posedness of the problem at large, and the recoverability of objects and their shapes in particular, remains an open question. The commonly employed Fermat path criterion is rather conservative with this regard, as it classifies some surfaces as unrecoverable, although they contribute to the signal. In this paper, we use a simpler necessary criterion for an opaque surface patch to be recoverable. Such piece of surface must be directly visible from some point on the wall, and it must occlude the space behind itself. Inspired by recent advances in neural implicit representations, we devise a new representation and reconstruction technique for NLoS scenes that unifies the treatment of recoverability with the reconstruction itself. Our approach, which we validate on various synthetic and experimental datasets, exhibits interesting properties. Unlike memory-inefficient volumetric representations, ours allows to infer adaptively tessellated surfaces from time-of-flight measurements of moderate resolution. It can further recover features beyond the Fermat path criterion, and it is robust to significant amounts of self-occlusion. We believe that this is the first time that these properties have been achieved in one system that, as an additional benefit, is trainable and hence suited for data-driven approaches.

Residuum-Condition Diagram and Reduction of Over-Complete Endmember-Sets

Extracting reference spectra, or endmembers (EMs) from a given multi- or hyperspectral image, as well as estimating the size of the EM set, plays an important role in multispectral image processing. In this paper, we present condition-residuum-diagrams. By plotting the residuum resulting from the unmixing and reconstruction and the condition number of various EM sets, the resulting diagram provides insight into the behavior of the spectral unmixing under a varying amount of endmembers (EMs). Furthermore, we utilize condition-residuum-diagrams to realize an EM reduction algorithm that starts with an initially extracted, over-complete EM set. An over-complete EM set commonly exhibits a good unmixing result, i.e. a lower reconstruction residuum, but due to its partial redundancy, the unmixing gets numerically unstable, i.e. the unmixed abundances values are less reliable. Our greedy reduction scheme improves the EM set by reducing the condition number, i.e. enhancing the set's stability, while keeping the reconstruction error as low as possible. The resulting set sequence gives hint to the optimal EM set and its size. We demonstrate the benefit of our condition-residuum-diagram and reduction scheme on well-studied datasets with known reference EM set sizes for several well-known EE algorithms.