Coding Depth through Mask Structure

TL;DR: A coded‐aperture method based on a family of masks obtained as the convolution of one “hole” with a structural component consisting of an arrangement of Dirac delta functions that uses the arrangement of delta functions to efficiently encode scene distance information.

Abstract: We present a coded-aperture method based on a family of masks obtained as the convolution of one “hole” with a structural component consisting of an arrangement of Dirac delta functions. We call the arrangement of delta functions the structural component of the mask, and use it to efficiently encode scene distance information. We illustrate the potential of our approach by analyzing a family of masks defined by a circular hole component and a structural component consisting of a linear combination of three Dirac deltas. We show that the structural component transitions from well conditioned to ill conditioned as the relative weight of the central peak varies with respect to the lateral ones. For the well-conditioned structural components, deconvolution is efficiently performed by inverse filtering, allowing for fast estimation of scene depth. We demonstrate the effectiveness of our approach by constructing a mask for distance coding and using it to recover pairs of distance maps and structurally-deconvolved images from single photographs. For this application, we obtain significant speedup, and extended range and depth resolution compared to previous techniques. © 2012 Wiley Periodicals, Inc.