Depth From Stereo: Variational Theory And A Hybrid Analog-Digital Network

Abstract

Recovering the three dimensional structure of objects viewed by two eyes or cameras is an ill-posed inverse visual problem. Instead of computing disparities at several spatial resolutions by stereo-matching, and then regularizing the disparities, the authors propose a direct method for recovering depth based on the formulation of the task as a problem in calculus of variations. This method makes use of brightness gradients of the textured surfaces in the scenes. Occlusion cues are also used for arriving at a final depth estimate. In its present form, the method works for nonconvergent (parallel optical axes) stereo images. Surfaces in the scenes are assumed to have a visual texture. The optical flow constraint equation is used. Depth is assumed to vary continuously almost everywhere (i.e., except at depth discontinuities). Standard regularization theory is applied to make the problem well posed. This leads to a quadratic energy function. Standard regularization theory cannot handle discontinuities in the solution space. Line processes are used to recover discontinuous depth fields. A deterministic sequential update procedure is used for estimating the state of the line processes. The solution obtained from standard regularization theory maps directly onto an analog resistive network. The nonlinear solution with line processes is mapped onto a hybrid analog-digital resistive network. The line process update is carried out using a digital computer while the local computation of depth values and smoothing of the solution is done by a resistive network.