A General Solution for Iso-Disparity Layers and Correspondence Field Model for Stereo Systems

Estimation of localization error and selection of system parameters are the key factors in evaluation of visual 3-D systems. Iso-disparity layers and correspondence field are recently introduced to present a graphical model for space sampling in general 3-D systems. The correspondence field describes the spatial topology of the intersecting rays of cameras, arranged in a number of layers or surfaces with same disparity values, referred as iso-disparity layers. This paper develops a mathematical framework to investigate the geometrical variations of these layers with respect to camera intrinsic and extrinsic parameters. It will be demonstrated that the layers in their general form appear as a set of quadric surfaces, where the coefficients of these quadrics depend on system parameters. The distance between the iso-disparity layers due to the quantization process is suggested as a measure of uncertainty and can be considered as a criterion for appropriate selection of parameters, such as focal length, position, and orientation of cameras for the system to achieve desirable precision. Here, we use an analytical solution to calculate the orthogonal distance between the two successive iso-disparity layers. These distances are representatives of depth uncertainty. Finally, we have simulated our model and the results verify that the total average error is less than 2%.