This work investigates the geometric foundations of modern stereo vision systems, with a focus on how 3D structure and human-inspired perception contribute to accurate depth reconstruction. We revisit the Cyclopean Eye model and propose novel geometric constraints that account for occlusions and depth discontinuities. Our analysis includes the evaluation of stereo feature matching quality derived from deep learning models, as well as the role of attention mechanisms in recovering meaningful 3D surfaces. Through both theoretical insights and empirical studies on real datasets, we demonstrate that combining strong geometric priors with learned features provides internal abstractions for understanding stereo vision systems.