Stereo vision is broadly employed in robotics and intelligent vehicles for recovering the 3D structure of the environment. The scene depth is typically estimated by triangulation after associating pixels between views using a dense stereo matching approach. In the last few years, the image resolution has steadily increased due to the advances in camera technology. Unfortunately, achieving real-time stereo using large size images is difficult because of the computational cost of dense matching. An obvious solution is to re-sample the acquired input images, but this implies decreasing the accuracy of depth estimates. We propose an alternative that consists in performing the stereo reconstruction of the contour C where a pre-defined virtual cut plane intersects the scene. This approach enables a trade-off between runtime and 3D model resolution that does not interfere with depth accuracy. The profile cuts C are independently recovered using the SymStereo framework that has been recently introduced in [1]. It is proved through comparative experiments that SymStereo is particularly well suited for recovering depth along virtual cut planes, outperforming state-of-the-art stereo cost functions both in terms of accuracy and runtime.