Many materials, including water surfaces, jewels, and glassware exhibit transparent refractions. The human visual system can somehow recover 3D shape from refracted images. While previous research has elucidated various visual cues that can facilitate visual perception of transparent objects, most of them focused on monocular material perception. The question of shape perception of transparent objects is much more complex and few studies have been undertaken, particular in terms of binocular vision. In this article, we first design a system for stereoscopic surface orientation estimation with photo-realistic stimuli. It displays pre-rendered stereoscopic images and a real-time S3D (Stereoscopic 3D) shape probe simultaneously. Then we estimate people's perception of the shape of thin transparent objects using a gauge figure task. Our results suggest that people can consistently perceive the surface orientation of thin transparent objects, and stereoscopic viewing improves the precision of estimates. To explain the results, we present an edge-aware orientation map based on image gradients and structure tensors to illustrate the orientation information in images. We also decomposed the normal direction of the surface into azimuth angle and slant angle to explain why additional depth information can improve the accuracy of perceived normal direction.