Determining the drivable area, or free space segmentation, is critical for mobile robots to navigate indoor environments safely. However, the lack of coherent markings and structures (e.g., lanes, curbs, etc.) in indoor spaces places the burden of traversability estimation heavily on the mobile robot. This paper explores the use of a self-supervised one-shot texture segmentation framework and an RGB-D camera to achieve robust drivable area segmentation. With a fast inference speed and compact size, the developed model, MOSTS is ideal for real-time robot navigation and various embedded applications. A benchmark study was conducted to compare MOSTS's performance with existing one-shot texture segmentation models to evaluate its performance. Additionally, a validation dataset was built to assess MOSTS's ability to perform texture segmentation in the wild, where it effectively identified small low-lying objects that were previously undetectable by depth measurements. Further, the study also compared MOSTS's performance with two State-Of-The-Art (SOTA) indoor semantic segmentation models, both quantitatively and qualitatively. The results showed that MOSTS offers comparable accuracy with up to eight times faster inference speed in indoor drivable area segmentation.