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Simultaneous Localization and Mapping (SLAM) plays an important role in outdoor and indoor applications ranging from autonomous driving to indoor robotics. Outdoor SLAM has been widely used with the assistance of LiDAR or GPS. For indoor applications, the LiDAR technique does not satisfy the accuracy requirement and the GPS signals will be lost. An accurate and efficient scene sensing technique is required for indoor SLAM. As the most promising 3D sensing technique, the opportunities for indoor SLAM with fringe projection profilometry (FPP) systems are obvious, but methods to date have not fully leveraged the accuracy and speed of sensing that such systems offer. In this paper, we propose a novel FPP-based indoor SLAM method based on the coordinate transformation relationship of FPP, where the 2D-to-3D descriptor-assisted is used for mapping and localization. The correspondences generated by matching descriptors are used for fast and accurate mapping, and the transform estimation between the 2D and 3D descriptors is used to localize the sensor. The provided experimental results demonstrate that the proposed indoor SLAM can achieve the localization and mapping accuracy around one millimeter.