Simultaneous Localization and Mapping (SLAM) is used in solving the problems of localization, navigation, and map construction for autonomous vehicles moving in unknown environments. Place recognition is an inevitable subject in SLAM, and the current lidar-based methods have been popularized for their rising environmental robustness. Currently, the place recognition method with lidar has attracted much attention due to its high environmental robustness. However, many 3D laser point cloud methods for place recognition descriptors construction with the local or global point-cloud data omitting some intrinsic properties of the point clouds. In this article, we propose a place recognition method based on the unitary invariance of the Frobenius norm for utilizing different attributes of ground points and non-ground points. Specifically, the interpretable filtering framework and a dynamic threshold adjustment strategy are raised according to different environments and sensors with intensity and geometric information. As commissioning, the comparative experiments are conducted with CHDloop datasets and public KITTI datasets of different scales and access types. Compared to the original Scan Context (SC) and Intensity Scan Context (ISC) methods, our proposed method achieves higher efficiency while maintaining a improved recall rate and precision. This novel method has been integrated into the existing LiDAR SLAM and formed a new framework FSC_ALOAM that reduces drifts in point-cloud mapping. The entire process improves the accordance of maps at the identical position in auto-driving.