To address the challenges of insufficient discrimination and low robustness of feature descriptors in complex scenes, an innovative local subdivision neighborhood feature statistics (LSNFS) descriptor is proposed. The core of LSNFS descriptors is a highly discriminative method called surface neighborhood deviation statistics (SNDS). SNDS comprehensively encodes local spatial information by introducing two types of spatial features. Statistically calculating the weighted neighborhood deviation angle in the subdivided space, combined with specific attribute partitioning strategies, significantly enhances the discriminative ability of descriptors. Linear interpolation and normalization are performed on the generated SNDS histogram to improve the robustness of descriptors to noise and point cloud resolution changes. The LSNFS descriptor encodes local geometric information by computing two angle features, and fuses the generated angle feature histogram with the SNDS histogram to achieve sufficient description of local information. A large number of experimental verifications are conducted on six datasets with different quality and interference types, and the results show that LSNFS performed significantly better than various advanced methods on all datasets, with high descriptive and strong robustness. In addition, applying LSNFS to 3D object registration and real scene registration, the results show that LSNFS not only achieves the best registration performance in 3D object registration, but also can generalize to large-scale real scene data, with good generalization performance.