This paper introduces a new hybrid descriptor for 3D point matching and point cloud registration, combining local geometrical properties and learning-based feature propagation for each point's neighborhood structure description. The proposed architecture first extracts prior geometrical information by computing each point's planarity, anisotropy, and omnivariance using a Principal Components Analysis (PCA). This prior information is completed by a descriptor based on the normal vectors estimated thanks to constructing a neighborhood based on triangles. The final geometrical descriptor is propagated between the points using local graph convolutions and attention mechanisms. The new feature extractor is evaluated on ModelNet40, Bunny Stanford dataset, KITTI and MVP (Multi-View Partial)-RG for point cloud registration and shows interesting results, particularly on noisy and low overlapping point clouds. The code will be released after publication.