This article introduces a novel method for 3D object recognition, which utilizes well-known local features in a more efficient way, without any reliance on partial or global planarity. Geometrically consistent local features, which form the crucial basis for object recognition, are identified using affine 3D geometric invariants. The utilization of 3D geometric invariants replaces the classical 2D affine transform estimation/verification step, and provides the ability to directly verify 3D geometric consistency. The main contribution of the proposed approach lies in this ability of incorporating highly discriminative affine invariant 3D information much earlier in the process of matching in comparison with its counterparts. The accuracy and robustness of the method in highly cluttered scenes, without any prior segmentation or post 3D reconstruction requirements, are presented in the experiments.