3D object recognition from point clouds is a fast-growing field of research in computer vision. 3D object recognition methods can be classified into two categories: global feature-based and local feature-based methods. The local feature-based methods are more popular than global ones. Because the global feature-based methods need a prior segmentation of the scene, they are not suitable for real-world scenes. Many previous local descriptor methods limit their performance by introducing a local reference frame or axis (LRF/A). Estimating the LRF/A for each keypoint leads to extra computational time and error. We use the fundamental theorem of surface theory to introduce a simple and efficient local feature descriptor based on the coefficients of discrete first and second fundamental forms. The proposed method overrides the necessity of an LRF/A, and it required a small feature dimension of seven, which means it is a low-complexity and fast procedure. To assess the proposed method, we have compared it with eight state-of-the-art descriptors and applied it to the three popular datasets to extract features and recognize the correspondences. Experimental results demonstrate the superiority of the proposed approach to the compared methods in terms of pairwise registration measurements, recall versus 1-precision curve, and the computational time.