This paper presents a novel approach for local 3D surface description, focusing on the uniqueness and repeatability of local reference frames (RFs). The authors categorize existing 3D descriptors into two types: Signatures and Histograms. They argue that the choice of RF is crucial for the performance of 3D descriptors and propose a new unique and repeatable RF, along with a new 3D descriptor that combines the strengths of both Signatures and Histograms. The new descriptor, called Signature of Histograms of OrienTations (SHOT), is designed to be efficient, descriptive, and robust to noise and clutter. The authors validate their approach through experiments on publicly available datasets and range scans obtained using Spacetime Stereo. The results show that SHOT outperforms existing methods in terms of robustness, descriptive power, and computational efficiency. The paper also addresses the issue of sign ambiguity in RFs and proposes a disambiguation method to ensure repeatability. The proposed method is shown to be effective in real-world scenarios, including 3D reconstruction from Spacetime Stereo data. The results demonstrate that SHOT provides a more accurate and efficient solution for 3D surface description compared to existing methods.This paper presents a novel approach for local 3D surface description, focusing on the uniqueness and repeatability of local reference frames (RFs). The authors categorize existing 3D descriptors into two types: Signatures and Histograms. They argue that the choice of RF is crucial for the performance of 3D descriptors and propose a new unique and repeatable RF, along with a new 3D descriptor that combines the strengths of both Signatures and Histograms. The new descriptor, called Signature of Histograms of OrienTations (SHOT), is designed to be efficient, descriptive, and robust to noise and clutter. The authors validate their approach through experiments on publicly available datasets and range scans obtained using Spacetime Stereo. The results show that SHOT outperforms existing methods in terms of robustness, descriptive power, and computational efficiency. The paper also addresses the issue of sign ambiguity in RFs and proposes a disambiguation method to ensure repeatability. The proposed method is shown to be effective in real-world scenarios, including 3D reconstruction from Spacetime Stereo data. The results demonstrate that SHOT provides a more accurate and efficient solution for 3D surface description compared to existing methods.