# A Local Discrete Feature Histogram for Point Cloud Feature Representation
## 1 Introduction  
Image processing [1, 2] is a fundamental aspect of computer vision, and as applications have expanded from 2D images to 3D spaces, tasks in computer vision have become increasingly complex. Local feature descriptors are a critical topic in the field of 3D computer vision, which are utilized extensively in applications involving 3D point cloud registration [3, 4], 3D object recognition [5, 6], and 3D shape retrieval [7, 8]. Typically, they are created by converting the local surface's spatial distribution and geometric attributes into a feature vector. Descriptiveness and robustness are the two most crucial attributes of a local feature descriptor. The descriptiveness is the capacity to provide sufficient description details to differentiate between local surfaces, while its robustness denotes the capacity to remain stable under a variety of disturbances, such as noise and changes in mesh resolution [9]. Additionally, compactness and efficiency are important characteristics as well, especially in real-time applications.  
In previous research, many local feature descriptors have been put forth, generally classified into three types [10, 11]: those based on the local reference frame (LRF), those based on the local reference axis (LRA), and those without any local reference system. Descriptors without local reference systems usually only use geometric features and lack spatial distribution information, so their description ability is weak. The descriptiveness of the descriptor can be significantly enhanced by combining geometric features withspatial information. Descriptors based on LRA or LRF generate spatial information by partitioning 3D space. An LRF comprises three mutually orthogonal and rotation-invariant coordinate axes, which can provide comprehensive local spatial details, such as radial, azimuth, and elevation directions. In contrast, LRA-based methods utilize a single axis, representing only radial and elevation information. Recent evaluations of standard datasets have shown performance advantages for LRF-based descriptors [10]. However, achieving a satisfactory balance between descriptiveness, robustness, compactness, and efficiency remains a challenge for most feature descriptors currently in use [9; 12].  
Therefore, we propose a novel local feature descriptor called the Local Discrete Feature Histogram (LDFH). The LDFH descriptor is constructed based on LRF, which divides the local space by radial distance, counts three geometric features (including the normal deviation angle, polar angle, and normal lateral angle) in each subspace, and discretizes the features. Finally, the three histograms are combined using weighted fusion to form the final descriptor.  
The remainder of this paper is organized as follows: Section 2 introduces the related work on local feature descriptors. Section 3 provides a detailed explanation of the LDFH method proposed in this paper. Section 4 presents the experimental results of our LDFH descriptor and other state-of-the-art algorithms on the B3R dataset and Kinect dataset. Section 5 includes conclusions and some future directions.