Local feature descriptors are a critical problem in computer vision; the majority of current approaches find it difficult to achieve a balance between descriptiveness, robustness, compactness, and efficiency. This paper proposes the local discrete feature histogram (LDFH), a novel local feature descriptor, as a solution to this problem. The LDFH descriptor is constructed based on a robust local reference frame (LRF). It partitions the local space based on radial distance and calculates three geometric features, including the normal deviation angle, polar angle, and normal lateral angle, in each subspace. These features are then discretized to generate three feature statistical histograms, which are combined using a weighted fusion strategy to generate the final LDFH descriptor. Experiments on public datasets demonstrate that, compared with the existing methods, LDFH strikes an excellent balance between descriptiveness, robustness, compactness, and efficiency, making it suitable for various scenes and sensor datasets.