SPFH

SPFH stands for Simplified Point Feature Histogram. It is a local descriptor used in 3D computer vision to describe the geometry around a point in a point cloud. Introduced as part of the Point Feature Histograms (PFH) framework by Rusu and colleagues, SPFH provides a computationally lighter alternative to the full PFH by focusing on the central point rather than all pairwise point relations. The descriptor captures the distribution of angular relationships between the center and its neighbors within a specified radius, using a locally defined reference frame to achieve partial rotation invariance.

Computation involves selecting a point p with an estimated normal, constructing a local reference frame, and for each neighbor q within a radius computing three angular features (alpha, phi, theta) based on pq and the frame. The features are binned into histograms, typically forming a 3xNbins vector, which constitutes the SPFH for p. The radius and bin sizes determine robustness and discriminability.

Relationship to PFH and FPFH: PFH encodes pairwise relations for all points in the neighborhood and can be computationally expensive. SPFH reduces complexity by using the center point as anchor. The Fast Point Feature Histogram (FPFH) then combines the SPFHs of neighboring points, weighted by distance, to produce a more robust descriptor.

Applications and limitations: SPFH is used in 3D object recognition, registration, and segmentation, particularly for data from depth sensors and LiDAR. It offers a favorable efficiency–discriminability trade-off but is sensitive to noisy normals and uneven sampling. Parameter choices such as radius and histogram bins influence performance; in practice SPFH is often used as a building block within FPFH pipelines.