FPFH

Fast Point Feature Histogram (FPFH) is a local 3D descriptor used to characterize the geometry of a point’s neighbourhood in a 3D point cloud. Introduced as a faster alternative to the Point Feature Histogram, it enables efficient correspondence estimation for tasks such as object recognition, pose estimation, and scene registration.

The descriptor relies on local geometry and normal information. For each point, normals are estimated and a neighbourhood is defined by a radius. A Simplified Point Feature Histogram (SPFH) is first computed by describing the angular relationships between the normals of the central point and each neighbor, capturing the local geometric structure. The final FPFH descriptor for a point is formed by aggregating the SPFH of the point and its surrounding points, with weighting by distance, yielding a more robust, compact representation that preserves discriminative information while being computationally efficient.

FPFH is designed to be rotation-invariant when a local reference frame is established and is relatively fast to compute compared with more exhaustive descriptors. It is widely used in 3D computer vision and robotics for establishing point correspondences, enabling rigid registration, and supporting robust alignment when used with RANSAC or iterative refinement pipelines.

Advantages of FPFH include moderate robustness to noise, partial views, and uneven sampling, along with lower computational cost than more complex descriptors. Limitations include reduced discriminative power for highly repetitive or textureless structures and reliance on accurate normal estimation and appropriate neighborhood size. It is commonly implemented in public toolkits such as the Point Cloud Library, where users can adjust radius, normal estimation, and other parameters to suit their data.