FPFH Revisited: Histogram Resolutions, Improved Features, and Novel Representation

3D local descriptors are essential for many computer vision-related tasks: point cloud registration, object recognition, etc. The first descriptors appeared decades ago, but new methods are still emerging today. To solve the above mentioned problems efficiently, we need robust and distinctive descriptors that are invariant to translation, rotation and normal orientation. In this paper, we revisit and analyze the well-known hand-crafted Fast Point Feature Histogram (FPFH) and the three geometric features underlying the FPFH. Modifications to the geometric features are proposed to increase the descriptiveness and improve robustness against inconsistent normal orientation. Thus, normal orientation methods with high computational complexity can be omitted and the performance of the descriptor is nearly doubled. We also propose a novel approach to representing descriptors: using cumulative distribution functions (CDF) instead of histograms. We mathematically analyze the point-pair features and their CDFs, focusing on a special case where two planes intersect. We use this knowledge to approximate functions on real point cloud data sets in the general case. CDFs can be represented by fitted parameters. By storing these parameters, which can be understood as a form of compression, the storage requirements can be reduced while maintaining the descriptiveness.