Point cloud angular similarity metric

Point clouds denote a 3D content representation which has recently gained a significant amount of interest. Among other challenges, objective quality assessment remains an open problem. In this study [1], we propose an objective quality metric that captures geometric impairments based on the angular similarity between two point clouds.

The proposed metric is full-reference and provides angular similarity scores for a point cloud under evaluation, when compared to a reference. The computation relies on normal vectors that are carried with the point clouds under comparison. After forming pairs of associated points that belong to the two models, the angular similarity between the corresponding tangent planes is computed in order to quantify their difference in terms of orientation. A tangent plane provides a local linear approximation of an underlying surface; thus, the angular similarity between two tangent planes provides an indication of the difference between the corresponding estimated local surfaces. An angular similarity score for a point cloud under evaluation is computed after pooling across the individual angular similarity values that are obtained from the pairs of associated points. In this implementation, the points are associated as nearest neighbors. This metric is also called as plane-to-plane.

Angular similarity between tangent planes (plane-to-plane) 

This metric requires the normals of both the original and the distorted contents. Although explicitly depending on normal vectors, no algorithm is imposed for normal estimation in case of absence.

For more details, the reader can refer to [1].

UPDATED: A benchmarking study on the performance of the metric as a function of the normal estimation algorithm and configuration, is reported in [2]. The impact of the neighborhood selection is examined and best-practices for high performance are indicated, using as ground truth widely-used subjectively annotated point cloud data sets.


A script with a prototype implementation for the plane-to-plane metric can be downloaded from the following GitHub repository.

Conditions of use

If you wish to use any of the provided material in your research, we kindly ask you to cite [1].


  1. E. Alexiou and T. Ebrahimi, “Point Cloud Quality Assessment Metric Based on Angular Similarity,” 2018 IEEE International Conference on Multimedia and Expo (ICME), San Diego, CA, 2018, pp. 1-6. doi: 10.1109/ICME.2018.8486512
  2. E. Alexiou and T. Ebrahimi, “Benchmarking of the plane-to-plane metric,” ISO/IEC JTC1/SC29/WG1 Doc. M88038, July 2020