On the RANSAC Performance for Quadric Surfaces in Noisy Conditions

Random sample consensus-based algorithm (RANSAC) is one of the standard approaches in the field of robust estimation of parametric objects. There are numerous versions of RANSAC that are tailored to specific problems such as homography estimation, point cloud registration, plane estimation and others. On the other hand, numerous attempts were made towards the development of modifications of RANSAC that are extremely robust to noise or highly efficient in terms of the computational demands. However, the general premise of these approaches remains all the same: instead of trying to fit a single model to all the data, a number of small models is produced and evaluated in terms of their ability to describe the data. In this work, an empirical study is carried out that is purposely limited to a specific application of RANSAC. Particularly, the dependency of the output quality on the noise is examined for the quadric surface evaluation. The data was presented in the form of 3D point clouds. A method for synthetic data generation was developed, allowing to mimic the geometric principles of the point cloud formation. The dependency of the error on the noise was examined on the synthetic point clouds. Finally, numerical experiments on real point clouds were carried out in the agricultural setting. The code can be found in the repository (<uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://github.com/aidagroup/SCUF/</uri>) and the proposed method can be used as a module (<uri xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">https://pypi.org/project/scuf/</uri>).