Nonrigid registration presents a significant challenge in the domain of point cloud processing. The general objective is to model complex nonrigid deformations between two or more overlapping point clouds. Applications are diverse and span multiple research fields, including registration of topographic data, scene flow estimation, and dynamic shape reconstruction. To provide context, the first part of the paper gives a general introduction to the topic of point cloud registration, including a categorization of existing methods. Then, a general mathematical formulation for the point cloud registration problem is introduced, which is then extended to address also nonrigid registration methods. A detailed discussion and categorization of existing approaches to nonrigid registration follows. In the second part of the paper, we propose a new method that uses piecewise tricubic polynomials for modeling nonrigid deformations. Our method offers several advantages over existing methods. These advantages include easy control of flexibility through a small number of intuitive tuning parameters, a closed-form optimization solution, and an efficient transformation of huge point clouds. We demonstrate our method through multiple examples that cover a broad range of applications, with a focus on remote sensing applications—namely, the registration of airborne laser scanning (ALS), mobile laser scanning (MLS), and terrestrial laser scanning (TLS) point clouds. The implementation of our algorithms is open source and can be found our public repository.

Non-rigid registration presents a significant challenge in the domain of point cloud processing. The general objective is to model complex non-rigid deformations between two or more overlapping point clouds. Applications are diverse and span multiple research fields, including registration of topographic data, scene flow estimation, and dynamic shape reconstruction. To provide context, we begin with a general introduction to the topic of point cloud registration, including a categorization of methods. Next, we introduce a general mathematical formulation for point cloud registration and extend it to address non-rigid registration. A detailed discussion and categorization of existing approaches to non-rigid registration follows. We then introduce our own method where the usage of piece-wise tricubic polynomials for modeling non-rigid deformations is proposed. Our method offers several advantages over existing methods. These advantages include easy control of flexibility through a small number of intuitive tuning parameters, a closed-form optimization solution, and an efficient transformation of huge point clouds. We demonstrate our method through multiple examples that cover a broad range of applications, with a focus on remote sensing applications - namely, the registration of Airborne Laser Scanning (ALS), Mobile Laser Scanning (MLS), and Terrestrial Laser Scanning (TLS) point clouds. The implementation of our algorithms is open source and can be found on GitHub.