Heritage documentation is implemented by digitally recording historical artifacts for the conservation and protection of these cultural heritage objects. As efficient spatial data acquisition tools, laser scanners have been widely used to collect highly accurate three-dimensional (3D) point clouds without damaging the original structure and the environment. To ensure the integrity and quality of the collected data, field inspection (i.e., on-spot checking the data quality) should be carried out to determine the need for additional measurements (i.e., extra laser scanning for areas with quality issues such as data missing and quality degradation). To facilitate inspection of all collected point clouds, especially checking the quality issues in overlaps between adjacent scans, all scans should be registered together. Thus, a point cloud registration method that is able to register scans fast and robustly is required. To fulfill the aim, this study proposes an efficient probabilistic registration for free-form cultural heritage objects by integrating the proposed principal direction descriptor and curve constraints. We developed a novel shape descriptor based on a local frame of principal directions. Within the frame, its density and distance feature images were generated to describe the shape of the local surface. We then embedded the descriptor into a probabilistic framework to reject ambiguous matches. Spatial curves were integrated as constraints to delimit the solution space. Finally, a multi-view registration was used to refine the position and orientation of each scan for the field inspection. Comprehensive experiments show that the proposed method was able to perform well in terms of rotation error, translation error, robustness, and runtime and outperformed some commonly used approaches.