This study presented established methods, along with new algorithmic developments, to automate point cloud processing in support of the Field Information Modeling (FIM)™ framework. More specifically, given a multi-dimensional (n-D) designed information model, and the point cloud’s spatial uncertainty, the problem of automatic assignment of point clouds to their corresponding model elements was considered. The methods addressed two classes of field conditions, namely (i) negligible construction errors and (ii) the existence of construction errors. Emphasis was given to defining the assumptions, potentials, and limitations of each method in practical settings. Considering the shortcomings of current frameworks, three generic algorithms were designed to address the point-cloud-to-model assignment. The algorithms include new developments for (i) point cloud vs. model comparison (negligible construction errors), (ii) robust point neighborhood definition, and (iii) Monte-Carlo-based point-cloud-to-model surface hypothesis testing (existence of construction errors). The effectiveness of the new methods was demonstrated in real-world point clouds, acquired from construction projects, with promising results. For the overall problem of point-cloud-to-model assignment, the proposed point cloud vs. model and point-cloud-to-model hypothesis testing methods achieved F-measures of 99.3% and 98.4%, respectively, on real-world datasets.