Point cloud models are prevalently utilized in the architectural and civil engineering sectors. The registration of point clouds can invariably introduce registration errors, adversely impacting the accuracy of point cloud models. While the domain of computer vision has delved profoundly into point cloud registration, limited research in the construction domain has explored these registration algorithms in the built environment, despite their inception in the field of computer vision. The primary objective of this study is to investigate the impact of mainstream point cloud registration algorithms—originally introduced in the computer vision domain—on point cloud models, specifically within the context of bridge engineering as a category of civil engineering data. Concurrently, this study examines the influence of noise removal on varying point cloud registration algorithms. Our research quantifies potential variables for registration quality based on two metrics: registration error (RE) and time consumption (TC). Statistical methods were employed for significance analysis and value engineering assessment. The experimental outcomes indicate that the GRICP algorithm exhibits the highest precision, with RE values of 3.02 mm and 2.79 mm under non-noise removal and noise removal conditions, respectively. The most efficient algorithm is PLICP, yielding TC values of 3.86 min and 2.70 min under the aforementioned conditions. The algorithm with the optimal cost-benefit ratio is CICP, presenting value scores of 3.57 and 4.26 for non-noise removal and noise removal conditions, respectively. Under noise removal conditions, a majority of point cloud algorithms witnessed a notable enhancement in registration accuracy and a decrease in time consumption. Specifically, the POICP algorithm experienced a 32% reduction in RE and a 34% decline in TC after noise removal. Similarly, PLICP observed a 34% and 30% reduction in RE and TC, respectively. KICP showcased a decline of 23% in RE and 28% in TC, CICP manifested a 27% and 31% drop in RE and TC, respectively, GRICP observed an 8% reduction in RE and a 40% decline in TC, and for FGRICP, RE and TC decreased by 8% and 52%, respectively, subsequent to noise removal.