To address the computer vision-based registration problems, this study proposes a new three-dimensional point cloud registration algorithm that combines fast point feature histogram (FPFH) feature description with Delaunay triangulation. First, the FPFH is used to comprehensively describe feature information; then, the local correlation of feature information is established using the Delaunay triangulation. Thereafter, according to the corresponding relation of point pair features, the initial conversion of the sampling consistency is performed to implement initial registration. Finally, the iterative closest point method based on the initial values is used for accurate registration to obtain a precise conversion relation. The registration experiments are conducted on simple and complex target objects. Results reveal that traditional point cloud registration can be improved by combining FPFH feature description and Delaunay triangulation. This registration simplifies the feature extraction complexity, reduces the search range of matching feature points, improves the registration speed and accuracy, achieves an efficient registration of target objects, and considerably improves the efficiency of matching feature points in machine vision.