In order to accurately extract the individual planes from various types of building roof point clouds, metric learning was used to learn separate high-dimensional depth features for the points on each plane, and each plane was considered as a separate instance. Then the extracted high-dimensional depth features were used to perform preliminary clustering of the plane points. The unclustered points were assigned to each plane by a combined metric of simple Euclidean distance and feature space distance. The proposed method was trained and tested on a synthetic dataset and the publicly available airborne point cloud building roof dataset RoofN3D, respectively. The results show that on the synthetic dataset, the accuracy, recall, and F1 scores of the extracted building planes are 0.990, 0.998, and 0.994, respectively. On the airborne point cloud dataset RoofN3D, the accuracy, recall, and F1 scores of the extracted building planes are 0.945, 0.971, and 0.957, respectively. The proposed method not only can accurately and effectively extract different building roof planes, but also the extracted plane edges are very accurate. In addition, the method can also accurately distinguish between the planar and non-planar contents of building roofs, which provides important help for further 3-D modeling of buildings.