We analyze the utility of multiscale supervised classification algorithms for object detection and extraction from laser scanning or photogrammetric point clouds. Only the geometric information (the point coordinates) was considered, thus making the method independent of the systems used to collect the data. A maximum of five features (input variables) was used, four of them related to the eigenvalues obtained from a principal component analysis (PCA). PCA was carried out at six scales, defined by the diameter of a sphere around each observation. Four multiclass supervised classification models were tested (linear discriminant analysis, logistic regression, support vector machines, and random forest) in two different scenarios, urban and forest, formed by artificial and natural objects, respectively. The results obtained were accurate (overall accuracy over 80% for the urban dataset, and over 93% for the forest dataset), in the range of the best results found in the literature, regardless of the classification method. For both datasets, the random forest algorithm provided the best solution/results when discrimination capacity, computing time, and the ability to estimate the relative importance of each variable are considered together.