Accurately classifying 3-D point clouds into woody and leafy components has been an interest for applications in forestry and ecology including the better understanding of radiation transfer between canopy and atmosphere. The past decade has seen an increase in the methods attempting to classify leaves and wood in point clouds based on radiometric or geometric features. However, classification purely based on radiometric features is sensor-specific, and the method by which the local neighborhood of a point is defined affects the accuracy of classification based on geometric features. Here, we present a leaf-wood classification method combining geometrical features defined by radially bounded nearest neighbors at multiple spatial scales in a machine learning model. We compared the performance of three different machine learning models generated by the random forest (RF), XGBoost, and lightGBM algorithms. Using multiple spatial scales eliminates the need for an optimal neighborhood size selection and defining the local neighborhood by radially bounded nearest neighbors makes the method broadly applicable for point clouds of varying quality. We assessed the model performance at the individual tree- and plot-level on field data from tropical and deciduous forests, as well as on simulated point clouds. The method has an overall average accuracy of 94.2% on our data sets. For other data sets, the presented method outperformed the methods in literature in most cases without the need for additional postprocessing steps that are needed in most of the existing methods. We provide the entire framework as an open-source python package.