Different approaches have been proposed in the literature to detect the fall of an elderly person. In this paper, we propose a fall detection method based on the classification of parameters extracted from depth images. Three supervised learning methods are compared: decision tree, K-Nearest Neighbors (K-NN) and Random Forests (RF). The methods have been tested on a database of depth images recorded in a nursing home over a period of 43 days. The Random Forests based method yields the best results, achieving 93% sensitivity and 100% specificity when we restrict our study around the bed. Furthermore, this paper also proposes a 37 days follow-up of the person, to try and estimate his or her daily habits.