Falls are one of the major causes leading to injury of elderly people. Using wearable devices for fall detection has a high cost and may cause inconvenience to the daily lives of the elderly. In this paper, we present an automated fall detection approach that requires only a low-cost depth camera. Our approach combines two computer vision techniques-shape-based fall characterization and a learning-based classifier to distinguish falls from other daily actions. Given a fall video clip, we extract curvature scale space (CSS) features of human silhouettes at each frame and represent the action by a bag of CSS words (BoCSS). Then, we utilize the extreme learning machine (ELM) classifier to identify the BoCSS representation of a fall from those of other actions. In order to eliminate the sensitivity of ELM to its hyperparameters, we present a variable-length particle swarm optimization algorithm to optimize the number of hidden neurons, corresponding input weights, and biases of ELM. Using a low-cost Kinect depth camera, we build an action dataset that consists of six types of actions (falling, bending, sitting, squatting, walking, and lying) from ten subjects. Experimenting with the dataset shows that our approach can achieve up to 91.15% sensitivity, 77.14% specificity, and 86.83% accuracy. On a public dataset, our approach performs comparably to state-of-the-art fall detection methods that need multiple cameras.